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Abstract: this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes. For example, we show that a property of graphs (respectively groups, binary strings, etc.) is in polynomial time if and only if it is expressible in the first order language of graphs (respectively groups, binary strings, etc.) together with a least fixed point operator. As another example, a property is in logspace if and only if it is expressible in... (Update)
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BibTeX entry: (Update)
Neil Immerman. Languages that capture complexity classes. SIAM Journal of Computing, 16:760-- 778, 1987. http://citeseer.ist.psu.edu/89379.html More
@article{ immerman87languages,
author = "Neil Immerman",
title = "Languages That Capture Complexity Classes",
journal = "SIAM Journal of Computing",
volume = "16",
number = "4",
pages = "760--778",
year = "1987",
url = "citeseer.ist.psu.edu/89379.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
163 Universality of Data Retrieval Languages (context) - Aho, Ullman - 1979 ACM
92 Constant Depth Reducibility (context) - Chandra, Stockmeyer et al. - 1984 DBLP
85 Upper and Lower Bounds for First Order Expressibility (context) - Immerman - 1982 DBLP
69 The Polynomial-Time Hierarchy (context) - Stockmeyer - 1977 DBLP
48 A Complexity Theory Based on Boolean Algebra (context) - Skyum, Valiant - 1985 ACM 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
43 Symmetric Space Bounded Computation (context) - Lewis, Papadimitriou - 1982
38 Simulation of Parallel Random Access Machines by Circuits (context) - Stockmeyer, Vishkin - 1984 DBLP
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
34 Alternation (context) - Chandra, Stockmeyer et al. - 1981 ACM DBLP
33 The Monotone and Planar Circuit Value Problems are Log Space.. (context) - Goldschlager - 1977 ACM
23 Reducibility By Algebraic Projections (context) - Valiant - 1982
20 Complexity Classes and Theories of Finite Models (context) - Lynch - 1982 DBLP
20 Random Walks, Universal Traversal Sequences, and the Complex.. (context) - Karp, Lov'az - 1979 DBLP
17 Symmetric Complementation (context) - Reif - 1984 ACM DBLP
15 Maze Recognizing Automata and Nondeterministic Tape Complexi.. (context) - Savitch - 1973 DBLP
11 One-Way Log Tape Reductions (context) - Hartmanis, Immerman et al. - 1978
11 Sigma 1 1 Formulae on Finite Structures (context) - Ajtai - 1983
10 The Spectra of First-Order Sentences and Computational Compl.. (context) - Grandjean - 1984 DBLP
9 the Definability of Properties of Finite Graphs (context) - Tur'an
4 Separating the Polynomial-Time Hierarchy by Oracles (context) - Yao - 1985 ACM
2 Some Remarks on Generalized Spectra (context) - Lov'asz, G'acs - 1977
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