One-Counter Automata with Counter Observability

Author Benedikt Bollig

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Benedikt Bollig

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Benedikt Bollig. One-Counter Automata with Counter Observability. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


In a one-counter automaton (OCA), one can produce a letter from some finite alphabet, increment and decrement the counter by one, or compare it with constants up to some threshold. It is well-known that universality and language inclusion for OCAs are undecidable. In this paper, we consider OCAs with counter observability: Whenever the automaton produces a letter, it outputs the current counter value along with it. Hence, its language is now a set of words over an infinite alphabet. We show that universality and inclusion for that model are PSPACE-complete, thus no harder than the corresponding problems for finite automata. In fact, by establishing a link with visibly one-counter automata, we show that OCAs with counter observability are effectively determinizable and closed under all boolean operations. Moreover, it turns out that they are expressively equivalent to strong automata, in which transitions are guarded by MSO formulas over the natural numbers with successor.
  • One-counter automata
  • inclusion checking
  • observability
  • visibly one- counter automata
  • strong automata


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