Decidable Problems for Unary PFAs
- 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
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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