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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Bibliographic Details
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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Summary: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.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2004.10.009