Abstract
We consider various decision problems for probabilistic finite automata (PFA)s with isolated cut-points. Recall that a cut-point x is said to be isolated for a PFA if the acceptance probability of all finite strings is bounded away from x. First we establish the exact level of undecidability of the problem of determining if a cut-point is isolated; we show this problem to be \(\mathbf{\Sigma^0_2}\)-complete. Next we introduce a new class of PFAs called eventually weakly ergodic PFAs that generalize ergodic and weakly ergodic PFAs. We show that the emptiness and universality problem for these PFAs is decidable provided the cut-point is isolated.
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Chadha, R., Sistla, A.P., Viswanathan, M. (2013). Probabilistic Automata with Isolated Cut-Points. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_24
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DOI: https://doi.org/10.1007/978-3-642-40313-2_24
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