A Nonarchimedian Discretization for Timed Languages

We give a new discretization of behaviors of timed automata. In this discretization, 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 automata that equals the class of languages that are discretizations of timed automata, and show that their emptiness problem is decidable.