Mutation testing from probabilistic finite state machines

Mutation testing traditionally involves mutating a program in order to produce a set of mutants and using these mutants in order to either estimate the effectiveness of a test suite or to drive test generation. Recently, however, this approach has been applied to specifications such as those written as finite state machines. This paper extends mutation testing to finite state machine models in which transitions have associated probabilities. The paper describes several ways of mutating a probabilistic finite state machine (PFSM) and shows how test sequences that distinguish between a PFSM and its mutants can be generated. Testing then involves applying each test sequence multiple times, observing the resultant output sequences and using results from statistical sampling theory in order to compare the observed frequency of each output sequence with that expected

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

The complexity of asynchronous model based testing

This is the post-print version of the final paper published in Theoretical Computer Science. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.In model based testing (MBT), testing is based on a model MM that typically is expressed using a state-based language such as an input output transition system (IOTS). Most approaches to MBT assume that communications between the system under test (SUT) and its environment are synchronous. However, many systems interact with their environment through asynchronous channels and the presence of such channels changes the nature of testing. In this paper we investigate the situation in which the SUT interacts with its environment through asynchronous channels and the problems of producing test cases to reach a state, execute a transition, or to distinguish two states. In addition, we investigate the Oracle Problem. All four problems are explored for both FIFO and non-FIFO channels. It is known that the Oracle Problem can be solved in polynomial time for FIFO channels but we also show that the three test case generation problems can also be solved in polynomial time in the case where the IOTS is observable but the general test generation problems are EXPTIME-hard. For non-FIFO channels we prove that all of the test case generation problems are EXPTIME-hard and the Oracle Problem in NP-hard, even if we restrict attention to deterministic IOTSs

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

A Method of Functional Alignment Verification in Hierarchical Enterprise Models

Enterprise modeling involves multiple domains of expertise: requirements engineering, business process modeling, IT development etc. Our experience has shown that hierarchical enterprise models, made of an assembly of system models, are effective. In these models, two hierarchies exist: an organizational level hierarchy (describing systems' construction) and a functional level hierarchy (describing systems' functionality). Using a uniform hierarchical modeling language, system models at different hierarchical levels can be aligned in the context of the enterprise model. Using an operational semantics, each system model can be translated into executable code for model simulation and testing. The possibility to simulate and test models leads to the alignment verification for all system models across both hierarchies. In this paper we propose a method and tool for functional alignment verification. We use the Abstract State Machine (ASM) and the ASM language (AsmL) to formalize our graphical models for simulation and testing. We illustrate this approach with an example

Generating a checking sequence with a minimum number of reset transitions

Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.This work was supported in part by Leverhulme Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research Council grant number GR/R43150, Formal Methods and Testing (FORTEST)

Distinguishing Sequences for Distributed Testing: Adaptive Distinguishing Sequences

This paper concerns the problem of testing from a finite state machine (FSM) M modelling a system that interacts with its environment at multiple physically distributed interfaces, called ports. We assume that the distributed test architecture is used: there is a local tester at each port, the tester at port p only observes events at p, and the testers do not interact during testing. This paper formalises the notion of an adaptive test strategy and what it means for an adaptive test strategy to be controllable. We provide algorithms to check whether a global strategy is controllable and to generate a controllable adaptive distinguishing sequence (ADS). We prove that controllable ADS existence is PSPACE-hard and that the problem of deciding whether M has a controllable ADS with length l is NP-hard. In practice, there is likely to be a polynomial upper bound on the length of ADS in which we are interested and for this case the decision problem is NP-complete

Parallel algorithms for generating distinguishing sequences for observable non-deterministic FSMs

A distinguishing sequence (DS) for a finite state machine (FSM) is an input sequence that distinguishes every pair of states of the FSM. There are techniques that generate a test sequence with guaranteed fault detection power and it has been found that shorter test sequence can be produced if DSs are used. Despite these benefits, however, until recently the only published DS generation algorithms have been for deterministic FSMs. This paper develops a massively parallel algorithm, which can be used in GPU Computing, to generate DSs from partial observable non-deterministic FSMs. We also present the results of experiments using randomly generated FSMs and some benchmark FSMs. The results are promising and indicate that the proposed algorithm can derive DSs from partial observable non-deterministic FSMs with 32,000 states in an acceptable amount of time.This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant #1059B191400424 and by the NVIDIA corporation

Reaching and distinguishing states of distributed systems

Some systems interact with their environment at physically distributed interfaces, called ports, and in testing such a system it is normal to place a tester at each port. Each tester observes only the events at its port and it is known that this limited observational power introduces additional controllability and observability problems into testing. Given a multiport finite state machine (FSM) $M$, we consider the problems of defining strategies for the testers either to reach a given state of $M$ or to distinguish two states of $M$. These are important problems since most techniques for testing from a single-port FSM use sequences that reach and distinguish states. Both problems can be solved in low-order polynomial time for single-port FSMs but we prove that the corresponding decision problems are undecidable for multiport FSMs. However, we also show that they can be solved in low-order polynomial times for deterministic FSMs if we restrict our attention to controllable tests. These results have important ramifications for testing from a multiport FSM since they suggest that methods for testing from a single-port FSM cannot be easily adapted. In addition, two FSMs can be distinguished if and only if their initial states can be distinguished and so the results suggest that, in contrast to single-port FSMs, we cannot expect to produce general complete test generation methods for multiport FSMs

Web services choreography testing using semantic service description

Web services have become popular due to their ability to integrate with and to interoperate heterogeneous applications. Several web services can be combined into a single application to meet the needs of users. In the course of web services selection, a web candidate service needs to conform to the behaviour of its client, and one way of ensuring this conformity is by testing the interaction between the web service and its user. The existing web services test approaches mainly focus on syntax-based web services description, whilst the semantic-based solutions mostly address composite process flow testing. The aim of this research is to provide an automated testing approach to support service selection during automatic web services composition using Web Service Modeling Ontology (WSMO). The research work began with understanding and analysing the existing test generation approaches for web services. Second, the weaknesses of the existing approaches were identified and addressed by utilizing the choreography transition rules of WSMO in an effort to generate a Finite State Machine (FSM). The FSM was then used to generate the working test cases. Third, a technique to generate an FSM from Abstract State Machine (ASM) was adapted to be used with WSMO. This thesis finally proposed a new testing model called the Choreography to Finite State Machine (C2FSM) to support the service selection of an automatic web service composition. It proposed new algorithms to automatically generate the test cases from the semantic description (WSMO choreography description). The proposed approach was then evaluated using the Amazon E-Commerce Web Service WSMO description. The quality of the test cases generated using the proposed approach was measured by assessing their mutation adequacy score. A total of 115 mutants were created based on 7 mutant operators. A mutation adequacy score of 0.713 was obtained. The experimental validation demonstrated a significant result in the sense that C2FSM provided an efficient and feasible solution. The result of this research could assist the service consumer agents in verifying the behaviour of the Web service in selecting appropriate services for web service composition