A Nonarchimedian Discretization for Timed Languages

Abstract

We give a discretization of behaviors of timed automata, in which timed languages are represented as sets of words containing action symbols, a clock tick symbol 1, and two delay symbols δ⁻ (negative delay) and δ⁺ (positive delay). Unlike the region construction, our discretization commutes with intersection. We show that discretizations of timed automata are, in general, context-sensitive languages over Σ ∪ {1, δ⁺, δ⁻}, and give a class of counter automata that accepts exactly the class of languages that are discretizations of timed automata, and show that its emptiness problem is decidable.