Synchronizing Words for Weighted and Timed Automata

Authors Laurent Doyen, Line Juhl, Kim G. Larsen, Nicolas Markey, Mahsa Shirmohammadi

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Laurent Doyen
Line Juhl
Kim G. Larsen
Nicolas Markey
Mahsa Shirmohammadi

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Laurent Doyen, Line Juhl, Kim G. Larsen, Nicolas Markey, and Mahsa Shirmohammadi. Synchronizing Words for Weighted and Timed Automata. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 121-132, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


The problem of synchronizing automata is concerned with the existence of a word that sends all states of the automaton to one and the same state. This problem has classically been studied for complete deterministic finite automata, with the existence problem being NLOGSPACE-complete. In this paper we consider synchronizing-word problems for weighted and timed automata. We consider the synchronization problem in several variants and combinations of these, including deterministic and non-deterministic timed and weighted automata, synchronization to unique location with possibly different clock valuations or accumulated weights, as well as synchronization with a safety condition forbidding the automaton to visit states outside a safety-set during synchronization (e.g. energy constraints). For deterministic weighted automata, the synchronization problem is proven PSPACE-complete under energy constraints, and in 3-EXPSPACE under general safety constraints. For timed automata the synchronization problems are shown to be PSPACE-complete in the deterministic case, and undecidable in the non-deterministic case.
  • Synchronizing words
  • weighted automata
  • timed automata


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