Decidability of infinite-state timed CCP processes and first-order LTL

The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing process specifications. A typical behavioral observation in ccp is the strongest postcondition ( sp). The ntcc sp denotes the set of all infinite...

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Published in:	Theoretical computer science Vol. 330; no. 3; pp. 577 - 607
Main Author:	Valencia, Frank D.
Format:	Journal Article Conference Proceeding
Language:	English
Published:	Amsterdam Elsevier B.V 09.02.2005 Elsevier
Subjects:	Algorithmics. Computability. Computer arithmetics Applied sciences Computer science; control theory; systems Decidability Exact sciences and technology First-order LTL General logic Infinite-state systems Logic and foundations Mathematical logic, foundations, set theory Mathematics Process calculi Programming theory Sciences and techniques of general use Temporal logic Theoretical computing Timed concurrent constraint programming Timed concurrent constraint programming First-order LTL Decidability Temporal logic Infinite-state systems Process calculi Concurrent constraint programming Linear logic Computer theory First order logic Concurrency Verification Infinite system Timed system Satisfiability Process calculus
ISSN:	0304-3975, 1879-2294
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Abstract	The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing process specifications. A typical behavioral observation in ccp is the strongest postcondition ( sp). The ntcc sp denotes the set of all infinite output sequences that a given process can exhibit. The verification problem is then whether the sequences in the sp of a given process satisfy a given ntcc LTL formula. This paper presents new positive decidability results for timed ccp as well as for LTL. In particular, we shall prove that the following problems are decidable: (1) the sp equivalence for the so-called locally-independent ntcc fragment; unlike other fragments for which similar results have been published, this fragment can specify infinite-state systems, (2) verification for locally-independent processes and negation-free first-order formulae of the ntcc LTL, (3) implication for such formulae, (4) Satisfiability for a first-order fragment of Manna and Pnueli's LTL. The purpose of the last result is to illustrate the applicability of ccp to well-established formalisms for concurrency.
AbstractList	The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing process specifications. A typical behavioral observation in ccp is the strongest postcondition ( sp). The ntcc sp denotes the set of all infinite output sequences that a given process can exhibit. The verification problem is then whether the sequences in the sp of a given process satisfy a given ntcc LTL formula. This paper presents new positive decidability results for timed ccp as well as for LTL. In particular, we shall prove that the following problems are decidable: (1) the sp equivalence for the so-called locally-independent ntcc fragment; unlike other fragments for which similar results have been published, this fragment can specify infinite-state systems, (2) verification for locally-independent processes and negation-free first-order formulae of the ntcc LTL, (3) implication for such formulae, (4) Satisfiability for a first-order fragment of Manna and Pnueli's LTL. The purpose of the last result is to illustrate the applicability of ccp to well-established formalisms for concurrency. The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing process specifications. A typical behavioral observation in ccp is the strongest postcondition (sp). The ntcc sp denotes the set of all infinite output sequences that a given process can exhibit. The verification problem is then whether the sequences in the sp of a given process satisfy a given ntcc LTL formula. This paper presents new positive decidability results for timed ccp as well as for LTL. In particular, we shall prove that the following problems are decidable: (1) the sp equivalence for the so-called locally-independent ntcc fragment; unlike other fragments for which similar results have been published, this fragment can specify infinite-state systems, (2) verification for locally-independent processes and negation-free first-order formulae of the ntcc LTL, (3) implication for such formulae, (4) Satisfiability for a first-order fragment of Manna and Pnueli's LTL. The purpose of the last result is to illustrate the applicability of ccp to well-established formalisms for concurrency.
Author	Valencia, Frank D.
Author_xml	– sequence: 1 givenname: Frank D. surname: Valencia fullname: Valencia, Frank D. email: frank.valencia@lix.polytechnique.fr organization: CNRS, LIX École Polytechnique de Paris, Rue de Saclay, 91128 Palaiseau Cedex, France
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Keywords	Timed concurrent constraint programming First-order LTL Decidability Temporal logic Infinite-state systems Process calculi Concurrent constraint programming Linear logic Computer theory First order logic Concurrency Verification Infinite system Timed system Satisfiability Process calculus
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Snippet	The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing... The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing...
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SubjectTerms	Algorithmics. Computability. Computer arithmetics Applied sciences Computer science; control theory; systems Decidability Exact sciences and technology First-order LTL General logic Infinite-state systems Logic and foundations Mathematical logic, foundations, set theory Mathematics Process calculi Programming theory Sciences and techniques of general use Temporal logic Theoretical computing Timed concurrent constraint programming
Title	Decidability of infinite-state timed CCP processes and first-order LTL
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