Stable Models for Stubborn Sets

The stubborn set method is one of the methods that try to relieve the state space explosion problem that occurs in state space generation. Spending some time in looking for \good" stubborn sets can pay oo in the total time spent in generating a reduced state space. This paper shows how the method can exploit tools that solve certain problems of logic programs. The restriction of a deenition of stubbornness to a given state can be translated into a variable-free logic program. When a stubborn set satisfying additional constraints is wanted, the additional constraints should be translated, too. It is easy to make the translation in such a way that each acceptable stubborn set of the state is represented by at least one stable model of the program, each stable model of the program represents at least one acceptable stubborn set of the state, and for each pair in the representation relation, the number of certain atoms in the stable model is equal to the number of enabled transitions of the represented stubborn set. So, in order to nd a stubborn set which is good w.r.t. the number of enabled transitions, it suuces to nd a stable model which is good w.r.t. the number of certain atoms.