Two-variable first order logic with counting quantifiers: Complexity results

Abstract

Etessami et al. [5] showed that satisfiability of two-variable first order logic (Formula presented) on word models is Nexptime-complete. We extend this upper bound to the slightly stronger logic (Formula presented), which allows checking whether a word position is congruent to r modulo q, for some divisor q and remainder r. If we allow the more powerful modulo counting quantifiers of Straubing, Thérien et al. [22] (we call this two-variable fragment (Formula presented) satisfiability becomes Expspace-complete. A more general counting quantifier, (Formula presented) makes the logic undecidable.