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

Applying SMT Solvers to the Test Template Framework

The Test Template Framework (TTF) is a model-based testing method for the Z notation. In the TTF, test cases are generated from test specifications, which are predicates written in Z. In turn, the Z notation is based on first-order logic with equality and Zermelo-Fraenkel set theory. In this way, a test case is a witness satisfying a formula in that theory. Satisfiability Modulo Theory (SMT) solvers are software tools that decide the satisfiability of arbitrary formulas in a large number of built-in logical theories and their combination. In this paper, we present the first results of applying two SMT solvers, Yices and CVC3, as the engines to find test cases from TTF's test specifications. In doing so, shallow embeddings of a significant portion of the Z notation into the input languages of Yices and CVC3 are provided, given that they do not directly support Zermelo-Fraenkel set theory as defined in Z. Finally, the results of applying these embeddings to a number of test specifications of eight cases studies are analysed.Comment: In Proceedings MBT 2012, arXiv:1202.582

Asynchronous Games over Tree Architectures

We consider the task of controlling in a distributed way a Zielonka asynchronous automaton. Every process of a controller has access to its causal past to determine the next set of actions it proposes to play. An action can be played only if every process controlling this action proposes to play it. We consider reachability objectives: every process should reach its set of final states. We show that this control problem is decidable for tree architectures, where every process can communicate with its parent, its children, and with the environment. The complexity of our algorithm is l-fold exponential with l being the height of the tree representing the architecture. We show that this is unavoidable by showing that even for three processes the problem is EXPTIME-complete, and that it is non-elementary in general

Model-based Testing

This paper provides a comprehensive introduction to a framework for formal testing using labelled transition systems, based on an extension and reformulation of the ioco theory introduced by Tretmans. We introduce the underlying models needed to specify the requirements, and formalise the notion of test cases. We discuss conformance, and in particular the conformance relation ioco. For this relation we prove several interesting properties, and we provide algorithms to derive test cases (either in batches, or on the fly)

A test generation framework for quiescent real-time systems

We present an extension of Tretmans theory and algorithm for test generation for input-output transition systems to real-time systems. Our treatment is based on an operational interpretation of the notion of quiescence in the context of real-time behaviour. This gives rise to a family of implementation relations parameterized by observation durations for quiescence. We define a nondeterministic (parameterized) test generation algorithm that generates test cases that are sound with respect to the corresponding implementation relation. Also, the test generation is exhaustive in the sense that for each non-conforming implementation a test case can be generated that detects the non-conformance

Test generation from P systems using model checking

This paper presents some testing approaches based on model checking and using different testing criteria. First, test sets are built from different Kripke structure representations. Second, various rule coverage criteria for transitional, non-deterministic, cell-like P systems, are considered in order to generate adequate test sets. Rule based coverage criteria (simple rule coverage, context-dependent rule coverage and variants) are defined and, for each criterion, a set of LTL (Linear Temporal Logic) formulas is provided. A codification of a P system as a Kripke structure and the sets of LTL properties are used in test generation: for each criterion, test cases are obtained from the counterexamples of the associated LTL formulas, which are automatically generated from the Kripke structure codification of the P system. The method is illustrated with an implementation using a specific model checker, NuSMV. (C) 2010 Elsevier Inc. All rights reserved

Runtime Verification Based on Executable Models: On-the-Fly Matching of Timed Traces

Runtime verification is checking whether a system execution satisfies or violates a given correctness property. A procedure that automatically, and typically on the fly, verifies conformance of the system's behavior to the specified property is called a monitor. Nowadays, a variety of formalisms are used to express properties on observed behavior of computer systems, and a lot of methods have been proposed to construct monitors. However, it is a frequent situation when advanced formalisms and methods are not needed, because an executable model of the system is available. The original purpose and structure of the model are out of importance; rather what is required is that the system and its model have similar sets of interfaces. In this case, monitoring is carried out as follows. Two "black boxes", the system and its reference model, are executed in parallel and stimulated with the same input sequences; the monitor dynamically captures their output traces and tries to match them. The main problem is that a model is usually more abstract than the real system, both in terms of functionality and timing. Therefore, trace-to-trace matching is not straightforward and allows the system to produce events in different order or even miss some of them. The paper studies on-the-fly conformance relations for timed systems (i.e., systems whose inputs and outputs are distributed along the time axis). It also suggests a practice-oriented methodology for creating and configuring monitors for timed systems based on executable models. The methodology has been successfully applied to a number of industrial projects of simulation-based hardware verification.Comment: In Proceedings MBT 2013, arXiv:1303.037

Discovery and Selection of Certified Web Services Through Registry-Based Testing and Verification

Reliability and trust are fundamental prerequisites for the establishment of functional relationships among peers in a Collaborative Networked Organisation (CNO), especially in the context of Virtual Enterprises where economic benefits can be directly at stake. This paper presents a novel approach towards effective service discovery and selection that is no longer based on informal, ambiguous and potentially unreliable service descriptions, but on formal specifications that can be used to verify and certify the actual Web service implementations. We propose the use of Stream X-machines (SXMs) as a powerful modelling formalism for constructing the behavioural specification of a Web service, for performing verification through the generation of exhaustive test cases, and for performing validation through animation or model checking during service selection