RECOGNIZABLE AND LOGICALLY DEFINABLE LANGUAGES OF INFINITE COMPUTATIONS IN CONCURRENT AUTOMATA

Abstract

Automata with concurrency relations [Formula: see text], which occurred in formal verification methods of concurrent programs, are labeled transition systems with a collection of binary relations describing when two actions in a given state of the automaton can happen independently of each other. The concurrency monoid M($\mathcal{A}$) comprises all finite computation sequences of [Formula: see text], modulo a canonical congruence induced by the concurrency relations, with composition as monoid operation. Then M∞($\mathcal{A}$) denotes the set of all infinite products in M($\mathcal{A}$); its elements can be represented by labeled partially ordered sets. Under suitable assumptions on [Formula: see text], we show that a language L in M∞($\mathcal{A}$) is recognizable iff it is definable by a formula of monadic second order logic, and that it is recognizable iff it can be constructed from recognizable languages in M($\mathcal{A}$) using co-rational expressions. This generalizes various recent results in trace theory.