Past Pushdown Timed Automata and Safety Verification

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Past Pushdown Timed Automata and Safety Verification

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by Zhe Dang , Tevfik Bultan , Oscar H. Ibarra , Richard A. Kemmerer

Venue:	Theoretical Computer Science
Citations:	6 - 0 self

BibTeX

@ARTICLE{Dang_pastpushdown,
    author = {Zhe Dang and Tevfik Bultan and Oscar H. Ibarra and Richard A. Kemmerer},
    title = {Past Pushdown Timed Automata and Safety Verification},
    journal = {Theoretical Computer Science},
    year = {},
    volume = {313},
    pages = {2004}
}

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Abstract

We consider past pushdown timed automata that are discrete pushdown timed automata with past formulas as enabling conditions. Using past formulas allows a past pushdown timed automaton to access the past values of the finite state variables in the automaton. We prove that the reachability (i.e., the set of reachable configurations from an initial configuration) of a past pushdown timed automaton can be accepted by a nondeterministic reversal-bounded counter machine augmented with a pushdown stack (i.e., a reversalbounded NPCM). By using the known fact that the emptiness problem for reversal-bounded NPCMs is decidable, we show that model-checking past pushdown timed automata against Presburger safety properties on discrete clocks and stack word counts is decidable. We also investigate the reachability problem for a class of transition systems under some fairness constraints in the form of generalized past formulas. Finally, we present an example ASTRAL specification to demonstrate the usefulness of the results.

Keyphrases

past pushdown past pushdown timed automaton safety verification past formula reversalbounded npcm pushdown stack fairness constraint reversal-bounded npcms stack word past value model-checking past pushdown reachable configuration initial configuration transition system generalized past formula emptiness problem presburger safety property finite state variable timed automaton reachability problem example astral specification nondeterministic reversal-bounded counter machine discrete clock

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