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We prove that branching-time temporal logics CTL and CT L ⁎ are polynomial-time embeddable into their single-variable fragments. It follows that satisfiability for CTL and CT L ⁎ , and therefore also for alternating-time temporal logics ATL and ATL ⁎ , in languages with one propositional variable is as algorithmically hard as satisfiability for the full logic: EXPTIME-complete for CTL and ATL , and 2EXPTIME-complete for CT L ⁎ and ATL ⁎. We discuss applicability of the technique used in the proofs to other modal and temporal logics, including propositional dynamic, epistemic, and temporal-epistemic logics, as well as many-dimensional and first-order modal and temporal logics. [ABSTRACT FROM AUTHOR]

We show how to represent polynomial time computation in an untyped version of proof-nets for elementary linear logic. This follows previous work by P. Baillot but which was developed in a typed and affine setting. We describe how these two properties can be adapted. [ABSTRACT FROM AUTHOR]

This paper introduces Graded Computation Tree Logic with finite path semantics (GCTL f ⁎ , for short), a variant of Computation Tree Logic CTL⁎, in which path quantifiers are interpreted over finite paths and can count the number of such paths. State formulas of GCTL f ⁎ are interpreted over Kripke structures. The syntax of GCTL f ⁎ has path quantifiers of the form E ≥ g ψ which express that there are at least g many distinct finite paths that satisfy ψ. After defining and justifying the logic GCTL f ⁎ , we solve its model checking problem and establish that its computational complexity is PSPACE-complete. Moreover, we investigate GCTL f ⁎ under the imperfect information setting. Precisely, we introduce GCTLK f ⁎ , an epistemic extension of GCTL f ⁎ and prove that the model checking problem also in this case is PSPACE-complete. [ABSTRACT FROM AUTHOR]

We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality comparison and combines their expressive powers. We prove Image 1 -completeness of the logic by presenting an optimal algorithm for solving its finite satisfiability problem. [ABSTRACT FROM AUTHOR]

Algorithms for answering XPath queries on Xml streams have been studied intensively in the last decade. Nevertheless, there still exists no solution with high efficiency and large coverage. In this paper, we introduce early nested word automata in order to approximate earliest query answering algorithms for nested word automata. Our early query answering algorithm is based on stack-and-state sharing for running early nested word automata on all answer candidates with on-the-fly determinization. We prove tight upper complexity bounds on time and space consumption. We have implemented our algorithm in the QuiXPath system and show that it outperforms all previous tools in coverage on the XPathMark benchmark, while obtaining very high time and space efficiency and scaling to huge Xml streams. Furthermore, it turns out that our early query answering algorithm is earliest in practice on most queries from the XPathMark benchmark. 1 1 Thanks to the QuiXProc project of Inria and Innovimax and the Cnrs Sosp project. [ABSTRACT FROM AUTHOR]

Abstract: Commutative, integral and bounded -algebras form a subvariety of residuated lattices which provides the algebraic semantics of an interesting common fragment of intuitionistic logic and of several fuzzy logics. It is known that both the equational theory and the quasiequational theory of commutative -algebras are decidable (in contrast to the noncommutative case), but their complexity has not been studied yet. In this paper, we prove that both theories are in , and that the quasiequational theory is -hard. [Copyright &y& Elsevier]

Abstract: This is a survey of results about versions of fine hierarchies and many-one reducibilities that appear in different parts of theoretical computer science. These notions and related techniques play a crucial role in understanding complexity of finite and infinite computations. We try not only to present the corresponding notions and facts from the particular fields but also to identify the unifying notions, techniques and ideas. [Copyright &y& Elsevier]

Abstract: Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic , an extension of Linear-Time Temporal Logic LTL with past-time operators whose atomic formulae are defined from a first-order constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a PSPACE-complete satisfiability problem, we establish that model-checking and satisfiability problems remain in PSPACE as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of has a language more concise than existing languages and the temporalization of our first-order language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to , EXPSPACE-complete problems. As another application, we establish that the equivalence problem for extended single-string automata, known to express the equality of time granularities, is PSPACE-complete by designing a reduction from QBF and by using our results for . [Copyright &y& Elsevier]

This paper gives some new logical characterizations of the class of rudimentary languages in the scope of descriptive complexity. These characterizations are based on a logic introduced by Parigot and Pelz to characterize Petri Net languages, and generalized quantifiers of comparison of cardinality. [Copyright &y& Elsevier]

The LA-logics (“logics with Local Agreement”) are polymodal logics defined semantically such that at any world of a model, the sets of successors for the different accessibility relations can be linearly ordered and the accessibility relations are equivalence relations. In a previous work, we have shown that every LA-logic defined with a finite set of modal indices has an NP-complete satisfiability problem. In this paper, we introduce a class of LA-logics with a countably infinite set of modal indices and we show that the satisfiability problem is PSPACE-complete for every logic of such a class. The upper bound is shown by exhibiting a tree structure of the models. This allows us to establish a surprising correspondence between the modal depth of formulae and the number of occurrences of distinct modal connectives. More importantly, as a consequence, we can show the PSPACE-completeness of Gargov''s logic DALLA and Nakamura''s logic LGM restricted to modal indices that are rational numbers, for which the computational complexity characterization has been open until now. These logics are known to belong to the class of information logics and fuzzy modal logics, respectively. [Copyright &y& Elsevier]