Abstract

. A specification formalism for reactive systems defines a class of !-languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability (nonemptiness) problem. There are two important, robust classes of !-languages that are definable by fully decidable formalisms. The !-regular languages are definable by finite automata, or equivalently, by the Sequential Calculus. The counter-free !-regular languages are definable by temporal logic, or equivalently, by the first-order fragment of the Sequential Calculus. The gap between both classes can be closed by finite counting (using automata connectives), or equivalently, by projection (existential second-order quantification over letters). A specification formalism for real-time systems defines a class of timed !-languages, whose letters have real-numbered time stamps. Two popular ways of specifying timing constraints rely on the use of clocks, and on the use...

Citations