Abstract
Many logics used in computer science have an intractable satisfiability (model-checking, derivability) problem. This restricts their general applicability severely. May be restricting to smaller classes of admissible formulas can bring down the complexity bounds. In the present paper we follow this strategy for the subset space logic proposed by Moss and Parikh recently [Moss and Parikh 1992], [Dabrowski et al. 1996]. Forming nSAT as in sentential logic, but with prefix formulas instead of literals, we obtain nice generalizations of the following results well-known from the prepositional case: nSAT ∃ P if n≤2 and nSAT is NP-complete if n>-3. Thus nSAT is “feasible”, iff n≤2. Moreover, full SAT turns out to be PSPACE-hard (as usual).
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Heinemann, B. (1997). On the complexity of prefix formulas in modal logic of subset spaces. In: Adian, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 1997. Lecture Notes in Computer Science, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63045-7_16
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DOI: https://doi.org/10.1007/3-540-63045-7_16
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