Technical Report CS-2000-04

Title: Simulation Based Minimization
Authors: Doron Bustan and Orna Grumberg
Abstract: This work presents a minimization algorithm. The algorithm receives a Kripke structure $M$ and returns the smallest structure that is simulation equivalent to $M$. The {\em simulation equivalence} relation is weaker than bisimulation but stronger than the simulation preorder. It strongly preserves ACTL and LTL (as sub-logics of ACTL$^*$). We show that every structure $M$ has a unique up to isomorphism {\em reduced} structure that is simulation equivalent to $M$ and smallest in size. We give a Minimizing Algorithm that constructs the reduced structure. It first constructs the quotient structure for $M$, then eliminates transitions to little brothers and finally deletes unreachable states. The first step has maximal space requirements since it is based on the simulation preorder over $M$. To reduce these requirements we suggest the \partAlg which constructs the quotient structure for $M$ without ever building the simulation preorder. The \partAlg has a better space complexity but might have worse time complexity.
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