Proving termination with multiset orderings

Dershowitz, Nachum; Manna, Zohar

doi:10.1145/359138.359142

Cited by 422 publications

(170 citation statements)

References 3 publications

(1 reference statement)

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“…5 Then the assertion checking problem for programs of size n, which are specified using nodes (a)-(d) and the language of T, can be solved in time O(n 4 TUnif(n 2 )).…”

Section: Theorem 1 Let T Be a Strict Unitary Theory Suppose That Tumentioning

confidence: 99%

“…Since each ψ i is a substitution mapping, this measure is a multiset on natural numbers. We compare two measures using a multiset extension of the ordering > on natural numbers [5].…”

Section: E Proof Of Lemmamentioning

confidence: 99%

“…Since the multiset extension of a well-founded ordering is wellfounded [5], the measure cannot infinitely decrease. Hence, the chain C is finite.…”

Section: E Proof Of Lemmamentioning

confidence: 99%

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Assertion Checking Unified

Gulwani

Tiwari

2007

Lecture Notes in Computer Science

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This paper establishes an interesting connection between assertion checking in programs and unification in the theory underlying the program expressions. Using this connection, we describe how unification algorithms from theorem proving can be used to perform backward analysis over programs for assertion checking. Interestingly enough, this connection also helps prove hardness results for assertion checking for classes of program abstractions. In particular, we show (a) Assertion checking is PTIME for programs with nondeterministic conditionals that use expressions from a strict unitary theory. (b) Assertion checking is coNP-hard for programs with nondeterministic conditionals that use expressions from a bitary theory. (c) Assertion checking is decidable for programs with disequality guards that use expressions from a convex finitary theory. (d) Summary computation for interprocedural analysis can be performed using backward analysis, enabled with unification, on generic assertions. This helps generalize result (a) to interprocedural analysis. These results generalize several recently published results using a uniform framework. They also provide several new results, and partially solve the long standing open problem of interprocedural global value numbering. In essence, they provide new techniques for backward analysis of programs based on novel integration of theorem proving technology in program analysis.

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“…5 Then the assertion checking problem for programs of size n, which are specified using nodes (a)-(d) and the language of T, can be solved in time O(n 4 TUnif(n 2 )).…”

Section: Theorem 1 Let T Be a Strict Unitary Theory Suppose That Tumentioning

confidence: 99%

“…Since each ψ i is a substitution mapping, this measure is a multiset on natural numbers. We compare two measures using a multiset extension of the ordering > on natural numbers [5].…”

Section: E Proof Of Lemmamentioning

confidence: 99%

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Assertion Checking Unified

Gulwani

Tiwari

2007

Lecture Notes in Computer Science

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“…The relation satisfies the ascending chain condition [21]. The set of non-negative reals is denoted by R + .…”

Section: Preliminariesmentioning

confidence: 99%

Precise Widening Operators for Convex Polyhedra

et al. 2003

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Abstract. Convex polyhedra constitute the most used abstract domain among those capturing numerical relational information. Since the domain of convex polyhedra admits infinite ascending chains, it has to be used in conjunction with appropriate mechanisms for enforcing and accelerating convergence of the fixpoint computation. Widening operators provide a simple and general characterization for such mechanisms. For the domain of convex polyhedra, the original widening operator proposed by Cousot and Halbwachs amply deserves the name of standard widening since most analysis and verification tools that employ convex polyhedra also employ that operator. Nonetheless, there is an unfulfilled demand for more precise widening operators. In this paper, after a formal introduction to the standard widening where we clarify some aspects that are often overlooked, we embark on the challenging task of improving on it. We present a framework for the systematic definition of new and precise widening operators for convex polyhedra. The framework is then instantiated so as to obtain a new widening operator that combines several heuristics and uses the standard widening as a last resort so that it is never less precise. A preliminary experimental evaluation has yielded promising results.

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“…As far as programming languages are concerned, termination means that computation in programs will eventually stop. In computer science, termination has been extensively investigated in term rewriting systems [DM79,DH95] and λ-calculi [Gan80,Mit96], where strong normalization is a more commonly used synonym.…”

Section: Introductionmentioning

confidence: 99%

Mobile Processes and Termination

Demangeon

Hirschkoff

Sangiorgi

2009

Semantics and Algebraic Specification

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Abstract. This paper surveys some recent works on the study of termination in a concurrent setting. Processes are π-calculus processes, on which type systems are imposed that ensure termination of the process computations. Two approaches are exposed. The rst one draws on the method of logical relations, which has been extensively used in the analysis of sequential languages. The second approach exploits notions from term rewriting.

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Proving termination with multiset orderings

Cited by 422 publications

References 3 publications

Assertion Checking Unified

Assertion Checking Unified

Precise Widening Operators for Convex Polyhedra

Mobile Processes and Termination

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