Complexity of two-variable dependence logic and IF-logic

Expressivity and Complexity of Dependence Logic

Complexity Results for First-Order Two-Variable Logic with Counting

Let C 2 p denote the class of rst order sentences with two variables and with additional quantiiers \there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken over all integers p. We prove that the satissability problem for C 2 1 sentences is NEXPTIME-complete. This strengthens the results by E. Grr adel, Ph. Kolaitis and M. Vardi 15] who showed that the sati...

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

Etessami, Vardi and Wilke [5] showed that satisfiability of two-variable first order logic FO[<] on word models is Nexptime-complete. We extend this upper bound to the slightly stronger logic FO[<, 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 ...

Two - Variable Logic on Data

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata and extended temporal logics. This paper shows that satisfiability for the two-variable fragment FO(∼,<,+1) of firstorder logic with data equality test ∼, is decidable over finite and over infin...

Complexity Results for Modal Dependence Logic

Modal dependence logic was introduced recently by Väänänen. It enhances the basic modal language by an operator =(). For propositional variables p1, . . . , pn, =(p1, . . . , pn−1, pn) intuitively states that the value of pn is determined by those of p1, . . . , pn−1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministi...