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Concurrent Dynamic Algebra

Concurrent Dynamic Algebra Concurrent Dynamic Algebra HITOSHI FURUSAWA, Kagoshima University, Japan GEORG STRUTH, University of Sheffield, UK We reconstruct Peleg's concurrent dynamic logic in the context of modal Kleene algebras. We explore the algebraic structure of its multirelational semantics and develop an axiomatization of concurrent dynamic algebras from that basis. In this context, sequential composition is not associative. It interacts with parallel composition through a weak distributivity law. The modal operators of concurrent dynamic algebra are obtained from abstract axioms for domain and antidomain operators; the Kleene star is modelled as a least fixpoint. Algebraic variants of Peleg's axioms are shown to be derivable in these algebras, and their soundness is proved relative to the multirelational model. Additional results include iteration principles for the Kleene star and a refutation of variants of Segerberg's axiom in the multirelational setting. The most important results have been verified formally with Isabelle/HOL. Categories and Subject Descriptors: F.1.2 [Computation by Abstract Devices]: Modes of Computation-- Alternation and nondeterminism; Parallelism and concurrency; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs--Logics of programs; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming Languages--Algebraic approaches to semantics; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2015 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2785967
Publisher site
See Article on Publisher Site

Abstract

Concurrent Dynamic Algebra HITOSHI FURUSAWA, Kagoshima University, Japan GEORG STRUTH, University of Sheffield, UK We reconstruct Peleg's concurrent dynamic logic in the context of modal Kleene algebras. We explore the algebraic structure of its multirelational semantics and develop an axiomatization of concurrent dynamic algebras from that basis. In this context, sequential composition is not associative. It interacts with parallel composition through a weak distributivity law. The modal operators of concurrent dynamic algebra are obtained from abstract axioms for domain and antidomain operators; the Kleene star is modelled as a least fixpoint. Algebraic variants of Peleg's axioms are shown to be derivable in these algebras, and their soundness is proved relative to the multirelational model. Additional results include iteration principles for the Kleene star and a refutation of variants of Segerberg's axiom in the multirelational setting. The most important results have been verified formally with Isabelle/HOL. Categories and Subject Descriptors: F.1.2 [Computation by Abstract Devices]: Modes of Computation-- Alternation and nondeterminism; Parallelism and concurrency; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs--Logics of programs; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming Languages--Algebraic approaches to semantics; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Aug 17, 2015

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