. In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIM t , under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starti...

In software engineering there is a growing demand for formal methods for the specification and validation of software systems. The formal development of a system might give rise to many proof obligations. We must prove the completeness of the specification and the validity of some inductive properties. In this framework, many provers have been developed. However they require much user interaction even for simple proof tasks. In this paper, we present new procedures to test sufficient completeness and to prove or disprove inductive properties automatically in parameterized conditional specifications. The method has been implemented in the prover SPIKE. Computer experiments illustrate the improvements in length and structure of proofs, due to parameterization. Moreover, SPIKE offers facilities to check and complete specifications.

We consider the process theory PA that includes an operation for parallel composition, based on the interleaving paradigm. We prove that the standard set of axioms of PA is not !-complete by providing a set of axioms that are valid in PA, but not derivable from the standard ones. We prove that extending PA with this set yields an !-complete specification, which is finite in a setting with finitely many actions. 1991 Mathematics Subject Classification: 68Q10; 68Q65; 68Q70 1991 ACM Computing Classification System: D.1.3; F.1.1; F.1.2 Keywords and Phrases: Process Algebra, Algebraic Specification, Interleaving, !-completeness. Note: Research supported by the Netherlands Organization for Scientific Research (NWO) under contract SION 612-33-008. Work carried out under project SEN 2.1 Process Specification and Analysis. 1. Introduction The interleaving paradigm consists of the assumption that two atomic actions cannot happen at the same time, so that concurrency reduces to nondetermini...

Abstract. We present a finite ω-complete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12]. 1

Abstract. We prove that if a finite alphabet of actions contains at least two elements, then the equational theory for the process algebra BCCSP modulo any semantics no coarser than readiness equivalence and no finer than possible worlds equivalence does not have a finite basis. This semantic range includes ready trace equivalence. 1

Abstract. This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a finite basis. In contrast, in the presence of an alphabet that is infinite or a singleton, the equational theory for simulation equivalence does have a finite basis. 1

. We present an !-complete algebra of a class of deterministic event structures, which are labelled prime event structures where the labelling function satisfies a certain distinctness condition. The operators of the algebra are summation, sequential composition and join. Each of these gives rise to a monoid; in addition a number of distributivity properties hold. Summation loosely corresponds to choice and join to parallel composition, with however some nonstandard aspects. The space of models is a complete partial order (in fact a complete lattice) in which all operators are continuous; hence minimal fixpoints can be defined inductively. Moreover, the submodel relation can be captured within the algebra by summation (x v y iff x + y = y); therefore the effect of fixpoints can be captured by an infinitary proof rule, yielding a complete proof system for recursively defined deterministic event structures. 1 Introduction It is generally recognised that prime event structures constitut...

Abstract. Chiba et al. (2005) proposed a framework of program transformation by template and automated verification of its correctness based on term rewriting. This paper describes a design and implementation of RAPT which implements this framework. RAPT transforms a term rewriting system according to a specified program transformation template. Presupposing the program transformation template is developed, the correctness of the transformation is automatically verified so that the transformation keeps the relationship between initial ground terms and their normal forms. 1

Abstract. We present a new procedure for testing sufficient completeness for conditional and constrained term rewriting systems in presence of constrained axioms for constructors. Such axioms allow to specify complex data structures like e.g. sets or sorted lists. Our approach is based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms in normal form. The procedure is sound and complete and has been successfully used for checking the sufficient completeness of several specifications where related former techniques fail.

We consider the process theory PA that includes an operation for parallel composition, based on the interleaving paradigm. We prove that the standard set of axioms of PA is not !-complete by providing a set of axioms that are valid in PA, but not derivable from the standard ones. We prove that extending PA with this set yields an !-complete specification, which is finite in a setting with finitely many actions. 2000 Mathematics Subject Classification: 68Q10; 68Q65; 68Q70 1998 ACM Computing Classification System: D.1.3; F.1.1; F.1.2 Keywords and Phrases: Process Algebra, Algebraic Specification, Interleaving, !-completeness. Note: Research supported by the Netherlands Organization for Scientific Research (NWO) under contract SION 612-33-008. Work carried out under project SEN 2.1 Process Specification and Analysis. 1. Introduction The interleaving paradigm consists of the assumption that two atomic actions cannot happen at the same time, so that concurrency reduces to nondetermini...