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19
Recursion Theory on the Reals and Continuoustime Computation
 Theoretical Computer Science
, 1995
"... We define a class of recursive functions on the reals analogous to the classical recursive functions on the natural numbers, corresponding to a conceptual analog computer that operates in continuous time. This class turns out to be surprisingly large, and includes many functions which are uncomp ..."
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Cited by 73 (4 self)
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We define a class of recursive functions on the reals analogous to the classical recursive functions on the natural numbers, corresponding to a conceptual analog computer that operates in continuous time. This class turns out to be surprisingly large, and includes many functions which are uncomputable in the traditional sense.
On the fixed parameter complexity of graph enumeration problems definable in monadic secondorder logic
, 2001
"... ..."
Dynamical Recognizers: Realtime Language Recognition by Analog Computers
 Theoretical Computer Science
, 1996
"... We consider a model of analog computation which can recognize various languages in real time. We encode an input word as a point in R d by composing iterated maps, and then apply inequalities to the resulting point to test for membership in the language. Each class of maps and inequalities, suc ..."
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Cited by 57 (4 self)
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We consider a model of analog computation which can recognize various languages in real time. We encode an input word as a point in R d by composing iterated maps, and then apply inequalities to the resulting point to test for membership in the language. Each class of maps and inequalities, such as quadratic functions with rational coefficients, is capable of recognizing a particular class of languages; for instance, linear and quadratic maps can have both stacklike and queuelike memories. We use methods equivalent to the VapnikChervonenkis dimension to separate some of our classes from each other, e.g. linear maps are less powerful than quadratic or piecewiselinear ones, polynomials are less powerful than elementary (trigonometric and exponential) maps, and deterministic polynomials of each degree are less powerful than their nondeterministic counterparts. Comparing these dynamical classes with various discrete language classes helps illuminate how iterated maps can...
Finite Presentations of Infinite Structures: Automata and Interpretations
 Theory of Computing Systems
, 2002
"... We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by modeltheoretic interpretations. ..."
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Cited by 42 (3 self)
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We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by modeltheoretic interpretations.
Finite Model Theory and Descriptive Complexity
, 2002
"... This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the ..."
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Cited by 23 (7 self)
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This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the
Descriptive Complexity Theory for Constraint Databases
 IN COMPUTER SCIENCE LOGIC, NUMBER 1683 IN LNCS
, 1999
"... We consider the data complexity of various logics on two important classes of constraint databases: dense order and linear constraint databases. For dense order databases, we present a general result allowing us to lift results on logics capturing complexity classes from the class of finite orde ..."
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Cited by 10 (3 self)
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We consider the data complexity of various logics on two important classes of constraint databases: dense order and linear constraint databases. For dense order databases, we present a general result allowing us to lift results on logics capturing complexity classes from the class of finite ordered databases to dense order constraint databases. Considering linear constraints, we show that there is a significant gap between the data complexity of firstorder queries on linear constraint databases over the real and the natural numbers. This is done by proving that for arbitrary high levels of the Presburger arithmetic there are complete firstorder queries on databases over (N; !; +). The proof of the theorem demonstrates a simple argument for translating complexity results for prefix classes in logical theories to results on the complexity of query evaluation in constraint databases.
Logics Which Capture Complexity Classes Over the Reals
 Journal of Symbolic Logic
"... this paper we continue the work initiated in [7]. Our starting point is the absence of a meaningful class of polynomial space over the reals. Michaux proved in [10] that such a class would contain all decidable problems. There are two natural candidates to ocuppy this vacancy. The class PAR IR of se ..."
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Cited by 9 (5 self)
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this paper we continue the work initiated in [7]. Our starting point is the absence of a meaningful class of polynomial space over the reals. Michaux proved in [10] that such a class would contain all decidable problems. There are two natural candidates to ocuppy this vacancy. The class PAR IR of sets decidable in parallel polynomial time and the class (EXP IR ; PSPACE IR ) of sets decidable by machines which work simultaneously in exponential time and polynomial space. Both classes yield PSPACE over IF 2 but it turns out that the first one is weaker over IR. We give logics for IRstructures which capture these two classes. Previously, we recall the basic concepts about IRstructures and their logics. Scattered along these sections some other complexity classes are characterized in terms of descriptive complexity. Among them, we find NC
A Framework for the Investigation of Aggregate Functions in Database Queries
 IN INTERNATIONAL CONFERENCE ON DATA BASE THEORY 1999, SPRINGER LNCS
, 1999
"... In this paper we present a new approach for studying aggregations in the context of database query languages. Starting from a broad definition of aggregate function, we address our investigation from two different perspectives. We first propose a declarative notion of uniform aggregate function ..."
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Cited by 9 (0 self)
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In this paper we present a new approach for studying aggregations in the context of database query languages. Starting from a broad definition of aggregate function, we address our investigation from two different perspectives. We first propose a declarative notion of uniform aggregate function that refers to a family of scalar functions uniformly constructed over a vocabulary of basic operators by a bounded Turing Machine. This notion yields an effective tool to study the effect of the embedding of a class of builtin aggregate functions in a query language. All the aggregate functions most used in practice are included in this classification. We then present an operational notion of aggregate function, by considering a highorder folding constructor, based on structural recursion, devoted to compute numeric aggregations over complex values. We show that numeric folding over a given vocabulary is sometimes not able to compute, by itself, the whole class of uniform aggre...