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Set Constraints are the Monadic Class
, 1992
"... We investigate the relationship between set constraints and the monadic class of firstorder formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. Mor ..."
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Cited by 71 (0 self)
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We investigate the relationship between set constraints and the monadic class of firstorder formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. More precisely, we prove that this problem has a lower bound of NTIME(c n= log n ). The relationship between set constraints and the monadic class also gives us decidability and complexity results for certain practically useful extensions of set constraints, in particular "negative projections" and subterm equality tests.
Average Case Completeness
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1991
"... We explain and advance Levin's theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions. ..."
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Cited by 71 (2 self)
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We explain and advance Levin's theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions.
Relational Transducers for Electronic Commerce
 JCSS
, 1998
"... Electronic commerce is emerging as one of the major Websupported applications requiring database support. We introduce and study highlevel declarative specifications of business models, using an approach in the spirit of active databases. More precisely, business models are specified as relational ..."
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Cited by 66 (11 self)
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Electronic commerce is emerging as one of the major Websupported applications requiring database support. We introduce and study highlevel declarative specifications of business models, using an approach in the spirit of active databases. More precisely, business models are specified as relational transducers that map sequences of input relations into sequences of output relations. The semantically meaningful trace of an inputoutput exchange is kept as a sequence of log relations. We consider problems motivated by electronic commerce applications, such as log validation, verifying temporal properties of transducers, and comparing two relational transducers. Positive results are obtained for a restricted class of relational transducers called Spocus transducers (for semipositive outputs and cumulative state). We argue that despite the restrictions, these capture a wide range of practically significant business models. 1 Introduction Electronic commerce is emerging as a major Webs...
FirstOrder Logic with Two Variables and Unary Temporal Logic
 INF. COMPUT
, 1997
"... We investigate the power of firstorder logic with only two variables over ωwords and finite words, a logic denoted by FO². We prove that FO² can express precisely the same properties as linear temporal logic with only the unary temporal operators: "next", "previously", "sometime in the future", ..."
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Cited by 56 (9 self)
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We investigate the power of firstorder logic with only two variables over ωwords and finite words, a logic denoted by FO². We prove that FO² can express precisely the same properties as linear temporal logic with only the unary temporal operators: "next", "previously", "sometime in the future", and "sometime in the past", a logic we denote by unaryTL. Moreover, our translation from FO² to unaryTL converts every FO² formula to an equivalent unaryTL formula that is at most exponentially larger, and whose operator depth is at most twice the quantifier depth of the firstorder formula. We show
On Logics with Two Variables
 Theoretical Computer Science
, 1999
"... This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable ..."
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Cited by 41 (8 self)
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This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable for satisfiability. One of the reasons for the significance of this result is that many propositional modal logics can be embedded into FO 2 . Logics that are of interest for knowledge representation, for the specification and verification of concurrent systems and for other areas of computer science are often defined (or can be viewed) as extensions of modal logics by features like counting constructs, path quantifiers, transitive closure operators, least and greatest fixed points etc. Examples of such logics are computation tree logic CTL, the modal ¯calculus L¯ , or popular description logics used in artificial intelligence. Although the additional features are usually not firstorder...
The Convenience of Tilings
 In Complexity, Logic, and Recursion Theory
, 1997
"... Tiling problems provide for a very simple and transparent mechanism for encoding machine computations. This gives rise to rather simple master reductions showing various versions of the tiling problem complete for various complexity classes. We investigate the potential for using these tiling proble ..."
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Cited by 36 (0 self)
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Tiling problems provide for a very simple and transparent mechanism for encoding machine computations. This gives rise to rather simple master reductions showing various versions of the tiling problem complete for various complexity classes. We investigate the potential for using these tiling problems in subsequent reductions showing hardness of the combinatorial problems that really matter. We ilustrate our approach by means of three examples: a short reduction chain to the Knapsack problem followed by a Hilbert 10 reduction using similar ingredients. Finally we reprove the Deterministic Exponential Time lowerbound for satisfiablility in Propositional Dynamic Logic. The resulting reductions are relatively simple; they do however infringe on the principle of orthogonality of reductions since they abuse extra structure in the instances of the problems reduced from which results from the fact that these instances were generated by a master reduction previously. 1 Introduction This paper...
On the Complexity of Dataflow Analysis of Logic Programs
, 1992
"... This article reports some results on this correlation in the context of logic programs. A formal notion of the "precision" of an analysis algorithm is proposed, and this is used to characterize the worstcase computational complexity of a number of dataflow analyses with different degrees of precisi ..."
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Cited by 35 (4 self)
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This article reports some results on this correlation in the context of logic programs. A formal notion of the "precision" of an analysis algorithm is proposed, and this is used to characterize the worstcase computational complexity of a number of dataflow analyses with different degrees of precision. While this article considers the analysis of logic programs, the technique proposed, namely the use of "exactness sets" to study relationships between complexity and precision of analyses, is not specific to logic programming in any way, and is equally applicable to flow analyses of other language families.
Negative Set Constraints With Equality
 In Ninth Annual IEEE Symposium on Logic in Computer Science
, 1994
"... Systems of set constraints describe relations between sets of ground terms. They have been successfully used in program analysis and type inference. So far two proofs of decidability of mixed set constraints have been given: by R. Gilleron, S. Tison and M. Tommasi [12] and A. Aiken, D. Kozen, and E. ..."
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Cited by 35 (10 self)
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Systems of set constraints describe relations between sets of ground terms. They have been successfully used in program analysis and type inference. So far two proofs of decidability of mixed set constraints have been given: by R. Gilleron, S. Tison and M. Tommasi [12] and A. Aiken, D. Kozen, and E.L. Wimmers [3]. However, both these proofs are long, involved and do not seem to extend to more general set constraints. Our approach is based on a reduction of set constraints to the monadic class given in a recent paper by L. Bachmair, H. Ganzinger, and U. Waldmann [7]. We first give a new proof of decidability of systems of mixed positive and negative set constraints. We explicitely describe a very simple algorithm working in NEXPTIME and we give in all detail a relatively easy proof of its correctness. Then, we sketch how our technique can be applied to get various extensions of this result. In particular we prove that the problem of consistency of mixed set constraints with restricted p...
Feature Logics
 HANDBOOK OF LOGIC AND LANGUAGE, EDITED BY VAN BENTHEM & TER MEULEN
, 1994
"... Feature logics form a class of specialized logics which have proven especially useful in classifying and constraining the linguistic objects known as feature structures. Linguistically, these structures have their origin in the work of the Prague school of linguistics, followed by the work of Chom ..."
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Cited by 33 (0 self)
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Feature logics form a class of specialized logics which have proven especially useful in classifying and constraining the linguistic objects known as feature structures. Linguistically, these structures have their origin in the work of the Prague school of linguistics, followed by the work of Chomsky and Halle in The Sound Pattern of English [16]. Feature structures have been reinvented several times by computer scientists: in the theory of data structures, where they are known as record structures, in artificial intelligence, where they are known as frame or slotvalue structures, in the theory of data bases, where they are called "complex objects", and in computati
Complexity Results for FirstOrder TwoVariable Logic with Counting
, 2000
"... Let C 2 p denote the class of first order sentences with two variables and with additional quantifiers "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 satisfiability problem for C 2 1 sentences is NEXPTIMEcomplete ..."
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Cited by 29 (1 self)
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Let C 2 p denote the class of first order sentences with two variables and with additional quantifiers "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 satisfiability problem for C 2 1 sentences is NEXPTIMEcomplete. This strengthens the results by E. Grädel, Ph. Kolaitis and M. Vardi [15] who showed that the satisfiability problem for the first order twovariable logic L 2 is NEXPTIMEcomplete and by E. Grädel, M. Otto and E. Rosen [16] who proved the decidability of C 2 . Our result easily implies that the satisfiability problem for C 2 is in nondeterministic, doubly exponential time. It is interesting that C 2 1 is in NEXPTIME in spite of the fact, that there are sentences whose minimal (and only) models are of doubly exponential size. It is worth noticing, that by a recent result of E. Gradel, M. Otto and E. Rosen [17], extensions of twovariables logic L 2 by a week access to car...