Online Simulation Reduction
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We study the problem of simultaneously performing reachability analysis and simulation reduction of transition systems, called online minimization by Lee and Yannakakis [1992] who settled the question for bisimulation. We call this problem online simulation reduction to reflect some significant dissimilarities w.r.t. Lee and Yannakakis' online bisimulation minimization. Indeed, by means of a reduction to an undecidable problem and of its relationship with graph st-connectivity, we show that by moving from bisimilarity to similarity this online reduction problem becomes fundamentally different. Then, we put forward a symbolic (i.e., processing state partitions) algorithm that performs online reduction in a complete way for the simulation quasiorder while yielding a sound over-approximation for simulation equivalence, and a second symbolic algorithm which is complete for simulation equivalence but, due to the undecidability result, reveals unavoidable limitations on its termination.
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