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Synchronization of Deterministic Visibly Push-Down Automata

Authors Henning Fernau , Petra Wolf

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Author Details

Henning Fernau
  • Universität Trier, Fachbereich IV, Informatikwissenschaften, Germany
Petra Wolf
  • Universität Trier, Fachbereich IV, Informatikwissenschaften, Germany

Funding

  • Wolf, Petra: DFG project FE 560/9-1.

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Henning Fernau and Petra Wolf. Synchronization of Deterministic Visibly Push-Down Automata. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSTTCS.2020.45

Abstract

We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same state but also fulfills some conditions on the stack content of each run after reading w. We consider three types of these stack constraints: after reading w, the stack (1) is empty in each run, (2) contains the same sequence of stack symbols in each run, or (3) contains an arbitrary sequence which is independent of the other runs. We show that in contrast to general deterministic push-down automata, it is decidable for deterministic visibly push-down automata whether there exists a synchronizing word with each of these stack constraints, more precisely, the problems are in EXPTIME. Under the constraint (1), the problem is even in P. For the sub-classes of deterministic very visibly push-down automata, the problem is in P for all three types of constraints. We further study variants of the synchronization problem where the number of turns in the stack height behavior caused by a synchronizing word is restricted, as well as the problem of synchronizing a variant of a sequential transducer, which shows some visibly behavior, by a word that synchronizes the states and produces the same output on all runs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Automata extensions
  • Theory of computation → Transducers
Keywords
  • Synchronizing word
  • Deterministic visibly push-down automata
  • Deterministc finite atuomata
  • Finite-turn push-down automata
  • Sequential transducer
  • Computational complexity

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