Verification, Model Checking, and Abstract Interpretation

Volume 7148 of the series Lecture Notes in Computer Science pp 396-411

A General Framework for Probabilistic Characterizing Formulae

  • Joshua SackAffiliated withDepartment of Mathematics and Statistics, California State University Long Beach
  • , Lijun ZhangAffiliated withDTU Informatics, Technical University of Denmark

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Recently, a general framework on characteristic formulae was proposed by Aceto et al. It offers a simple theory that allows one to easily obtain characteristic formulae of many non-probabilistic behavioral relations. Our paper studies their techniques in a probabilistic setting. We provide a general method for determining characteristic formulae of behavioral relations for probabilistic automata using fixed-point probability logics. We consider such behavioral relations as simulations and bisimulations, probabilistic bisimulations, probabilistic weak simulations, and probabilistic forward simulations. This paper shows how their constructions and proofs can follow from a single common technique.