Decidable Problems for Unary PFAs

  • Rohit Chadha
  • Dileep Kini
  • Mahesh Viswanathan
Conference paper

DOI: 10.1007/978-3-319-10696-0_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8657)
Cite this paper as:
Chadha R., Kini D., Viswanathan M. (2014) Decidable Problems for Unary PFAs. In: Norman G., Sanders W. (eds) Quantitative Evaluation of Systems. QEST 2014. Lecture Notes in Computer Science, vol 8657. Springer, Cham

Abstract

Given a PFA A and a cut-point λ, the isolation problem asks if there is a bound ε > 0 such that the acceptance probability of every word is bounded away from λ by ε. In this paper we show that the isolation problem for PFAs with a unary input alphabet is (a) coNPcomplete, if the cut-point is 0 or 1, and (b) is in coNPRP and coNP-hard, if the cut-point is in (0, 1). We also show that the language containment problem, language equivalence problem, the emptiness problem and the universality problem for unary PFAs with limit isolated cut-points is in the fourth level of counting hierarchy C4P (and hence in PSPACE).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rohit Chadha
    • 1
  • Dileep Kini
    • 2
  • Mahesh Viswanathan
    • 2
  1. 1.University of MissouriUSA
  2. 2.University of Illinois at Urbana-ChampaignUSA

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