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Bisimulation relation has been successfully applied to computer science andcontrol theory. In our previous work, simulation-based controllability andsimulation-based observability are proposed, under which the existence ofbisimilarity supervisor is guaranteed. However, a given specification automatonmay not satisfy these conditions, and a natural question is how to compute amaximum permissive subspecification. This paper aims to answer this questionand investigate the computation of the supremal simulation-based controllableand strong observable subautomata with respect to given specifications by thelattice theory. In order to achieve the supremal solution, three monotoneoperators, namely simulation operator, controllable operator and strongobservable operator, are proposed upon the established complete lattice. Then,inequalities based on these operators are formulated, whose solution is thesimulation-based controllable and strong observable set. In particular, asufficient condition is presented to guarantee the existence of the supremalsimulation-based controllable and strong observable subautomata. Furthermore,an algorithm is proposed to compute such subautomata.

Computation for Supremal Simulation-Based Controllable and Strong Observable Subautomata