On the Hardness of PCTL Satisfiability

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.

arXiv commentThis paper has been withdrawn by the author due to a crucial error in Theorem 2