Existence of reduction hierarchies

Orna Kupferman, Robert P. Kurshan, Mihalis Yannakakis

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

In the automata-theoretic approach to verification, we model programs and specifications by automata on infinite words. Correctness of a program with respect to a specification can then be reduced to the language-containment problem. In a concurrent setting, the program is typically a parallel composition of many coordinating processes, and the language-containment problem that corresponds to verification is (formula presented), where P1, P2, … Pn are automata that model the underlying coordinating processes, and T is the task they should perform. In 1994, Kurshan suggested the heuristic of Reduction Hierarchies for circumventing the exponential blow-up introduced by conventional methods that solve the problem (†). In the reduction hierarchy heuristic, we solve the problem (†) by solving a sequence of easier problems, which involve only automata of tractable sizes. Complexity-theoretic conjectures (NP ≠ PSPACE) imply that there are settings in which the heuristic cannot circumvent the exponential blow-up. In this paper, we demonstrate the strength of the heuristic, study its properties, characterize settings in which it performs effectively, and suggest a method for searching for reduction hierarchies. In particular, we prove, independently of the NP ≠ PSPACE question, that reduction hierarchies of tractable sizes do not always exist.

Original languageAmerican English
Title of host publicationComputer Science Logic - 11th International Workshop, CSL 1997 Annual Conference of the EACSL, Selected Papers
EditorsMogens Nielsen, Wolfgang Thomas
PublisherSpringer Verlag
Pages327-340
Number of pages14
ISBN (Print)3540645705, 9783540645702
DOIs
StatePublished - 1998
Externally publishedYes
Event11th International Workshop on Computer Science Logic, CSL 1997, Annual Conference of the European Association for Computer Science, EACSL 1997 - Aarhus, Denmark
Duration: 23 Aug 199729 Aug 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1414
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Workshop on Computer Science Logic, CSL 1997, Annual Conference of the European Association for Computer Science, EACSL 1997
Country/TerritoryDenmark
CityAarhus
Period23/08/9729/08/97

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

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