A Perfect Class of Context-Sensitive Timed Languages

Abstract

Perfect languages--a term coined by Esparza, Ganty, and Majumdar--are the classes of languages that are closed under Boolean operations and enjoy decidable emptiness problem. Perfect languages form the basis for decidable automata-theoretic model-checking for the respective class of models. Regular languages and visibly pushdown languages are paradigmatic examples of perfect languages. Alur and Dill initiated the language-theoretic study of timed languages and introduced timed automata capturing a timed analog of regular languages. However, unlike their untimed counterparts, timed regular languages are not perfect. Alur, Fix, and Henzinger later discovered a perfect subclass of timed languages recognized by event-clock automata. Since then, a number of perfect subclasses of timed context-free languages, such as event-clock visibly pushdown languages, have been proposed. There exist examples of perfect languages even beyond context-free languages:--La Torre, Madhusudan, and Parlato characterized first perfect class of context-sensitive languages via multistack visibly pushdown automata with an explicit bound on number of stages where in each stage at most one stack is used. In this paper we extend their work for timed languages by characterizing a perfect subclass of timed context-sensitive languages called dense-time multistack visibly pushdown languages and provide a logical characterization for this class of timed languages.