Parameterized Complexity of Fixed Variable Logics
نویسندگان
چکیده
We study the complexity of model checking formulas in first-order logic parameterized by the number of distinct variables in the formula. This problem, which is not known to be fixedparameter tractable, resisted to be properly classified in the context of parameterized complexity. We show that it is complete for a newly-defined complexity class that we propose as an analog of the classical class PSPACE in parameterized complexity. We support this intuition by the following findings: First, the proposed class admits a definition in terms of alternating Turing machines in a similar way as PSPACE can be defined in terms of polynomial-time alternating machines. Second, we show that parameterized versions of other PSPACE-complete problems, like winning certain pebble games and finding restricted resolution refutations, are complete for
منابع مشابه
Finite variable logics in descriptive complexity theory
Throughout the development of finite model theory, the fragments of first-order logic with only finitely many variables have played a central role. This survey gives an introduction to the theory of finite variable logics and reports on recent progress in the area. For each k 1 we let Lk be the fragment of first-order logic consisting of all formulas with at most k (free or bound) variables. Th...
متن کاملComparing the Succinctness of Monadic Query Languages over Finite Trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than mona...
متن کاملA On the Complexity of Existential Positive Queries
We systematically investigate the complexity of model checking the existential positive fragment of firstorder logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted to fall into the set; a natural question is then to classify which sentence sets are tractable and which are intractable. With respect to fixed-parameter tract...
متن کاملBounded Variable Logics and Counting: A Study in Finite Models
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the 9th publication in the Lecture Notes in Logic series, Martin Otto gives an introduction to finite model theory that indicates the m...
متن کاملParameterized Complexity Results for Symbolic Model Checking of Temporal Logics
Reasoning about temporal knowledge is a fundamental task in the area of artificial intelligence and knowledge representation. A key problem in this area is model checking, and indispensable for the state-of-the-art in solving this problem in large-scale settings is the technique of bounded model checking. We investigate the theoretical possibilities of this technique using parameterized complex...
متن کامل