Axiomatizing GSOS with Predicates

Abstract

In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.

Exploiting Algebraic Laws to Improve Mechanized Axiomatizations

“…the study of algorithms for the automatic generation of ground-complete axiomatizations for bisimilarity from SOS specifications (see, for instance, [3,5,6,18,22,30,46]) and the development of rule formats guaranteeing the validity of algebraic laws, such as those presented in [4,8,9,15,26,37]. More specifically, we have presented a rule format for commutativity that refines the one offered in [37] in that it allows one to consider various sets of commutative arguments, and we have used the information provided by that rule format to refine the algorithm for the automatic generation of ground-complete axiomatizations for bisimilarity from [5].…”

“…This approach is also at the heart of the algorithm proposed in [5] for the automatic generation of finite, equational, ground-complete axiomatizations for bisimilarity over language specifications in the GSOS format. A variation on that algorithm for GSOS language specifications with termination has been presented in [18]; see [6] for an extension of the algorithm from [5] dealing with arbitrary predicates. In [46], Ulidowski has instead offered algorithms for the automatic generation of finite axiom systems for the testing preorder over de Simone process languages [45].…”

Meta SOS - A Maude Based SOS Meta-Theory Framework

“…As an alternative method for reasoning about strong bisimilarity, Meta SOS includes a component for generating axiom schemas that are sound and ground-complete modulo bisimilarity. There has been a notable amount of effort put into developing algorithms for axiomatizations for GSOS-like systems [2,3,11], yet all involve several transformations of the original system before deriving the axioms. After implementing one such algorithm in the tool PREG Axiomatizer [4], a simpler method was developed in [18].…”

PREG Axiomatizer – A Ground Bisimilarity Checker for GSOS with Predicates

“…Proving that two process terms are related by some notion of behavioural equivalence is at the heart of the equivalence-checking approach to verification. In this paper we introduce a tool named PREG Axiomatizer 1 that tackles this problem focusing on ground (i.e., fully specified) terms built using operations defined using the preg format, a pr edicates extension of the GSOS format presented in [3]. GSOS [8] is a restricted, yet powerful, way of defining Structural Operational Semantics (SOS) for programming and specification languages in the style introduced by Plotkin in [14].…”

“…GSOS [8] is a restricted, yet powerful, way of defining Structural Operational Semantics (SOS) for programming and specification languages in the style introduced by Plotkin in [14]. We refer the reader to [3] for the detailed description and intuition behind the preg rule format and the considered notion of behavioural equivalence, which is a natural extension to predicates of the classic strong bisimulation equivalence.…”