Polynomials, Fragments of Temporal Logic and the Variety DA over Traces

Abstract

AbstractWe show that some language theoretic and logical characterizations of recognizable word languages whose syntactic monoid is in the variety DA also hold over traces. To this aim we give algebraic characterizations for the language operations of generating the polynomial closure and generating the unambiguous polynomial closure over traces.We also show that there exist natural fragments of local temporal logic that describe this class of languages corresponding to DA. All characterizations are known to hold for words.KeywordsTemporal LogicLanguage VarietySemigroup VarietyCommutative MonoidsAlgebraic CharacterizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.