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arXiv · 1506.02483

On the Hardness of PCTL Satisfiability

Souymodip Chakraborty·Joost-Pieter Katoen
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Abstract

This paper shows that the satisfiability problem for probabilistic CTL (PCTL, for short) is undecidable. By a reduction from $1\frac{1}{2}$-player games with PCTL winning objectives, we establish that the PCTL satisfiability problem is ${\Sigma}_1^1$-hard. We present an exponential-time algorithm for the satisfiability of a bounded, negation-closed fragment of PCTL, and show that the satisfiability problem for this fragment is EXPTIME-hard.

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Souymodip Chakraborty, Joost-Pieter Katoen. 2015-06-08. On the Hardness of PCTL Satisfiability. https://arxiv.org/abs/1506.02483

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