Model checking Markov chains : techniques and tools

This dissertation deals with four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking procedures. First, we introduce MRMC, a model checker for DMRMs and CMRMs, that supports reward extensions of PCTL and CSL. We study the efficiency, of the tool in comparison with probabilistic model checkers such as E -MC2, PRISM, Ymer and VESTA, and focus on fully probabilistic systems. Further, we provide a precise procedure for steady-state detection for time-bounded reachabiity on CTMCs. After what we study the effect of bisimulation minimization in model checking of monolithic DTMCs, CTMCs and the variants thereof with rewards. We conclude our work by deriving techniques based on discrete-event sijulation and sequential confidence intervals for model checking CSL properties on CTMCs.