2016/04/20 by Andrey Gorlin, Gorlin, Andrey, C. R. Ramakrishnan +1
Computer Science · #FOS: Computer and information sciences #I.2.3 #Logic in Computer Science (cs.LO) #cs.LO
paper · pdf · doi:10.48550/arxiv.1604.06118
arxiv created 2017/05/09 · arxiv updated 2017/05/10
Generalized Probabilistic Logic (GPL) is a temporal logic, based on the modal mu-calculus, for specifying properties of reactive probabilistic systems. We explore XPL, an extension to GPL allowing the semantics of nondeterminism present in Markov decision processes (MDPs). XPL is expressive enough that a number of independently studied problems--- such as termination of Recursive MDPs (RMDPs), PCTL* model checking of MDPs, and reachability for Branching MDPs--- can all be cast as model checking over XPL. Termination of multi-exit RMDPs is undecidable; thus, model checking in XPL is undecidable in general. We define a subclass, called separable XPL, for which model checking is decidable. Decidable problems such as termination of 1-exit RMDPs, PCTL* model checking of MDPs, and reachability for Branching MDPs can be reduced to model checking separable XPL. Thus, XPL forms a uniform framework for studying problems involving systems with non-deterministic and probabilistic behaviors, while separable XPL provides a way to solve decidable fragments of these problems.