Alternating timed automata

Abstract

A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages that is closed under boolean operations and which has an effective presentation. We prove that the complexity of the emptiness problem for alternating timed automata with one clock is nonprimitive recursive. The proof gives also the same lower bound for the universality problem for nondeterministic timed automata with one clock. We investigate extension of the model with epsilon-transitions and prove that emptiness is undecidable. Over infinite words, we show undecidability of the universality problem.

Towards nominal computation

“…However, the definition can also be interpreted in the classical symmetry, in which case we get standard alternating automata without data values [4,5]. Finally, the definition can also be interpreted in the total order symmetry, in which case we get alternating automata on ordered data values, a model that has been studied in [8] and closely related to one-clock timed automata [12,13,15]. In all these cases (equality, classical, total order), the same program in Nλ decides emptiness for alternating automata with one register; the program only needs to be fed into different interpreters (each symmetry defines a different interpreter).…”

“…Emptiness is known to be undecidable for k ≥ 2, and decidable for k = 1. In the latter case, the complexity of the problem is very high: it is not bounded by any primitive recursive function [1,12].…”

LTL with the Freeze Quantifier and Register Automata

“…The definition of register automata above is suited to the uses in this paper, and has similarities with definitions in [6,5,16,23]. Thus, it differs in some technical details from the definition of register automata in [14,26,21].…”

Computing Blocker Sets for the Regular Post Embedding Problem

“…Thus, although it is decidable, PEP reg is not primitive-recursive, and not even multiply-recursive (see [3] and the references therein). Finally, PEP reg is an abstract problem that is inter-reducible with a growing list of decidable problems having the same F ω ω complexity: metric temporal logic [4], alternating one-clock timed automata [5,6], leftist grammars [7,8], products of modal logics [9], etc.…”