Decidability and Complexity Results for Timed Automata via Channel Machines [chapter]

Parosh Aziz Abdulla, Johann Deneux, Joël Ouaknine, James Worrell
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
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
more &raquo; ... anguage 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 over both finite and infinite words.
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