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Abstract: We study two important extensions of first-order logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain can be reduced to a while computation over an ordered domain via a fixpoint query. The... (Update)
Context of citations to this paper: More
...models for FO logic and monadic 1 logic, respectively. Vaguely similar machine models are known for relational databases [Lei89, GPPdB94, AV95]. Informally the FO automaton works as follows. First it nondeterministically pebbles vertices b 1 ; b g of its input...
.... known cases when expressivity bounds for query languages cannot be proved without separating complexity classes; see, for example, [2]. 7. CONCLUSIONS In this paper we studied the problem of adding aggregate operators to logics. We were primarily motivated by problems...
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30: Relational queries computable in polynomial time - Immerman - 1986
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BibTeX entry: (Update)
S. Abiteboul and V. Vianu. Computing with firstorder logic. J. of Computer and System Sciences, 50(2):309--335, 1995. http://citeseer.ist.psu.edu/abiteboul95computing.html More
@article{ abiteboul95computing,
author = "Serge Abiteboul and Victor Vianu",
title = "Computing with First-Order Logic",
journal = "Journal of Computer and System Sciences",
volume = "50",
number = "2",
pages = "309-335",
year = "1995",
url = "citeseer.ist.psu.edu/abiteboul95computing.html" }
Citations (may not include all citations):1911 Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
981 Principles of Database and Knowledge Base Systems (context) - Ullman - 1988
775 Foundations of Databases (context) - Abiteboul, Hull et al. - 1994
379 The complexity of relational query languages (context) - Vardi - 1982
280 Object identity as a query language primitive (context) - Abiteboul, Kanellakis - 1989
245 Relational queries computable in polynomial time - Immerman - 1986
232 Optimal implementation on conjunctive queries in relational .. (context) - Chandra, Merlin - 1977
198 Structure and complexity of relational queries - Chandra, Harel - 1982
189 Computable queries for relational databases - Chandra, Harel - 1980
149 Logic and the challenge of computer science (context) - Gurevich - 1988
124 Datalog extensions for database queries and updates (context) - Abiteboul, Vianu - 1991
114 Generic computation and its complexity (context) - Abiteboul, Vianu - 1991
95 Fixed-point extensions of first-order logic (context) - Gurevich, Shelah - 1986
90 Horn clause queries and generalizations (context) - Chandra, Harel - 1985
88 Elements of relational database theory (context) - Kanellakis - 1991
57 Infinitary logic and inductive definability over finite stru.. - Dawar, Lindell et al. - 1991
49 Theory of database queries (context) - Chandra - 1988
46 Finite model theory -- a personal perspective - Fagin - 1990
44 Procedural languages for database queries and updates (context) - Abiteboul, Vianu - 1990
39 Expressibility as a complexity measure: Results and directio.. (context) - Immerman - 1987
38 Languages which capture complexity classes (context) - Immerman - 1987
36 and computational complexity (context) - Abiteboul, Vardi et al. - 1992
36 laws and decision problems for fragments of second-order log.. (context) - Kolaitis, Vardi - 1990
32 Programming primitives for database languages (context) - Chandra - 1981
29 Descriptive characterization of computational complexity (context) - Leivant - 1989
18 Kombinatorische anzahlbestimmungen fur gruppen (context) - P'olya - 1937
15 An analysis of fixed-point queries on binary trees (context) - Lindell - 1990
10 The number of finite relational structures (context) - Fagin - 1977
10 The power of reflective relational machines - Abiteboul, Papadimitriou et al. - 1994
10 Computing with infinitary logic - Abiteboul, Vardi et al. - 1992
8 Monotonic use of space and computational complexity over abs.. (context) - Leivant - 1989
7 Optimizing active databases using the split technique - Abiteboul, Van Gelder - 1992
6 Queries are easier than you thought (context) - Abiteboul, Compton et al. - 1992
6 Axiomatic recursive function theory (context) - Friedman - 1971
6 The power of methods with parallel semantics (context) - Denninghoff, Vianu - 1991
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www-cse.ucsd.edu/~vianu/): More
Databases and Finite-Model Theory - Vianu (1997) (Correct)
A Probabilistic View of Datalog Parallelization - Lifschitz, Vianu (1993) (Correct)
Computing with Infinitary Logic - Abiteboul, Vardi (1995) (Correct)
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