Two-Variable First Order Logic with Counting Quantifiers: Complexity Results [chapter]

Kamal Lodaya, A. V. Sreejith
2017 Lecture Notes in Computer Science  
Etessami, Vardi and Wilke [5] showed that satisfiability of two-variable first order logic FO 2 [<] on word models is Nexptime-complete. We extend this upper bound to the slightly stronger logic FO 2 [<, succ, ≡], 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 and Thomas [22] (we call this two-variable fragment FOmod 2 [<, succ]), satisfiability becomes
more » ... xpspace-complete. A more general counting quantifier, FOunC 2 [<, succ], makes the logic undecidable.
doi:10.1007/978-3-319-62809-7_19 fatcat:yoiajoyy55apxbgktpjc5a53ni