Satisfiability problem for modal logic with global counting operators coded in binary is NExpTime-complete

Authors:
Michał Zawidzki;Renate A. Schmidt;Dmitry Tishkovsky
Affiliations:
School of Computer Science, The University of Manchester, United Kingdom and Department of Logic, University of Lodz, Poland;School of Computer Science, The University of Manchester, United Kingdom;School of Computer Science, The University of Manchester, United Kingdom
Venue:
Information Processing Letters
Year:
2013

Citing 5
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Abstract

This paper provides a proof of NExpTime-completeness of the satisfiability problem for the logic K(E"n) (modal logic K with global counting operators), where number constraints are coded in binary. Hitherto the tight complexity bounds (namely ExpTime-completeness) have been established only for this logic with number restrictions coded in unary. The upper bound is established by showing that K(E"n) has the exponential-size model property and the lower bound follows from reducibility of exponential bounded tiling problem to K(E"n).