Automated unique input output sequence generation for conformance testing of FSMs

This paper describes a method for automatically generating unique input output (UIO) sequences for FSM conformance testing. UIOs are used in conformance testing to verify the end state of a transition sequence. UIO sequence generation is represented as a search problem and genetic algorithms are used to search this space. Empirical evidence indicates that the proposed method yields considerably better (up to 62% better) results compared with random UIO sequence generation

K-branching UIO sequences for partially specified observable non-deterministic FSMs

In black-box testing, test sequences may be constructed from systems modelled as deterministic finite-state machines (DFSMs) or, more generally, observable non-deterministic finite state machines (ONFSMs). Test sequences usually contain state identification sequences, with unique input output sequences (UIOs) often being used with DFSMs. This paper extends the notion of UIOs to ONFSMs. One challenge is that, as a result of non-determinism, the application of an input sequence can lead to exponentially many expected output sequences. To address this scalability problem, we introduce K-UIOs: K-UIOs that lead to at most K output sequences from states of M. We show that checking K-UIO existence is PSPACE-Complete if the problem is suitably bounded; otherwise it is in EXPSPACE and PSPACE-Hard. We provide a massively parallel algorithm for constructing K-UIOs and the results of experiments on randomly generated and real FSM specifications. The proposed algorithm was able to construct UIOs in cases where the existing UIO generation algorithm could not and was able to construct UIOs from FSMs with 38K states and 400K transitions

Using formal methods to support testing

Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing

Optimizing the length of checking sequences

A checking sequence, generated from a finite state machine, is a test sequence that is guaranteed to lead to a failure if the system under test is faulty and has no more states than the specification. The problem of generating a checking sequence for a finite state machine M is simplified if M has a distinguishing sequence: an input sequence D~ with the property that the output sequence produced by M in response to D is different for the different states of M. Previous work has shown that, where a distinguishing sequence is known, an efficient checking sequence can be produced from the elements of a set A of sequences that verify the distinguishing sequence used and the elements of a set /spl gamma/ of subsequences that test the individual transitions by following each transition t by the distinguishing sequence that verifies the final state of t. In this previous work, A is a predefined set and /spl gamma/ is defined in terms of A. The checking sequence is produced by connecting the elements of /spl gamma/ and A to form a single sequence, using a predefined acyclic set E/sub c/ of transitions. An optimization algorithm is used in order to produce the shortest such checking sequence that can be generated on the basis of the given A and E/sub c/. However, this previous work did not state how the sets A and E/sub c/ should be chosen. This paper investigates the problem of finding appropriate A and E/sub c/ to be used in checking sequence generation. We show how a set A may be chosen so that it minimizes the sum of the lengths of the sequences to be combined. Further, we show that the optimization step, in the checking sequence generation algorithm, may be adapted so that it generates the optimal E/sub c/. Experiments are used to evaluate the proposed method

Checking sequences for distributed test architectures

Controllability and observability problems may manifest themselves during the application of a checking sequence in a test architecture where there are multiple remote testers. These problems often require the use of external coordination message exchanges among testers during testing. However, the use of coordination messages requires the existence of an external network that can increase the cost of testing and can be difficult to implement. In addition, the use of coordination messages introduces delays and this can cause problems where there are timing constraints. Thus, sometimes it is desired to construct a checking sequence from the specification of the system under test that will be free from controllability and observability problems without requiring the use of external coordination message exchanges. This paper gives conditions under which it is possible to produce such a checking sequence, using multiple distinguishing sequences, and an algorithm that achieves this

Oracles for distributed testing

Copyright @ 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The problem of deciding whether an observed behaviour is acceptable is the oracle problem. When testing from a finite state machine (FSM) it is easy to solve the oracle problem and so it has received relatively little attention for FSMs. However, if the system under test has physically distributed interfaces, called ports, then in distributed testing we observe a local trace at each port and we compare the set of local traces with the set of allowed behaviours (global traces). This paper investigates the oracle problem for deterministic and non-deterministic FSMs and for two alternative definitions of conformance for distributed testing. We show that the oracle problem can be solved in polynomial time for the weaker notion of conformance but is NP-hard for the stronger notion of conformance, even if the FSM is deterministic. However, when testing from a deterministic FSM with controllable input sequences the oracle problem can be solved in polynomial time and similar results hold for nondeterministic FSMs. Thus, in some cases the oracle problem can be efficiently solved when using stronger notion of conformance and where this is not the case we can use the decision procedure for weaker notion of conformance as a sound approximation

Canonical finite state machines for distributed systems

There has been much interest in testing from finite state machines (FSMs) as a result of their suitability for modelling or specifying state-based systems. Where there are multiple ports/interfaces a multi-port FSM is used and in testing, a tester is placed at each port. If the testers cannot communicate with one another directly and there is no global clock then we are testing in the distributed test architecture. It is known that the use of the distributed test architecture can affect the power of testing and recent work has characterised this in terms of local s-equivalence: in the distributed test architecture we can distinguish two FSMs, such as an implementation and a specification, if and only if they are not locally s-equivalent. However, there may be many FSMs that are locally s-equivalent to a given FSM and the nature of these FSMs has not been explored. This paper examines the set of FSMs that are locally s-equivalent to a given FSM M. It shows that there is a unique smallest FSM χmin(M) and a unique largest FSM χmax(M) that are locally s-equivalent to M. Here smallest and largest refer to the set of traces defined by an FSM and thus to its semantics. We also show that for a given FSM M the set of FSMs that are locally s-equivalent to M defines a bounded lattice. Finally, we define an FSM that, amongst all FSMs locally s-equivalent to M, has fewest states. We thus give three alternative canonical FSMs that are locally s-equivalent to an FSM M: one that defines the smallest set of traces, one that defines the largest set of traces, and one with fewest states. All three provide valuable information and the first two can be produced in time that is polynomial in terms of the number of states of M. We prove that the problem of finding an s-equivalent FSM with fewest states is NP-hard in general but can be solved in polynomial time for the special case where there are two ports

Constraint-Based Heuristic On-line Test Generation from Non-deterministic I/O EFSMs

We are investigating on-line model-based test generation from non-deterministic output-observable Input/Output Extended Finite State Machine (I/O EFSM) models of Systems Under Test (SUTs). We propose a novel constraint-based heuristic approach (Heuristic Reactive Planning Tester (xRPT)) for on-line conformance testing non-deterministic SUTs. An indicative feature of xRPT is the capability of making reasonable decisions for achieving the test goals in the on-line testing process by using the results of off-line bounded static reachability analysis based on the SUT model and test goal specification. We present xRPT in detail and make performance comparison with other existing search strategies and approaches on examples with varying complexity.Comment: In Proceedings MBT 2012, arXiv:1202.582

Distinguishing sequences for partially specified FSMs

Distinguishing Sequences (DSs) are used inmany Finite State Machine (FSM) based test techniques. Although Partially Specified FSMs (PSFSMs) generalise FSMs, the computational complexity of constructing Adaptive and Preset DSs (ADSs/PDSs) for PSFSMs has not been addressed. This paper shows that it is possible to check the existence of an ADS in polynomial time but the corresponding problem for PDSs is PSPACE-complete. We also report on the results of experiments with benchmarks and over 8 * 106 PSFSMs. © 2014 Springer International Publishing

Testing from a nondeterministic finite state machine using adaptive state counting

The problem of generating a checking experiment from a nondeterministic finite state machine has been represented in terms of state counting. However, test techniques that use state counting traditionally produce preset test suites. This paper extends the notion of state counting in order to allow the input/output sequences observed in testing to be utilized: Adaptive state counting is introduced. The main benefit of the proposed approach is that it may result in a reduction in the size of the test suite used. An additional benefit is that, where a failure is observed, it is possible to terminate test generation at this point