Carlos Gregorio-Rodríguez

Denotational Semantics for Probabilistic Refusal Testing

Abstract In this paper, refusal testing ideas are applied to define a testing semantics for a probabilistic process algebra. A testing equivalence is defined by combining the greater discriminatory power of refusal testing and a simple treatment of the probabilistic component of processes. This testing equivalence is characterized by two fully abstract denotational semantics. The first of them is based on probabilistic refusal traces. These traces condense the set of tests that a process passes with probability greater than zero. The second one is based on a probabilistic extension of classical acceptance trees, where semantic processes can be viewed as (syntactic) normal forms. We would like to thank the anonymous referees of this paper for their valuable comments, specially one who pointed out a mistake in a previous version.

Input-Output Conformance Simulation (iocos) for Model Based Testing

A new model based testing theory built on simulation semantics is presented. At the core of this theory there is an input-output conformance simulation relation (iocos). As a branching semantics iocos can naturally distinguish the context of local choices. We show iocos to be a finer relation than the classic ioco conformance relation. It turns out that iocos is a transitive relation and therefore it can be used both as a conformance relation and a refinement preorder. An alternative characterisation of iocos is provided in terms of testing semantics. Finally we present an algorithm that produces a test suite for any specification. The resulting test suite is sound and exhaustive for the given specification with respect to iocos.

Axiomatizing weak ready simulation semantics over BCCSP

Ready simulation has proven to be one of the most significant semantics in process theory. It is at the heart of a number of general results that pave the way to a comprehensive understanding of the spectrum of process semantics. Since its original definition by Bloom, Istrail and Meyer in 1995, several authors have proposed generalizations of ready simulation to deal with internal actions. However, a thorough study of the (non-)existence of finite (in)equational bases for weak ready simulation semantics is still missing in the literature. This paper presents a complete account of positive and negative results on the axiomatizability of weak ready simulation semantics over the language BCCSP. In addition, this study offers a thorough analysis of the axiomatizability properties of weak simulation semantics.

Extending mCRL2 with ready simulation and iocos input-output conformance simulation

The mCRL2 toolset is a leading tool for the use of formal methods. It integrates modelling, analysis and verification methods and techniques strongly based on up to date research results and algorithms. In this paper we describe an extension of mCRL2 that integrates two branching semantics initially not present at the original bundle, the classic ready simulation and the newer input-output conformance simulation (iocos). We use systems from the Very Large Transition Systems (VLTS) benchmark, with states ranging from 103 to 106, to check the implementations and to compare the results with the simpler simulation semantics already included in mCRL2. The results show the feasibility and applicability of the ready and iocos semantics introduced in mCRL2. The good results, in general, highlights the interest of the family of branching semantics for their use in formal methods.

Unifying the Linear Time-Branching Time Spectrum of Process Semantics

Van Glabbeeks linear time-branching time spectrum is one of the most relevant work on comparative study on process semantics, in which semantics are partially ordered by their discrimination power. In this paper we bring forward a refinement of this classification and show how the process semantics can be dealt with in a uniform way: based on the very natural concept of constrained simulation we show how we can classify the spectrum in layers; for the families lying in the same layer we show how to obtain in a generic way equational, observational, logical and operational characterizations; relations among layers are also very natural and differences just stem from the constraint imposed on the simulations that rule the layers. Our methodology also shows how to achieve a uniform treatment of semantic preorders and equivalences.

Effectiveness for Input Output Conformance Simulation iocos̱

In this paper we continue the study of the input-output conformance simulation (ioco s). In particular, we focus on implementation aspects to show that ioco s is indeed an interesting semantic relation for formal methods. We address two complementary issues: a) In the context of model based testing (MBT) we present an online, also called on-the-fly, testing algorithm that checks whether an implementation conforms a given specification. Online testing combines test generation and execution and avoids the generation of the complete test suite for the specification. We prove both soundness and completeness of the online algorithm with respect to the ioco s relation. b) In the context of formal verification and model checking minimisation a key issue is to efficiently compute the considered semantic relations; we show how the coinductive flavour of our conformance relation ioco s makes it appropriate to be cast into an instance of the Generalised Coarsest Partition Problem (GCPP) and thus it can be efficiently computed.

Axiomatizing weak simulation semantics over BCCSP

This paper is devoted to the study of the (in)equational theory of the largest (pre)congruences over the language BCCSP induced by variations on the classic simulation preorder and equivalence that abstract from internal steps in process behaviours. In particular, the article focuses on the (pre)congruences associated with the weak simulation, the weak complete simulation and the weak ready simulation preorders. We present results on the (non)existence of finite (ground-)complete (in)equational axiomatizations for each of these behavioural semantics. The axiomatization of those semantics using conditional equations is also discussed in some detail.

Complete and ready simulation semantics are not finitely based over BCCSP, even with a singleton alphabet

This note shows that the complete and the ready simulation preorders do not have a finite inequational basis over the language BCCSP when the set of actions is a singleton. Moreover, the equivalences induced by those preorders do not have a finite (in)equational axiomatization either. These results are in contrast with a claim of finite axiomatizability for those semantics in the literature, which was based on the erroneous assumption that they coincide with complete trace semantics in the presence of a singleton set of actions.

Logical Characterisations and Compositionality of Input-Output Conformance Simulation

Input-output conformance simulation Open image in new window has been proposed by Gregorio-Rodriguez, Llana and Martinez-Torres as a simulation-based behavioural preorder underlying model-based testing. This relation is inspired by Tretman’s classic Open image in new window relation, but has better worst-case complexity than Open image in new window and supports stepwise refinement. The goal of this paper is to develop the theory of Open image in new window by studying logical characterisations of this relation and its compositionality. More specifically, this article presents characterisations of Open image in new window in terms of modal logics and compares them with an existing logical characterisation for Open image in new window proposed by Beohar and Mousavi. A precongruence rule format for Open image in new window and a rule format ensuring that operations take quiescence properly into account are also given. Both rule formats are based on the GSOS format by Bloom, Istrail and Meyer.

An axiomatic semantics for iocos_ conformance relation

Abstract ioco s _ is a preorder on the states of a transition system with input and output actions. Its aim is to establish a new branching-time conformance framework. In this paper, we continue the study of ioco s _ . We consider an algebraic language (BCCS) with input and output actions. Then we define a structured operational semantics for the terms in BCCS. We prove that this operational semantics faithfully models the quiescent behaviour assumed by the conformance semantics. To model the test execution on systems, a language to express tests is described and the formal interaction between BCCS process terms and tests is defined. Then, we show that ioco s _ has a testing characterisation and an algorithm that produces a test suite for a given specification. The test suite produced by this algorithm discriminates exactly the implementations that are ioco s _ -conforming with that specification. The issue of effectively computing the ioco s _ relation is also addressed, we prove how the branching nature of ioco s _ makes it suitable to be solved as an instance of the Generalised Coarsest Partition Problem (GCCP). Finally, we describe a sound and ground-complete axiomatisation of ioco s _ for the syntactic terms in BCCS. That is, we propose a set of inequations characterising ioco s _ .