4 Learning Callback Typestates using L{}^{*}

DroidStar: Callback Typestates for Android Classes


Event-driven programming frameworks, such as Android, are based on components with asynchronous interfaces. The protocols for interacting with these components can often be described by finite-state machines we dub callback typestates. Callback typestates are akin to classical typestates, with the difference that their outputs (callbacks) are produced asynchronously. While useful, these specifications are not commonly available, because writing them is difficult and error-prone.

Our goal is to make the task of producing callback typestates significantly easier. We present a callback typestate assistant tool, DroidStar, that requires only limited user interaction to produce a callback typestate. Our approach is based on an active learning algorithm, L. We improved the scalability of equivalence queries (a key component of L), thus making active learning tractable on the Android system.

We use DroidStar to learn callback typestates for Android classes both for cases where one is already provided by the documentation, and for cases where the documentation is unclear. The results show that DroidStar learns callback typestates accurately and efficiently. Moreover, in several cases, the synthesized callback typestates uncovered surprising and undocumented behaviors.

typestate, specification inference, Android, active learning

2018 \acmYear2018 \setcopyrightacmlicensed \acmConference[ICSE ’18]ICSE ’18: 40th International Conference on Software Engineering May 27-June 3, 2018Gothenburg, Sweden \acmBooktitleICSE ’18: ICSE ’18: 40th International Conference on Software Engineering , May 27-June 3, 2018, Gothenburg, Sweden \acmPrice15.00 \acmDOI10.1145/3180155.3180232 \acmISBN978-1-4503-5638-1/18/05


This work was done while Arjun Radhakrishna was employed at the University of Pennsylvania.

1 Introduction

Event-driven programming frameworks interact with client code using callins and callbacks. Callins are framework methods that the client invokes and callbacks are client methods that the framework invokes. The client-framework interaction is often governed by a protocol that can be described by a finite-state machine we call callback typestate. Callback typestates are akin to classical typestates [36], with the key difference that their outputs (callbacks) are produced asynchronously. Our goal is to make the task of producing callback typestates significantly easier for developers.

As an example of a callback typestate, consider a typical interaction between a client application and the framework when the client wants to use a particular service. The client asks for the service to be started by invoking an startService() callin. After the framework receives the callin, it asynchronously starts initializing the service. When the service is started and ready to be used, the framework notifies the client by invoking a callback. The client can then use the service. After the client finishes using the service, it invokes a shutdownService() callin to ask the framework to stop the service.

Callback typestates.

Callback typestates are useful in a number of ways, but they are notoriously hard to produce. First, callback typestates are a form of documentation. They tell client application programmers in what order to invoke callins and which callback to expect. Android framework documentation for some classes already uses pictures very similar to callback typestates (Figure 1). Second, callback typestates are useful in verification of client code. They enable checking that a client uses the framework correctly. Third, even though we infer the callback typestates from framework code, they can be used for certain forms of framework verification. For instance, one can infer typestates for different versions of the framework, and check if the interface has changed.

Callback typestates are very hard to produce manually. On one hand, inspecting code to see in what situation a callback arrives, and what callins are enabled after that is error-prone. Even developers familiar with the framework often miss corner-case behaviors. On the other hand, obtaining the callback typestate with manual testing is hard. One would need to run all sequences of callins, mixed in sequence with the callbacks they produce. We systematize this testing approach using an active learning algorithm.

Callback typestate assistant DroidStar.

We present a tool that makes producing callback typestates significantly easier. Our target user is a developer who wrote an Android class that interacts asynchronously using callbacks with client code. DroidStar is a comprehensive framework for semi-automatically inferring callback typestates. The required user interaction happens in multiple steps. In the first step, the user provides code snippets to perform local tasks, such as code for class initialization and code for invoking each callin (similarly as in unit tests). This is sufficient as long as certain widely applicable assumptions hold. First, we assume that each sequence of callins produces a sequence of callbacks deterministically (this assumption fails when for instance a callback has a parameter that is ignored at first by DroidStar but that influences the typestate). Second, we assume that the resulting typestate is finite. If these assumptions fail, in the following steps, DroidStar asks the user for a solution to the problem. For instance, one way to remove non-determinism is to refine one callback into two separate logical callbacks, based on the parameter values. This design allows DroidStar to offer the user control over the final result while requiring only limited, local, insight from the user. DroidStar is available for download at https://github.com/cuplv/droidstar


We present a method for inferring typestates for Android classes. However, our method is equally applicable in other contexts. The core algorithm is based on Angluin’s L algorithm [5] adapted to Mealy machines [32]. In this algorithm, a learner tries to learn a finite-state machine — in our case a callback typestate — by asking a teacher membership and equivalence queries. Intuitively, a membership query asks for outputs corresponding to a sequence of input callins, and the equivalence query asks if the learned typestate is correct. We note that the teacher does not need to know the solution, but only needs to know how to answer the queries.

The key question we answer is how to implement oracles for the membership and equivalence queries. We show how to implement membership queries on Android classes using black-box testing. Our main contribution here is an efficient algorithm for implementing the equivalence query using membership query. The insight here is that the number of membership queries can be bounded by a function of a new bound we call the distinguisher bound. We empirically confirmed that for Android classes, the distinguisher bound is significantly smaller than the state bound used in previous work [12, 16]. Given that the number of required membership queries depends exponentially on the distinguisher bound, the novel bound is what enables our tool to scale to Android classes.


We use DroidStar to synthesize callback typestates for 16 Android framework classes and classes from Android libraries. The results show that DroidStar learns callback typestates accurately and efficiently. This is confirmed by documentation, code inspection, and manual comparison to simple Android applications. The running time of DroidStar on these benchmarks ranged between 43 seconds and 72 minutes, with only 3 benchmarks taking more than 10 minutes. The usefulness of the distinguisher bound was also confirmed. Concretely, using previously known bounds, learning the callback typestate for one of our examples (MediaPlayer) would take more than a year, whereas with the distinguisher bound, this example takes around 72 minutes. Furthermore, by inspecting our typestates, we uncovered corner cases with surprising behavior that are undocumented and might even be considered as bugs in some cases. For instance, for the commonly used AsyncTask class, if execute() is called after cancel() but before the callback is received, it will not throw an exception but will never cause the asynchronous task to be run. Section 6 presents our results in more detail.


The contributions of this paper are: (a) We introduce the notion of callback typestates and develop an approach, based on the L algorithm, to infer them. (b) We show how to implement efficiently membership and equivalence oracles required by the L algorithm. (c) We evaluate our approach on examples from the Android framework, and show its accuracy and effectiveness.

2 Workflow and Illustrative Example

We use the Android Framework’s MediaPlayer class to explain the standard workflow for inferring callback typestate using DroidStar. This class is highly stateful—its interface includes many methods that are only meaningful or enabled in one or two particular player states—and makes extensive use of callins and callbacks to handle the delays of loading and manipulating large media files. These properties make callback typestate a perfect fit; in fact, MediaPlayer has one of the very few examples where we found a complete callback typestate specification in the Android libraries documentation. This callback typestate is shown in Figure 1.

Figure 1: Part of MediaPlayer’s callback typestate from https://developer.android.com/reference/android/media/MediaPlayer.html

In Figure 1, callins are represented by single arrows and callbacks by double arrows. Let us look at one part of the protocol that governs the client-framework interaction. The client first invokes the callin setDataSource(), and the protocol transitions to the Initialized state. In this state, the client can invoke the callin prepareAsync(), and the protocol transitions to the Preparing state. In the Preparing state, the client cannot invoke any callins, but the framework can invoke the callback, and then the protocol transitions to the Prepared state. At this point, the client can invoke the start() callin, and the media starts playing.

Our goal is to semi-automatically infer the callback typestate from the figure using the tool DroidStar. The developer interacts with DroidStar in several steps, which we describe now.

2.1 Developer-Provided Snippets

To apply DroidStar to the MediaPlayer class, the developer provides a number of code snippets detailed below that act as an interface through which the tool can examine MediaPlayer instances.

Test object and environment instantiation.

The main callback typestate inference algorithm of DroidStar works roughly by repeatedly performing tests in the form of sequences of method calls on an object of the given class, i.e., the MediaPlayer. Each test must begin with an identical, isolated, class object, and if necessary, a standard environment. In the first step, the developer provides a snippet to initialize such an object and environment. In the case of MediaPlayer, this snippet is as simple as discarding the previous instance, creating a new one with new MediaPlayer(), and registering the necessary callback listeners (explained in the Callback instrumentation paragraph below). In some cases this snippet is more complex. As an example, we cannot create new instances of the BluetoothAdapter class, so for that class this snippet would need to bring the existing instance back to a uniform initial state.

Callin declaration.

The next step is to declare the alphabet of “input symbols” that represent the callins in the interface of our class—the final callback typestate will be written using these symbols—and map each symbol to the concrete code snippet it represents. In most cases, there is a one-to-one correspondence between input symbols and callin methods. For example, the code snippets associated with the input symbols , , and are prepare();, prepareAsync();, and start();, respectively.

In some cases, such as when a callin takes a parameter, the developer may instead map a symbol to a set of code snippets representing alternative forms of the input which are suspected to have different behavior. In the MediaPlayer class, the setDataSource() callin method takes a URL argument. The developer might (rightly) believe that depending on the validity and reachability of the given URL, the behavior of the callin in the typestate may differ. In this case, the developer may provide the two snippets setDataSource(goodURL); and setDataSource(badURL); for the same callin. DroidStar will consider both snippets for generating tests, and further, it will indicate if they behave differently with respect to the typestate. In case a difference is detected, the “non-determinism” is handled as explained later in this section.

The complete set of input symbols which would be declared and mapped for the MediaPlayer class are setDataSource, prepare, prepareAsync, start, stop, reset, release, and pause.

Callback instrumentation.

As for the callin methods, which act as the input symbols in the callback typestate, the callback methods act as the output symbols in the callback typestate. The developer specifies the set of output callback symbols and associated snippets to detect when callbacks occur. In most cases, this involved adding the listeners for the callbacks in the initialization snippet as mentioned above. In the MediaPlayer class, the output symbols are onCompleted and onPrepared.

2.2 Automated Callback-Typestate Inference

Once the developer provides the input and output symbols and the associated snippets, DroidStar attempts to automatically learn the callback typestate following the framework of the L algorithm.

L inference.

In L, the learner tests sequences of inputs until she can form a consistent hypothesis automaton. Each such test (or sequence of inputs) is called a membership query. Once a hypothesis automaton is produced, an equivalence query is performed; i.e., the hypothesis automaton is checked for equivalence with the true callback typestate. If the two are equivalent, we are done; otherwise, a counter-example test is returned from which the tool learns. This process repeats until the produced hypothesis automaton is correct.

For MediaPlayer, the first set of membership queries each consist of a single different callin. Of these, only the query containing setDataSource() succeeds. The learner continues with longer membership queries while building the hypothesis automaton. For instance, it learns that prepareAsync() and prepare() do not lead to the same state: it is possible to invoke the start() after prepare(), but not after prepareAsync(). Once the client receives the callback , start() may be called. The learner thus hypothesizes a transition from the Preparing to the Prepared on . Once the hypothesis is complete, the learner asks the equivalence query. Initially, a counter-example to equivalence is returned using which the learner refines its hypothesis. The final solution is found after equivalence queries.

Answering Equivalence Queries.

The equivalence query, i.e., checking if a learned callback typestate is in fact the true callback typestate is undecidable in general. However, assuming a bound on the size of the typestate, the equivalence query can be implemented using further testing. However, equivalence queries are still expensive and to make them practical we present an new optimization based on a distinguisher bound. We can observe in Figure 1 that for any pair of states there is a transition in one state which leads to an error in the other. This corresponds to a distinguisher bound of 1. Small distinguisher bounds arise because typestates are not random automata but part of an API designed for ease of use and robustness. Such APIs are coded defensively and are fail-fast [35], i.e., errors are not buffered but reported immediately. Each state in the typestate has a specific function and an associated set of callins and callbacks. In automata terms, the alphabet is roughly the same size as the number of states and each state has only a few transitions, making any two states easy to distinguish. In Section 4.3, we explain how to use the distinguisher bound to implement equivalence queries and discuss why distinguisher bounds are small in practice.

2.3 Obstacles to Inference and Solutions

The L based callback typestate inference algorithm makes several assumptions about the behavior of the class that do not always hold. DroidStar is designed to detect these violations of assumptions and notify the developer. Here, we discuss two such assumptions, the exceptional situations that arise when the assumptions are violated, and the additional developer intervention needed to handle such cases.


In input-output automata learning theory, non-determinism makes learning impossible. Non-determinism is the possibility of the same sequence of input callins producing different sequences of output callbacks across tests. Non-determinism may be due to various controllable and non-controllable factors. Controllable factors include cases where behavior depends on if a file exists, if a URL is reachable, etc. On the other hand, non-controllable factors include random number generators, device sensors, etc. In practice, most of the non-determinism was controllable.

The main technique for handling non-determinism is via refinement of input or output alphabets. Here, a single callin or callback is split into multiple ”logical” inputs or outputs.

(a) Controllable non-determinism can be eliminated by incorporating the controlling factor into the inputs. For example, in the SQLiteOpenHelper class, the behavior of the constructor callin changes depending on if a file exists. However, after splitting the callin into two separate callins constructor/fileExists and constructor/noFileExists, the behavior of each of each callin becomes deterministic with respect to these callins.

(b) Another source of non-determinism is when the same callback is used to notify logically different events. For example, a class may use a generic onComplete callback which is passed a status parameter that can have the values “Success” and “Failure”. Based on this value, different further callins are enabled, leading to non-determinism. Here, the developer may manually refine the callback into two output symbols onEvent/Success and onEvent/Failure, and the behavior is deterministic with respect to these.

In summary, for controllable non-determinism, the onus is on the developer to identify the source of the detected non-determinism and provide a refinement of the input or output alphabet and corresponding code snippets to control the source. No general technique exists to handle non-controllable non-determinism, but specific cases can be handled using techniques shown in Section 5.


Another basic assumption that L based inference algorithm makes is that the callback typestate under consideration is regular. This assumption is commonly violated in request-response style behavior of classes where the number of responses (output callbacks) invoked is exactly equal to the number of requests (input callins). Our solution to this problem is to restrict the learning to a subset of the class behavior, such as inputs with at most one pending request callin using a learning purpose [1]. These restrictions makes the behavior regular and amenable to learning.

3 The Callback Typestate Learning Problem

We introduce formal models of interfaces, define the callback typestate learning problem, and present an impossibility result about learning typestates. Callback typestates have both inputs (corresponding to callins) and outputs (corresponding to callbacks). In automata theory, callback typestates can be seen as interface automata. Interface automata [14] are a well-studied model of automata that can produce outputs asynchronously w.r.t. inputs. We use the name callback typestates to emphasize that they are a generalization of typestates as used in the programming languages literature.

3.1 Definitions and Problem Statement

Asynchronous interfaces.

Let and be the set of callins and callbacks of an asynchronous interface. We abstract away parameter and return values of callins and callbacks, and model a behavior of the interface as a trace . The interface is given by where is the prefix-closed set of all feasible traces of the interface.

Interface automata.

We use interface automata [14] to represent asynchronous interfaces. An interface automaton is given by where: (a) is a finite set of states, (b) is the initial state, (c) and are finite sets of input and output symbols, and (d) are a set of transitions. A trace of is given by if . is the set of all traces of .

Problem statement.

Given an interface , the callback typestate learning problem is to learn an interface automaton such that . We allow the learner to ask a membership oracle membership queries. For a membership query, the learner picks and the membership oracle returns either: (a) a trace whose sequence of callins is exactly , or (b) if no such trace exists.

3.2 The Theory and Practice of Learning Typestates

In general, it is impossible to learn callback typestates using only membership queries; no finite set of membership queries fixes a unique interface automaton. However, callback typestates can be effectively learned given extra assumptions. We now analyze the causes behind the impossibility and highlight the assumptions necessary to overcome it.

Unbounded asynchrony.

Membership queries alone do not tell us if the interface will emit more outputs (callbacks) at any point in time. Hence, we assume:

Assumption 1: Quiescence is observable.

This assumption is commonly used in ioco-testing frameworks [37]. In our setting, we add an input and an output , where is returned after a only if there are no other pending callbacks. In practice, can be implemented using timeouts, i.e., pending callbacks are assumed to arrive within a fixed amount of time. If no callbacks are seen within the timeout, is output.


Using and , in the MediaPlayer example, we have that setDataSource()prepareAsync()waitquiet is a valid trace, but setDataSource()prepareAsync()waitquiet is not.

Behavior unboundedness.

For any set of membership queries, let be the length of the longest query. It is not possible to find out if the interface exhibits different behavior for queries much longer than . This is a theoretical limitation, but is not a problem in practice [7]; most callback typestates are rather small ( states).

Assumption 2: An upper bound on the size of

the typestate being learned is known.


We need to be able to observe the systems’ behaviors to learn them and non-determinism can prevent that. Therefore, we assume:

Assumption 3: The interface is deterministic.

We assume that for every trace of the interface, there is at most one output such that . In practice, the non-determinism problem is somewhat alleviated due to the nature of callback typestates (see Section 5). See [1] for a detailed theoretical discussion of how non-determinism affects learnability.


Consider an interface with traces given by . All membership queries are a sequence of input’s; however, it is possible that the membership oracle never returns any trace containing . In that case, no learner will be able to learn the interface exactly.

4 Learning Callback Typestates using L

Given Assumption 1 and Assumption 3, we first build a “synchronous closure” of an asynchronous interface (Section 4.1). Then, we show how to learn the synchronous closure effectively given Assumption 2 (Section 4.2 and 4.3).

4.1 From Asynchronous to Synchronous Interfaces

Using Assumption 1 and 3, we build a synchronous version of an interface in which inputs and outputs strictly alternate following [1]. For synchronous interfaces, we can draw learning techniques from existing work [5, 1, 25, 32].

Define and . The purpose of the extra inputs and outputs is discussed below. For any , we define where is had from by erasing all occurrences of , , , and .

Synchronous closures.

The synchronous closure of an asynchronous interface is given by where and are as above, and is defined as the smallest set satisfying the following:

Informally, in : (a) Each input is immediately followed by a dummy output ; (b) Each output is immediately preceded by a wait input ; (c) Any call to an input disabled in is immediately followed by an . Further, all outputs after an are ’s. (d) Any call to in a quiescent state is followed by .

Given and Assumption 1, it is easy to construct the membership . Note that due to Assumption 3, there is exactly one possible reply for each query . Further, by the construction of the synchronous closure, the inputs and outputs in alternate.

Mealy machines.

We model synchronous interfaces using the simpler formalism of Mealy machines rather than interface automata. A Mealy machine is a tuple where: (a) , , , and are states, initial state, inputs and outputs, respectively, (b) is a transition function, and (c) is an output function. We abuse notation and write and if . A sequence is a trace of if . We often abuse notation and write instead of . We denote by the set of all traces of .

4.2 L: Learning Mealy Machines

For the sake of completeness, we describe the classical L learning algorithm by Angluin [5] as adapted to Mealy machines in [32]. A reader familiar with the literature on inference of finite-state machines may safely skip this subsection.

Fix an asynchronous interface and its synchronous closure . In L, in addition to a membership oracle , the learner has access to an equivalence oracle . For an equivalence query, the learner passes a Mealy machine to , and is in turn returned: (a) A counterexample input such that and , or (b) if no such exists.

The full L algorithm is in Algorithm 1. In Algorithm 1, the learner maintains: (a) a set of state-representatives (initially set to ), (b) a set of experiments (initially set to ), and (c) an observation table . The observation table maps each prefix and suffix to , where is the suffix of the output sequence of of length . The entries are computed by the sub-procedure .

Intuitively, represent Myhill-Nerode equivalence classes of the Mealy machine the learner is constructing, and distinguish between the different classes. For to form valid set of Myhill-Nerode classes, each state representative extended with an input, should be equivalent to some state representative. Hence, the algorithm checks if each is equivalent to some (line 5) under , and if not, adds to . If no such exists, the learner constructs a Mealy machine using the Myhill-Nerode equivalence classes, and queries the equivalence oracle (line 7). If the equivalence oracle returns a counterexample, the learner adds a suffix of the counterexample to ; otherwise, it returns . For the full description of the choice of suffix, see [30, 32].

1:Membership oracle , Equivalence oracle
2:Mealy machine
3:; ;
4:while   do
5:       while   do
6:             ;        
7:       ;
8:       if   then return        
9:       ;
10:function (,,,)
12:          if
13:          if
14:       return
15:function (,)
16:       for all  and such that  do
19:             if   then return                     
20:procedure (,,,)
21:       for all ,  do
Algorithm 1 L for Mealy machines

[[32]] Let there exist a Mealy machine with states such that is the set of traces of . Then, given and , Algorithm 1 returns making at most membership and equivalence queries, where is the maximum length of counterexamples returned by . If returns minimal counterexamples, .

4.3 An Equivalence Oracle Using Membership Queries

Given a black-box interface in practice, it is not feasible to directly implement the equivalence oracle required for the L algorithm. Here, we demonstrate a method of implementing an equivalence oracle using the membership oracle using the boundedness assumption (Assumption 2). As before fix an asynchronous interface and its synchronous closure . Further, fix a target minimal Mealy machine such that is the set of traces of .

State bounds.

A state bound of implies that the target Mealy machine has at most states. Given a state bound, we can replace an equivalence check with a number of membership queries using the following theorem. {theorem} Let and be Mealy machines having and states, respectively, such that . Then, there exists an input word of length at most such that . The proof is similar to the proof of the bound for finite automata (see [33, Theorem 3.10.5]). We can check equivalence of and any given by testing that they have equal outputs on all inputs of length at most , i.e., using membership queries. While this simple algorithm is easy to implement, it is inefficient and the number of required membership queries make it infeasible to implement in practice. Other algorithms based on state bounds have a similar problems with efficiency (see Remark in Section 4.3). Further, the algorithm does not take advantage of the structure of . The following discussion and algorithm rectifies these short-comings.

Distinguisher bounds.

A distinguisher bound of implies that for each pair of states in the target Mealy machine can be distinguished by an input word of length at most , i.e., . Intuitively, a small distinguisher bound implies that each state is “locally” different, i.e., can be distinguished from others using small length input sequences. The following theorem shows that a state bound implies a comparable distinguisher bound. {theorem} State bound implies distinguisher bound .

Small distinguisher bound.

In practice, distinguishers are much smaller than the bound implied by the state bound. For the media-player, the number of states is , but only distinguishers of length are required. This pattern tends to hold in general due to the following principles of good interface design:

  • Clear separation of the interface functions. Each state in the interface has a specific function and a specific set of callins and callbacks. There is little reuse of names across state. The typestate’s alphabet is roughly the same size as the number of states.

  • Fail-fast. Incorrect usage of the interface is not silently ignored but reported as soon as possible. This makes it easier to distinguish states as disabled callins lead directly to errors.

  • No buffering. More than just fail-fast, a good interface is interactive and the effect of callins must be immediately visible rather than hidden. A good interface is not a combination lock that requires many inputs that are silently stored and only acknowledged at the very end.

This observation also is not specific to callbacks typestates and it has been already observed for libraries [11].

Equivalence algorithm.

Algorithm 2 is an equivalence oracle for Mealy machines using the membership oracle, given a distinguisher bound. First, it computes state representatives : for each , (line 3). Then, for each transition in , the algorithm first checks whether the output symbol is correct (line 7). Then, the algorithm checks the “fidelity” of the transition up to the distinguisher bound, i.e., whether the representative of the previous state followed by the transition input, and the representative of the next state can be distinguished using a suffix of length at most . If so, the algorithm returns a counterexample. If no transition shows a different result, the algorithm returns .

Two optimizations further reduce the number of membership queries: (a) Quiescence transitions.Transitions with input and output need not be checked at line 9; it is a no-op at the interface level. (b) Error transitions.Similarly, transition with the output need not be checked as any extension of an error trace can only have error outputs.


Note that if Algorithm 2 is being called from Algorithm 1, the state representatives from L can be used instead of recomputing in line 3. Similarly, the counterexample analysis stage can be skipped in the L algorithm, and the relevant suffix can be directly returned ( in lines 12 and 13; and in line 7).

1:Mealy machine , Distinguisher bound , and Membership oracle
2: if , or s. t. 
3:for all   do s. t.  is minimal
4:for all   do
6:       if   then
7:             return        
8:       ;
10:       if  then
11:             if  then
12:                    return              
13:             else return        
15:function (, )
16:       for all   do
19:             if the last symbols of and differ then
20:                    return                     
21:       return
Algorithm 2 Equivalence oracle with distinguisher bound

Assuming the distinguisher bound of for the target Mealy machine , either (a) Algorithm 2 returns and , or (b) Algorithm 2 returns a counterexample and . Further, it performs at most membership queries.

Remark (Relation to conformance testing algorithms).

Note that the problem being addressed here, i.e., testing the equivalence of a given finite-state machine and a system whose behavior can be observed, is equivalent to the conformance testing problem from the model-based testing literature. However, several points make the existing conformance testing algorithms unsuitable in our setting.

Popular conformance testing algorithms, like the W-method [12] and the W-method [16], are based on state bounds and have an unavoidable factor in the complexity. In our experiments, the largest typestate had states and inputs. The factor leads to an infeasible (i.e., ) number of membership queries. However, since distinguisher bounds are often much smaller than state bounds, membership queries are feasible (i.e., ). The W- and W-methods cannot directly use distinguisher bounds.

The other common algorithm, the D-method [22, 20], does not apply in our setting either. The D-method is based on building a distinguishing sequence, i.e., an input sequence which produces a different sequence of outputs from every single state in the machine. However, for callback typestates, such single distinguishing sequences do not exist in practice. For similar reasons, conformance testing algorithms such as the UIO-method [31] do not apply either.

In this light, we believe that Algorithm 2 is a novel conformance testing algorithm useful in specific settings where resets are inexpensive and systems are designed to have small distinguisher bounds.

4.4 Putting It All Together

We now present the full callback typestate learning solution.


Given a deterministic interface with observable quiescence and the membership oracle . Assume there exists an interface automaton with states with distinguisher bound modeling the typestate of . Interface automaton can be learned with membership queries.

Proof sketch.

Starting with an asynchronous interface and a membership oracle , using Assumption 1 and Assumption 3 we can construct the membership oracle for the synchronous closure of . Given the distinguisher bound (or a state bound using Assumption 2 and Theorem 4.3), we can construct an equivalence oracle using Algorithm 2. Oracles and can then be used to learn a Mealy machine with the same set of traces as . This Mealy machine can be converted into the interface automata representing the callback typestate of by: (a) Deleting all transitions with output and all self-loop transitions with output , and (b) Replacing all transitions with input with the output of the transition.

5 Active Learning for Android

We implemented our method in a tool called DroidStar. In this section we describe how it works, the practical challenges we faced when working with Android, and our solutions to overcome them. DroidStar is implemented as an Android application and learns callback typestates from within a live Android system.

5.1 Designing an Experiment

To learn a typestate, a DroidStar user creates a test configuration (an extension of the LearningPurpose class) providing necessary information about a Java class under study. If known, the distinguisher bound can be provided here directly; otherwise, it can be obtained from Assumption 2 by Theorem 4.3. The instrumented alphabet, also defined here, specifies an abstract alphabet for the learning algorithm and translation between the abstract alphabet and concrete callins/callbacks of the class under study. Several other options are available for adjusting the learning, the most important being the quiescence timeout which determines Assumption 1.

5.2 Observing Asynchronous Callbacks

In our approach we assume bounded asynchrony (Assumption 1) and, therefore, we can observe when the interface does not produce any new output (quiescence). We enforce this assumption on a real system with timeouts: the membership query algorithm waits for a new output for a fixed amount of time , assuming that quiescence is reached when this time is elapsed. However, Android does not provide any worst case execution time for the asynchronous operations and we rely on the user to choose a large enough . The membership query also assumes the existence of a minimum time before a callback occurs. This ensures that we can issue a membership query with two consecutive callins (so, without a input in between), i.e., we have the time to execute the second callin before the output of the first callin.

Consider the MediaPlayer example from Section 2. The membership query setDataSource(URL)prepareAsync() may not return the if is violated, i.e., if the callback does not arrive before the timeout, and while testing it is possible that the prepareAsync()start() might not return an error as expected if the lower bound is violated. To avoid such issues we try to control the execution environment and parameters to ensure that callbacks occurred between and . In the MediaPlayer case, we must pick the right media source file.

5.3 Checking and Enforcing Our Assumptions

The simplest experiment to learn a class’s callback typestate ties a single input symbol to each of its callins and a single output symbol to each of its callbacks. However, many Android classes have behaviors which cause this simple experiment to fail and require more detailed experiments to succeed.

The main challenges when designing an experiment are (a) Non-deterministic behaviors, i.e., the state of the device and external events may influence an application. These elements are inherently non-deterministic; however, non-determinism violates Assumption 3. (b) The parameter space required to drive concrete test cases to witness a membership query is potentially infinite. Though we have ignored callin parameters till now, they are a crucial issue for testing. (c) The protocol we are learning may not be a regular language. Note that this is a violation of Assumption 2.

Non-Deterministic Behavior.

Non-deterministic behavior is disallowed by our Assumption 3. However, to make this assumption reasonable we must make non-determinism straightforward to eliminate when it arises. We explain two primary classes of non-deterministic behaviors and strategies to eliminate these behaviors. The first class is related to controllable inputs and the second to uncontrollable ones (such as inputs from the device sensors).

Because the learning algorithm cannot learn from non-deterministic systems, DroidStar will terminate if such behavior is detected. To assist in this process, DroidStar will report a non-deterministic behavior is detected and display the disagreeing sequences to the user. It detects this by caching all membership queries as input/output sequence pairs. When a new trace is explored, DroidStar checks that the trace prefixes are compatible with the previously seen traces.

In the first case, a hidden (not modeled) controllable input influences the typestate. We resolve this non-determinism by manually adding the input value and create a finer alphabet that explicate the previously hidden state of the environment. For example, in the class SQLiteOpenHelper, the getReadableDatabase() may either trigger a callback or not, depending on the parameter value to a previous callin (constructor)was the name of an existing database file. Hence, the behavior of the callin is non-deterministic, depending on the status of the database on disk. In the SQLiteOpenHelper example, we split the constructor callin into constructor/fileExists and constructor/noFileExists and pass the right parameter values in each case. With this extra modeling we can learn the interface automaton, since the execution getReadableDatabase() ends in two different states of the automaton (see Figure 2).











Figure 2: Eliminating non-determinism in SQLiteOpenHelper

The second class is the effect of the uncontrollable inputs on a typestate. Such effects, by definition, cannot be controlled or made explicit prior to the call. We can sometimes to remove this non-determinism by merging different outputs, considering them to be the same. This is the dual of the previous solution.

An example is the SpeechRecognizer, for which calling startListening() produces different callbacks depending on the environment. As the environment cannot be reasonably controlled, we merge outputs to go to the same state. If outputs are erroneously merged, the non-determinism will propagate and continue to manifest. Thus there is no risk of unsound results.

Handling Callin Parameters.

While parameter-less callins such as start() and stop() are common in Android classes, many parameterized callins exist. Because input symbols need to be listed in the experiment definition, the full range of parameter values cannot be explored. In practice, we found that parameters often have little effect on the typestate automaton. In cases where they do affect the automaton, multiple input symbols can be defined to represent the same method called with several different parameters. This solution is similar to splitting on environmental effects when dealing with non-determinism.

Learning from Non-Regular Languages.

An intrinsic limitation of L is that it learns only regular languages. However, some classes expose non-regular protocols. Common cases include situations where a request callin invoked times trigger exactly response callbacks. In the SpellCheckerSession class, callin getSuggestion() and callback follow this pattern.

However, even in such cases, it can be useful to build a regular approximation of the typestate. For example, restricting the typestate to behaviors where there is at most one pending request (a regular subset) provides all the information a programmer would need. Hence, in such cases, we use the technique of learning purposes [1] to learn a regular approximations of the infinite typestate.

6 Empirical Evaluation

We evaluated our interface-learning technique, as implemented in DroidStar, by using it to generate callback typestates for classes, sampled from the Android Framework and popular third-party libraries. DroidStar is available at https://github.com/cuplv/droidstar. For these experiments, DroidStar was run on an LG Nexus 5 with Android framework version 23. Our evaluation was designed to answer the following questions:

  1. Does our technique learn typestates efficiently?

  2. What size distinguisher bounds occur in practice? Do they support the small distinguisher bound hypothesis?

  3. Do the callback typestates we learn reveal interesting or unintended behavior in the interfaces?


For each experimental class, we manually identified a reduced alphabet of relevant callins and callbacks and provided them (along with other necessary information as explained in Section 5) to DroidStar through instances of the LearningPurpose. Relevant callins and callbacks for these experiments were those which, according to the available documentation, appeared to trigger or depend on typestate changes (enabling or disabling of parts of the interface). Each instance consisted of lines of, mostly boiler-plate, Java or Scala code.

To evaluate efficiency, we measured the overall time taken for learning, as well as the number of membership (MQ) and equivalence queries (EQ). The number of queries is likely a better measure of performance than running time: the running time depends on external factors. For example, in the media player the running time depends on play-length of the media file chosen during testing.

We validated the accuracy of learned callback typestates using two approaches. First, for classes whose documentation contains a picture or a description of what effectively is an callback typestate, we compared our result to the documentation. Second, for all other classes we performed manual code inspection and ran test apps to evaluate correctness of the produced typestates.

We used a distinguisher bound of for our experiments; further, we manually examined the learned typestate and recorded the actual distinguisher bound. For our third question, i.e., does the learned callback typestate reveal interesting behaviors, we manually examined the learned typestate, compared it against the official Android documentation, and recorded discrepancies.

Class name LP LoC states Time (s) MQ EQ MQ per EQ (needed)
AsyncTask 79 5 49 372 (94) 1 356 (0) 2 (1)
BluetoothAdapter 161 12 1273 839 (157) 2 420 (16) 2 (1)
CountDownTimer 94 3 134 232 (61) 1 224 (0) 2 (1)
DownloadManager 84 4 136 192 (43) 1 190 (0) 2 (1)
FileObserver 134 6 104 743 (189) 2 351 (8) 2 (1)
ImageLoader (UIL) 80 5 88 663 (113) 2 650 (33) 2 (1)
MediaCodec 152 8 371 1354 (871) 1 973 (482) 2 (1)
MediaPlayer 171 10 4262 13553 (2372) 5 2545 (384) 2 (1)
MediaRecorder 131 8 248 1512 (721) 1 1280 (545) 2 (1)
MediaScannerConnection 72 4 200 403 (161) 2 163 (57) 2 (1)
OkHttpCall (OkHttp) 79 6 463 839 (166) 2 812 (13) 2 (2)
RequestQueue (Volley) 79 4 420 475 (117) 1 460 (0) 2 (1)
SpeechRecognizer 168 7 3460 1968 (293) 3 646 (35) 2 (1)
SpellCheckerSession 109 6 133 798 (213) 4 374 (8) 2 (1)
SQLiteOpenHelper 140 8 43 1364 (228) 2 665 (6) 2 (2)
VelocityTracker 63 2 98 1204 (403) 1 1156 (0) 2 (1)
Table 1: DroidStar experimental results.

6.1 Results

We discuss the results (in Table 1) and our three questions.

Question : Efficiency. The table shows that our technique is reasonably fast: most typestates learned within a few minutes. The longest one takes minutes, still applicable to nightly testing. The numbers for membership queries are reported as is the number of membership queries asked by the algorithm, while is the number actually executed by the membership oracle. This number is lower as the same query may be asked multiple times, but is executed only once and the result is cached. For each benchmark, the accuracy validation showed that the produced typestate matched the actual behavior.

Question : Distinguisher Bounds. As mentioned before, we used a distinguisher bound of for all experiments. However, a manual examination of the learned callback typestates showed that a bound of would be sufficient in all cases except the SQLiteOpenHelper and the OkHttpCall where bounds of are necessary. This supports our conjecture that, in practice, interfaces are designed with each state having a unique functionality (see Section 4.3).

Question : Interesting Learned Behavior. Of the three questions, our experiments to examine the learned callback typestate for interesting behavior turned out to be the most fruitful, uncovering several discrepancies, including corner cases, unintended behavior and likely bugs, in the Android framework. These results reaffirm the utility of our main goal of automatically learning callback typestate, and suggest that learning typestate can serve valuable roles in documentation and validation of callback interfaces.

In cases, the learned typestate and documented behavior differed in certain corner cases. We carefully examined the differences, by framework source examination and manually writing test applications, and found that the learned typestate was correct and the documentation was faulty. In other cases, we believe the implemented behavior is not the intended behavior, i.e., these are likely bugs in the Android implementation. These discrepancies mostly fall into two separate categories:

Incorrect documentation. In such cases, it turned out that the discrepancy is minor and unlikely to produce bugs in client programs.

Race conditions. Several likely bugs were due to a specific category of race conditions. These interfaces have (a) a callin to start an action and a corresponding callback which is invoked when the action is successfully completed; (b) a callin to cancel an already started action and a corresponding callback which is invoked if the action is successfully cancelled. When the start action and cancel action callins are called in sequence, the expectation is that exactly one of the two callbacks are called. However, when the time between the two callins is small, we were able to observe unexpected behaviors, including neither or both callbacks being invoked.

6.2 Selected Experiments

Of our benchmarks, we briefly explain here. The remaining experiments are discussed in the technical report [29]1.

MediaPlayer. This is the class from the example in Section 2. The learned typestate differs from the existing documentation. The learned typestate: (a) has the pause() callin enabled in the “playback completed” state, and (b) shows that is invoked even after the synchronous callin prepare(). Though undocumented, these behaviors are unlikely to cause any issues.

AsyncTask. The AsyncTask class turns arbitrary computations into callback operations with progress tracking and results are delivered via callbacks. For our experiment, the computation is a simple timer. A constructed AsyncTask object performs its task when it receives the execute() callin, and then either returns the results with the callback, or returns an if cancel() is called first. The object is single-use; after it has returned a callback it will accept no further execute() commands.

Our experiment revealed an unexpected edge-case: if execute() is after cancel() but before the callback is received, it will not throw an exception but will never cause the callback task to be run. The learned interface is in Figure 3.












Figure 3: Learned typestate of the AsyncTask class

SpeechRecognizer. This class provides an example of uncontrollable environmental non-determinism. The particular callback that signals the end of the speech session—either an or an —is determined by the environment (in particular, the sound around the phone during the test). In this case, to reduce the system to a deterministic one we can learn, we supposed that the state after an or is the same and merged the two callbacks into a single symbol.

Our results revealed two interesting corner cases for the ordering of inputs. First, if an app calls cancel() between calling startListening() and receiving the callback (represented by our “starting” output symbol), calling startListening() again will have no effect until after a certain amount of time, as shown by the wait transition from state “Cancelling” to “Finished”. Delays in readiness like this can be generally considered bugs; if a system will not be ready immediately for inputs it should provide a callback to announce when the preparations are complete, so as not to invite race conditions.

Our second corner case is where the app calls stopListening() as the very first input on a fresh SpeechRecognizer. This will not throw an exception, but calling startListening() at any point after will fail, making the object effectively dead.

SQLiteOpenHelper. This class provides a more structured interface for apps to open and set up SQLite databases. It has callbacks for different stages of database initialization, allowing apps to perform setup operations only as they are needed. When a database is opened with getWritableDatabase(), a callback is called, followed by an if the database didn’t exist yet or an if the database had a lower version number than was passed to the SQLiteOpenHelper constructor, all followed finally by an when the database is ready for reading. The database can then be closed with a close().

Our experiment observed the callbacks when opening databases in different states (normal, non-existent, and out of date) and performing the close() operation at different points in the sequence. We found that once the getWritableDatabase() method is called, calling close() will not prevent the callbacks from being run.

VelocityTracker. This class was a special case with no asynchronous behavior; it was a test of our tool’s ability to infer traditional, synchronous typestates. The class has a recycle() method that we expected to disable the rest of the interface, but our tool found (and manual tests confirmed) that the other methods can still be called after recycling. The documentation’s warning that “You must not touch the object after calling [recycle]” is thus not enforced.

7 Related Work

Works which automatically synthesize specifications of the valid sequences of method calls (e.g. [3, 34, 4, 18]) typically ignore the asynchronous callbacks.

Static analysis has been successfully used to infer typestates specifications (importantly, without callbacks) [3, 23, 34]. The work in [3] infers classical typestates for Java classes using L. In contrast, our approach is based on testing. Therefore, we avoid the practical problem of abstracting the framework code. On the other hand, the use of testing makes our L oracles sound only under assumptions. Similarly,  [19] uses L to infer classical typestates, including ranges of input parameters that affect behavior. However, their tool is based on symbolic execution, and thus would not scale to systems as large and complex as the Android Framework.

Inferring interfaces using execution traces of client programs using the framework is another common approach [4, 40, 2, 13, 17, 38, 41, 28]. In contrast to dynamic mining, we do not rely on the availability of client applications or a set of execution traces. The L algorithm drives the testing.

The analysis of event-driven programming frameworks has recently gained a lot of attention (e.g.  [6, 9, 10, 26]). However, none of the existing works provide an automatic approach to synthesize interface specifications. Analyses of Android applications mostly focus on either statically proving program correctness or security properties [6, 9, 21, 39, 15] or dynamically detecting race conditions [27, 24, 8]. These approaches manually hard-code the behavior of the framework to increase the precision of the analysis. The callback typestate specifications that we synthesize can be used here, avoiding the manual specification process.

Our work builds on the seminal paper of Angluin [5] and the subsequent extensions and optimizations. In particular, we build on L for I/O automata [1, 32]. The optimizations we use include the counterexample suffix analysis from [30] and the optimizations for prefix-closed languages from [25]. The relation to conformance testing methods [12, 16, 22, 20, 31] has been discussed in Section 4.3.

8 Conclusion

We have shown how to use active learning to infer callback typestates. We introduce the notion of distinguisher bound which take advantage of good software engineering practices to make active learning tractable on the Android system. Our method is implemented in the freely available tool called DroidStar. This paper enables several new research directions. We plan to investigate mining parameters of callins from instrumented trace from real user interactions, as well as the inference of structured typestates (for instance, learning a typestate as a product of simpler typestates).


This research was supported in part by DARPA under agreement FA8750-14-2-0263. Damien Zufferey was supported in part by the European Research Council Grant Agreement No. 610150 (ERC Synergy Grant ImPACT (http://www.impact-erc.eu/)).


  1. http://arxiv.org/abs/1701.07842


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