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19
A Complete Transformational Toolkit for Compilers
 ACM Transactions on Programming Languages and Systems
, 1996
"... . 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 ..."
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Cited by 23 (9 self)
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. 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...
Using Induction and Rewriting to Verify and Complete Parameterized Specifications
 THEORETICAL COMPUTER SCIENCE
, 1996
"... 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 properti ..."
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Cited by 14 (8 self)
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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.
On finite alphabets and infinite bases: From ready pairs to possible worlds
 In Proceedings 7th Conference on Foundations of Software Science and Computation Structures (FOSSACS’04), Barcelona, LNCS 2987
, 2004
"... 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 ..."
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Cited by 9 (7 self)
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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
A finite basis for failure semantics
 In Proceedings 32nd Colloquium on Automata, Languages and Programming (ICALP’05), Lisbon, LNCS 3580
, 2005
"... Abstract. We present a finite ωcomplete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12]. 1 ..."
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Cited by 9 (7 self)
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Abstract. We present a finite ωcomplete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12]. 1
An omegacomplete Equational Specification of Interleaving
, 2000
"... 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 exten ..."
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Cited by 8 (6 self)
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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 61233008. 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...
On finite alphabets and infinite bases III: Simulation
 Proc. CONCUR’06, LNCS 4137
, 2006
"... 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 fin ..."
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Cited by 5 (1 self)
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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
A Complete Theory of Deterministic Event Structures
 Concur '95: Concurrency Theory, vol. 962 of LNCS
, 1995
"... . 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 ..."
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Cited by 3 (2 self)
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. 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...
Sufficient Completeness Verification for Conditional and Constrained TRS
 JOURNAL OF APPLIED LOGIC
, 2011
"... We present a procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. s ..."
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Cited by 1 (0 self)
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We present a procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our approach is integrated into a framework for inductive theorem proving 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 presented by an inference system which is shown sound and complete. A precondition of one inference of this system refers to a (undecidable) property called strong ground reducibility which is discharged to the above inductive theorem proving system. We have successfully applied our method to several examples, yielding readable proofs and, in case of negative answer, a counterexample suggesting how to complete the specification. Moreover, we show that it is a decision procedure when the TRS is unconditional but constrained, for an expressive class of constrained constructor axioms.
Automatic Verification of Sufficient Completeness for Specifications of Complex Data Structures
, 2005
"... 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 c ..."
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Cited by 1 (0 self)
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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.
Automating Sufficient Completeness Check for Conditional and Constrained TRS
 in &quot;Proceedings of the 20th International Workshop on Unification (UNIF’06
, 2006
"... Abstract. We present a procedure for checking sufficient completeness for conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures ..."
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Cited by 1 (0 self)
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Abstract. We present a procedure for checking sufficient completeness for conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our approach is integrated in a framework for inductive theorem proving based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms in normal form. The key technique used in the procedure is a generalized form of narrowing where, given a term, instead of unifying it with left members of rewrite rules, we instantiate it, at selected variables, following the productions of a constrained tree grammar, and test whether it can be rewritten. Our procedure is sound and complete and has been successfully applied to several examples, yielding very natural proofs and, in case of negative answer, a counter example suggesting how to complete the specification. Moreover, it is a decision procedure when the TRS is unconditional but constrained, for a large class of constrained constructor axioms.