Markov regenerative processes solution and stochastic model checking: an on-the-fly approach

Stochastic model checking is a technique to check if a Markov chain satisfies a path property. This typically requires the computation of the probability of the set of paths of the continuous Time Markov chain (CTMC) that satisfy a given set of requirements that are given in terms of visited states, events occurrence and time constraints at which the events occur. In particular we shall address the stochastic logic CSLTA [12], in which the properties to be satisfied are specified as one-clock timed automaton [1]. CSLTA is strictly more expressive than the well known stochastic logic CSL [8]. It has been proved in [12] that the computation of the set of states that satisfy a CSLTA property requires the solution, in steady-state, of a Markov Regenerative Process (MRgP) of a size that is of the order of the size of the CTMC multiplied by the size of the timed automata state space: space and time can be a severe impairment for the efficacy of stochastic model checking. In this talk we shall review advanced techniques for MRgP solution [4, 6, 7, 10, 13] and standard techniques for the state space construction of timed automata [9], to show how they can work in a synergic manner to devise a model checking algorithm for CSLTA that works on components (to save time), and that is able to build the components on-the-fly, only when needed (to save space), leading to the OTF technique, the main topic of this talk [2]. A comparison with the component-based technique in [15] for the CSLTA model-checking of infinite Markov chain will also be discussed. OTF (as well as other component-based model-checking algorithms) has been implemented both as an in-line tools called MC4CSLTA [5] and as a fully integrated component of the graphical interface of GreatSPN [3], a tool for the solution and the (stochastic) verification of (stochastic) Petri nets. We shall compare the time and space complexity of OTF with previous approaches based on components. Moreover we shall also compare the performances of OTF with those of two CSL model checkers: Prism [14] and Storm [11], clearly limited to CSL formulas.