DellaPenna_etal2004
Proceedings
Springer
2004
Formal Methods in Computer-Aided Design, 5th International Conference, FMCAD 2004, Austin, Texas, USA, November 15-17, 2004, Proceedings
3312
214-229
Della PennaGiuseppe
IntrigilaBenedetto
MelattiIgor
TronciEnrico
Venturini ZilliMarisa
HuA.J.
MartinA.K.
Bounded Probabilistic Model Checking with the Mur$\varphi$ Verifier
In this paper we present an explicit verification algorithm for Probabilistic Systems defining discrete time/finite state Markov Chains. We restrict ourselves to verification of Bounded PCTL formulas (BPCTL), that is, PCTL formulas in which all Until operators are bounded, possibly with different bounds. This means that we consider only paths (system runs) of bounded length. Given a Markov Chain $\cal M$ and a BPCTL formula Φ, our algorithm checks if Φ is satisfied in $\cal M$. This allows to verify important properties, such as reliability in Discrete Time Hybrid Systems. We present an implementation of our algorithm within a suitable extension of the Mur$\varphi$ verifier. We call FHP-Mur$\varphi$ (Finite Horizon Probabilistic Mur$\varphi$) such extension of the Mur$\varphi$ verifier. We give experimental results comparing FHP-Mur$\varphi$ with (a finite horizon subset of) PRISM, a state-of-the-art symbolic model checker for Markov Chains. Our experimental results show that FHP-Mur$\varphi$ can effectively handle verification of BPCTL formulas for systems that are out of reach for PRISM, namely those involving arithmetic operations on the state variables (e.g. hybrid systems).