Alternating Timed Automata

TL;DR

This paper introduces alternating timed automata with one clock, demonstrating their decidable emptiness problem over finite words, and explores extensions leading to undecidability results for infinite words.

Contribution

It proposes a new class of alternating timed automata with decidable emptiness and analyzes their computational complexity and extensions.

Findings

Decidability of emptiness for automata with one clock over finite words

Non-primitive recursive complexity of the emptiness problem

Undecidability results for extensions and infinite words

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 which 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 non-primitive 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.