The Satisfiability Problem for a Quantitative Fragment of PCTL

We give a sufficient condition under which every finite-satisfiable formula of given PCTL fragment has model with at most doubly exponential number states (consequently, the finite satisfiability problem for is in \(\mathbf{2}\text {-}{} \mathbf{EXPSPACE}\)). The semantic and it based on enforcing form “progress” non-bottom SCCs contributing to satisfaction formula. show that satisfied by fragments beyond reach existing methods.