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Abstract: We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result... (Update)
Cited by: More
Toward Logic Tailored for Computational Complexity - Yuri Gurevich Computer (1984) (Correct)
Existential Second-Order Logic over Strings (Extended.. - Eiter, Gottlob, Gurevich (1997) (Correct)
Metafinite Model Theory - Erich Gradel Yuri (1995) (Correct)
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0.2: Fixpoint Logics, Relational Machines, and Computational.. - Abiteboul, Vardi, Vianu (1997) (Correct)
0.2: Logical Characterizations of Complexity Classes - Stewart (1997) (Correct)
0.2: Padding and the Expressive Power of Existential Second-Order.. - Schwentick (1997) (Correct)
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0.3: Structure and Complexity of Relational Queries - Chandra, Harel (1982) (Correct)
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83: The complexity of relational query languages (context) - Vardi - 1982
45: Structure and complexity of relational queries - Chandra, Harel - 1982
36: Fixed-point extensions of first-order logic (context) - Gurevich, Shelah - 1986
BibTeX entry: (Update)
N. Immerman. Relational queries computable in polynomial time. Information and Control, 68:86--104, 1986. http://citeseer.ist.psu.edu/immerman86relational.html More
@inproceedings{ immerman82relational,
author = "Neil Immerman",
title = "Relational Queries Computable in Polynomial Time (Extended Abstract)",
booktitle = "{ACM} Symposium on Theory of Computing",
pages = "147-152",
year = "1982",
url = "citeseer.ist.psu.edu/immerman86relational.html" }
Citations (may not include all citations):1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
379 Complexity of Relational Query Languages (context) - Vardi - 1982
370 A Mathematical Introduction to Logic (context) - Enderton - 1972
245 Relational Queries Computable in Polynomial Time - Immerman - 1982 ACM DBLP
210 Generalized First-Order Spectra and Polynomial-Time Recogniz.. (context) - Fagin - 1974
189 Computable Queries for Relational Databases - Chandra, Harel - 1980
185 Principles of Database Systems (context) - Ullman - 1982 ACM
163 Universality of Data Retrieval Languages (context) - Aho, Ullman - 1979 ACM
120 Elementary Induction on Abstract Structures (context) - Moschovakis - 1974
108 Relational Completeness of Database Sublanguages (context) - Codd - 1972
95 Fixed-Point Extensions of First-Order Logic (context) - Gurevich, Shelah - 1985 DBLP
85 Upper and Lower Bounds for First Order Expressibility (context) - Immerman - 1982 DBLP
48 Borel Sets and Circuit Complexity (context) - Sipser - 1983 ACM DBLP
45 Parity, Circuits, and the PolynomialTime Hierarchy (context) - Furst, Saxe et al. - 1981
38 Languages Which Capture Complexity Classes (context) - Immerman - 1983 ACM
36 Number of Quantifiers is Better than Number of Tape Cells (context) - Immerman - 1981 ACM DBLP
32 Programming Primitives for Database Languages (context) - Chandra - 1981 ACM DBLP
5 Uniform Definability on Finite Structures with Successor (context) - de Rougemont - 1984 ACM DBLP
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cs.umass.edu/~immerman/pub_immerman.html): More
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