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| HAL: hal-00585835, version 5 |
| arXiv: 1104.3055 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2011-04-14) | v2 (2011-04-28) | v3 (2011-04-29) | v4 (2011-10-25) | v5 (2012-01-26) |
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| Deciding the Value 1 Problem of Probabilistic Leaktight Automata |
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| Nathanaël Fijalkow 1, 2Hugo Gimbert 3 |
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| (2011-04-13) |
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| The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability result holds even if the probabilistic automata have only one probabilistic transition. Our main contribution is to introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is shown decidable (and PSPACE-complete). We construct an algorithm based on the computation of a monoid abstracting the behaviours of the automaton, and rely on algebraic techniques developed by Simon for the correctness proof. The class of leaktight automata is decidable in PSPACE, subsumes all subclasses of probabilistic automata whose value 1 problem is known to be decidable (in particular deterministic automata), and is closed under two natural composition operators. |
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| 1: | Ecole Normale Supérieure de Cachan (ENS Cachan) |
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École normale supérieure de Cachan - ENS Cachan |
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| 2: | Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA) |
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CNRS : UMR7089 – Université Paris VII - Paris Diderot |
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| 3: | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
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CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II |
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| Subject | : | Computer Science/Computer Science and Game Theory Computer Science/Formal Languages and Automata Theory |
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| Probabilistic automata – Value 1 problem – Decidability |
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| hal-00585835, version 5 | |
| http://hal.archives-ouvertes.fr/hal-00585835 | |
| oai:hal.archives-ouvertes.fr:hal-00585835 | |
| From: Nathanaël Fijalkow | |
| Submitted on: Thursday, 26 January 2012 13:34:02 | |
| Updated on: Thursday, 26 January 2012 16:40:23 | |
