Folk theorems on the determinization and minimization of timed automata

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Folk theorems on the determinization and minimization of timed automata (2006)

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by Stavros Tripakis

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@MISC{Tripakis06folktheorems,
    author = {Stavros Tripakis},
    title = {Folk theorems on the determinization and minimization of timed automata},
    year = {2006}
}

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Abstract

Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable. Minimizing the “resources” of a TA (number of clocks or size of constants) are also unsolvable problems. In this paper we provide simple undecidability proofs using a “constructive” version of the problems where we require not just a yes/no answer, but also a “witness”. Proofs are then simple reductions from the universality problem. Recent work of Finkel shows that the corresponding decision problems are also undecidable [1].

Keyphrases

timed automaton formal modeling timed system simple reduction formal method unsolvable problem key word corresponding decision problem constructive version simple undecidability proof natural question universality problem specification language recent work

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