Generalized modal satisfiability
Copyright policy )Generalized modal satisfiability
It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits. We consider both the uni-modal and the multi-modal case, and study the dual problem of validity as well.
32 pages, 3 figures. Some of the results appeared in STACS 2006
- Rochester Institute of Technology United States
- Rochester Institute of Technology United States
- Institut für Informatik Germany
- University of Lübeck Germany
- Kiel University Germany
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, computational complexity, Computer Networks and Communications, Modal logic, Analysis of algorithms and problem complexity, Applied Mathematics, Computational Complexity (cs.CC), Theoretical Computer Science, Logic in Computer Science (cs.LO), Computational complexity, Computer Science - Computational Complexity, Computational Theory and Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Modal logic (including the logic of norms), modal logic
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, computational complexity, Computer Networks and Communications, Modal logic, Analysis of algorithms and problem complexity, Applied Mathematics, Computational Complexity (cs.CC), Theoretical Computer Science, Logic in Computer Science (cs.LO), Computational complexity, Computer Science - Computational Complexity, Computational Theory and Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Modal logic (including the logic of norms), modal logic
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