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127
Feasible Computation through Model Theory
, 1993
"... The computational complexity of a problem is usually defined in terms of the resources required on some machine model of computation. An alternative view looks at the complexity of describing the problem (seen as a collection of relational structures) in a logic, measuring logical resources such as ..."
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Cited by 36 (7 self)
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The computational complexity of a problem is usually defined in terms of the resources required on some machine model of computation. An alternative view looks at the complexity of describing the problem (seen as a collection of relational structures) in a logic, measuring logical resources such as the number of variables, quantifiers, operators, etc. A close correspondence has been observed between these two, with many natural logics corresponding exactly to independently defined complexity classes. For the complexity classes that are generally identified with feasible computation, such characterizations require the presence of a linear order on the domain of every structure, in which case the class PTIME is characterized by an extension of firstorder logic by means of an inductive operator. No logical characterization of feasible computation is known for unordered structures. We approach this question from two directions. On the one hand, we seek to accurately characterize the expre...
Fixpoint Logics, Relational Machines, and Computational Complexity
 In Structure and Complexity
, 1993
"... We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1storder operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have t ..."
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Cited by 36 (5 self)
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We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1storder operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have the complexity classes between P and EXPTIME. Our parameterized fixpoint logics capture the complexity classes P, NP, PSPACE, and EXPTIME, but equality is achieved only over ordered structures. There is, however, an inherent mismatch between complexity and logic  while computational devices work on encodings of problems, logic is applied directly to the underlying mathematical structures. To overcome this mismatch, we develop a theory of relational complexity, which bridges tha gap between standard complexity and fixpoint logic. On one hand, we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complex...
Revision Programming
 THEORETICAL COMPUTER SCIENCE
, 1994
"... In this paper we introduce revision programming  a logicbased framework for describing constraints on databases and providing a computational mechanism to enforce them. Revision programming captures those constraints that can be stated in terms of the membership (presence or absence) of items (re ..."
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Cited by 36 (1 self)
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In this paper we introduce revision programming  a logicbased framework for describing constraints on databases and providing a computational mechanism to enforce them. Revision programming captures those constraints that can be stated in terms of the membership (presence or absence) of items (records) in a database. Each such constraint is represented by a revision rule ff / ff 1 ; : : : ; ff k , where ff and all ff i are of the form in(a) and out(b). Collections of revision rules form revision programs. Similarly as logic programs, revision programs admit both declarative and imperative (procedural) interpretations. In our paper, we introduce a semantics that reflects both interpretations. Given a revision program, this semantics assigns to any database B a collection (possibly empty) of Pjustified revisions of B. The paper contains a thorough study of revision programming. We exhibit several fundamental properties of revision programming. We study the relationship of revision programming to logic programming. We investigate complexity of reasoning with revision programs as well as algorithms to compute P justified revisions. Most importantly from the practical database perspective, we identify two classes of revision programs, safe and stratified, with a desirable property that they determine for each initial database a unique revision.
Pattern Discovery in Temporal Databases: A Temporal Logic Approach
, 1996
"... The work of Mannila et al. [4] of finding frequent episodes in sequences is extended to finding temporal logic patterns in temporal databases. It is argued that temporal logic provides an appropriate formalism for expressing temporal patterns defined over categorical data. It is also proposed t ..."
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Cited by 32 (0 self)
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The work of Mannila et al. [4] of finding frequent episodes in sequences is extended to finding temporal logic patterns in temporal databases. It is argued that temporal logic provides an appropriate formalism for expressing temporal patterns defined over categorical data. It is also proposed to use Temporal Logic Programming as a mechanism for the discovery of frequent patterns expressible in temporal logic. It is explained in the paper how frequent temporal patterns can be discovered by constructing temporal logic programs. To test these methods , temporal logic programs were constructed for certain classes of patterns and were implemented in OPS5. Introduction In this paper, we address the problem of finding interesting patterns in temporal databases [1,2] defined over categorical (symbolic) data. This is an important problem that frequently occurs in various applications such as molecular biology (finding patterns in genetic sequences), telecommunications (finding pat...
Inductive Definability with Counting on Finite Structures
 IN PROC. OF COMPUTER SCIENCE LOGIC 92
, 1993
"... ..."
Programming with Nondeterminism in Deductive Databases
 Annals of Mathematics and Artificial Intelligence
, 1997
"... This paper provides an overview of recent results on this topic with the aim of providing an introduction to the theory and practice of nondeterminism in deductive databases. In particular we (i) recall the main results linking nondeterministic constructs in database languages to the theory of dat ..."
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Cited by 25 (3 self)
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This paper provides an overview of recent results on this topic with the aim of providing an introduction to the theory and practice of nondeterminism in deductive databases. In particular we (i) recall the main results linking nondeterministic constructs in database languages to the theory of data complexity and the expressibility hierarchy of query languages (ii) provide a reasoned introduction to effective programming with nondeterministic constructs (iii) compare the usage of nondeterministic constructs in languages such as
Database Query Languages Embedded in the Typed Lambda Calculus
, 1993
"... We investigate the expressive power of the typed calculus when expressing computations over finite structures, i.e., databases. We show that the simply typed calculus can express various database query languages such as the relational algebra, fixpoint logic, and the complex object algebra. In ..."
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Cited by 25 (6 self)
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We investigate the expressive power of the typed calculus when expressing computations over finite structures, i.e., databases. We show that the simply typed calculus can express various database query languages such as the relational algebra, fixpoint logic, and the complex object algebra. In our embeddings, inputs and outputs are terms encoding databases, and a program expressing a query is a term which types when applied to an input and reduces to an output.
Sequences, Datalog and Transducers
, 1996
"... This paper develops a query language for sequence databases, such as genome databases and text databases. The language, called SequenceDatalog, extends classical Datalog with interpreted function symbols for manipulating sequences. It has both a clear operational and declarative semantics, based on ..."
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Cited by 24 (5 self)
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This paper develops a query language for sequence databases, such as genome databases and text databases. The language, called SequenceDatalog, extends classical Datalog with interpreted function symbols for manipulating sequences. It has both a clear operational and declarative semantics, based on a new notion called the extended active domain of a database. The extended domain contains all the sequences in the database and all their subsequences. This idea leads to a clear distinction between safe and unsafe recursion over sequences: safe recursion stays inside the extended active domain, while unsafe recursion does not. By carefully limiting the amountof unsafe recursion, the paper develops a safe and expressive subset of Sequence Datalog. As part of the development, a new type of transducer is introduced, called a generalized sequence transducer. Unsafe recursion is allowed only within these generalized transducers. Generalized transducers extend ordinary transducers by allowing them to invoke other transducers as "subroutines." Generalized transducers can be implemented in Sequence Datalog in a straightforward way. Moreover, their introduction into the language leads to simple conditions that guarantee safety and finiteness. This paper develops two such conditions. The first condition expresses exactly the class of ptime sequence functions; and the second expresses exactly the class of elementary sequence functions.
The Expressive Power of Finitely Many Generalized Quantifiers
 Information and Computation
, 1995
"... We consider extensions of first order logic (FO) and fixed point logic (FP) by means of generalized quantifiers in the sense of Lindstrom. We show that adding a finite set of such quantifiers to FP fails to capture PTIME, even over a fixed signature. This strengthens results in [10] and [15]. We als ..."
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Cited by 24 (5 self)
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We consider extensions of first order logic (FO) and fixed point logic (FP) by means of generalized quantifiers in the sense of Lindstrom. We show that adding a finite set of such quantifiers to FP fails to capture PTIME, even over a fixed signature. This strengthens results in [10] and [15]. We also prove a stronger version of this result for PSPACE, which enables us to establish a weak version of a conjecture formulated in [16]. These results are obtained by defining a notion of element type for bounded variable logics with finitely many generalized quantifiers. Using these, we characterize the classes of finite structures over which the infinitary logic L ! 1! extended by a finite set of generalized quantifiers Q is no more expressive than first order logic extended by the quantifiers in Q . 1 Introduction Computational complexity measures the complexity of a problem in terms of the resources, such as time, space, or hardware, required to solve the problem relative to a given ma...
Constraint Databases: A Survey
 Semantics in Databases, number 1358 in LNCS
, 1998
"... . Constraint databases generalize relational databases by finitely representable infinite relations. This paper surveys the state of the art in constraint databases: known results, remaining open problems and current research directions. The paper also describes a new algebra for databases with inte ..."
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Cited by 23 (3 self)
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. Constraint databases generalize relational databases by finitely representable infinite relations. This paper surveys the state of the art in constraint databases: known results, remaining open problems and current research directions. The paper also describes a new algebra for databases with integer order constraints and a complexity analysis of evaluating queries in this algebra. In memory of Paris C. Kanellakis 1 Introduction There is a growing interest in recent years among database researchers in constraint databases, which are a generalization of relational databases by finitely representable infinite relations. Constraint databases are parametrized by the type of constraint domains and constraint used. The good news is that for many parameters constraint databases leave intact most of the fundamental assumptions of the relational database framework proposed by Codd. In particular, 1. Constraint databases can be queried by constraint query languages that (a) have a semantics ba...