On the connections between PCTL and Dynamic Programming

Details On the connections between PCTL and Dynamic Programming On the connections between PCTL and Dynamic Programming

2009-10-25

arxiv.org/abs/0910.4738v1

HSCC Stockholm, 2010, pages 253-262

Mathematics

Optimization and Control

Submitted

Scientific paper

10.1145/1755952.1755988

Probabilistic Computation Tree Logic (PCTL) is a well-known modal logic which has become a standard for expressing temporal properties of finite-state Markov chains in the context of automated model checking. In this paper, we give a definition of PCTL for noncountable-space Markov chains, and we show that there is a substantial affinity between certain of its operators and problems of Dynamic Programming. After proving some uniqueness properties of the solutions to the latter, we conclude the paper with two examples to show that some recovery strategies in practical applications, which are naturally stated as reach-avoid problems, can be actually viewed as particular cases of PCTL formulas.

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