Decidability and Complexity Results for Timed Automata via Channel Machines

Abstract. This paper is concerned with the language inclusion problem for timed automata: given timed automata A and B, is every word accepted by B also accepted by A? Alur and Dill [5] showed that the language inclusion problem is decidable if A has no clocks and undecidable if A has two clocks (with no restriction on B). However, the status of the problem when A has one clock is not determined by [5]. In this paper we close this gap for timed automata over infinite words by showing that the one-clock language inclusion problem is undecidable. For timed automata over finite words, building on our earlier paper [19], we show that the one-clock language inclusion problem is decidable with nonprimitive recursive complexity. This reveals a surprising divergence between the theory of timed automata over finite words and over infinite words. Finally, we show that if ε-transitions or non-singular postconditions are allowed, then the one-clock language inclusion problem is undecidable ov...

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Parosh Aziz Abdulla, Johann Deneux, Joël Ouaknine, James Worrell
• Keywords: ICALP 2005, Language Inclusion Problem, One-clock Language Inclusion, Theoretical Computer Science, Timed Automata