On the Hardness of PCTL Satisfiability
release_l47flsf5qzdbfh3v6twvtmmv4i
by
Souymodip Chakraborty, Joost-Pieter Katoen
2015
Abstract
This paper shows that the satisfiability problem for probabilistic CTL (PCTL,
for short) is undecidable. By a reduction from 11/2-player games with
PCTL winning objectives, we establish that the PCTL satisfiability problem is
Σ_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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