2011
DOI: 10.1007/978-3-642-22993-0_27
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Infinite Synchronizing Words for Probabilistic Automata

Abstract: Abstract. Probabilistic automata are finite-state automata where the transitions are chosen according to fixed probability distributions. We consider a semantics where on an input word the automaton produces a sequence of probability distributions over states. An infinite word is accepted if the produced sequence is synchronizing, i.e. the sequence of the highest probability in the distributions tends to 1. We show that this semantics generalizes the classical notion of synchronizing words for deterministic au… Show more

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Cited by 15 publications
(22 citation statements)
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“…ity distributions accumulate all the probability mass in a single state, or in a given set of states. They generalize synchronizing properties of finite automata [63,26]. Formally, for 0 ≤ p ≤ 1 let a probability distribution d : Q → [0, 1] be p-synchronized if it assigns probability at least p to some state.…”
Section: Introductionmentioning
confidence: 96%
“…ity distributions accumulate all the probability mass in a single state, or in a given set of states. They generalize synchronizing properties of finite automata [63,26]. Formally, for 0 ≤ p ≤ 1 let a probability distribution d : Q → [0, 1] be p-synchronized if it assigns probability at least p to some state.…”
Section: Introductionmentioning
confidence: 96%
“…This conjecture states that the length of a shortest synchronizing word for a DFA with n states is at most (n − 1) 2 . Synchronizing words moreover have applications in planning, control of discrete event systems, biocomputing, and robotics [3,30,15]. More recently the notion has been generalized from automata to games [21,28,20] and infinite-state systems [14,9], with applications to modelling complex systems such as distributed data networks or real-time embedded systems.…”
Section: Introductionmentioning
confidence: 99%
“…MDPs with the same semantics as we use have been compared with PFAs for the qualitative problem called almost-sure synchronization. This problem has been shown to be decidable in PSPACE for MDPs [13], while it is undecidable for PFAs [12], using a simple reduction to the undecidable reachability for PFAs. Recently, qualitative questions on PFAs presented as discrete (nonfluid) populations have been proved decidable, using results on parametric control [7].…”
Section: Introductionmentioning
confidence: 99%