Alternating Fixed Points in Boolean Equation Systems as Preferred Stable Models

We formally characterize alternating fixedp oints of boolean equation systems as models of (propositional) normal logic programs. To this end, we introduce the notion of a preferred stable model of a logic program, and define a mapping that associates a normal logic program with a boolean equation system such that the solution to the equation system can be "readoff" the preferredstable model of the logic program. We also show that the preferredmo del cannot be calculateda-p osteriori (i.e. compute stable models and choose the preferredone) but rather must be computedin an intertwinedfashion with the stable model itself. The mapping reveals a natural relationship between the evaluation of alternating fixedp oints in boolean equation systems and the Gelfond-Lifschitz transformation usedin stable-model computation.For alternation-free boolean equation systems, we show that the logic programs we derive are stratified, while for formulas with alternation, the corresponding programs are non-stratified. Consequently, our mapping of boolean equation systems to logic programs preserves the computational complexity of evaluating the solutions of special classes of equation systems (e.g., linear-time for the alternation-free systems, exponential for systems with alternating fixed points).