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 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.