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Stable Models for Stubborn Sets


Kimmo Varpaaniemi. Stable models for stubborn sets. Fundamenta Informaticae (Annales Societatis Mathematicae Polonae, Series IV), 43(1–4):355–375, August 2000. IOS Press, Amsterdam, The Netherlands.


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 off in the total time spent in generating a reduced state space. This article shows how the method can exploit tools that solve certain problems of logic programs. The restriction of a definition 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 find a stubborn set which is good w.r.t. the number of enabled transitions, it suffices to find a stable model which is good w.r.t. the number of certain atoms. The article also presents a new NP-completeness result concerning stubborn sets.


reachability analysis, reduced state space generation, stubborn sets, variable-free logic programs, stable models, NP-completeness

Suggested BibTeX entry:

    author = {Kimmo Varpaaniemi},
    journal = {Fundamenta Informaticae (Annales Societatis Mathematicae Polonae, Series IV)},
    month = {August},
    note = {IOS Press, Amsterdam, The Netherlands},
    number = {1--4},
    pages = {355--375},
    title = {{S}table Models for Stubborn Sets},
    volume = {43},
    year = {2000},

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