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Abstract: Gregory McColm conjectured that positive elementary inductions are bounded in a class K of finite structures if every (FO + LFP) formula is equivalent to a first-order formula in K. Here (FO + LFP) is the extension of first-order logic with the least fixed point operator. We disprove the conjecture. Our main results are two model-theoretic constructions, one deterministic and the other randomized, each of which refutes McColm's conjecture. 1 Introduction Gregory McColm conjectured in [?] that, ... (Update)
Context of citations to this paper: More
...arbitrary class of finite structures. Although in its full generality McColm s conjecture was refuted by Gurevich, Immerman and Shelah [GIS94], it sparked a sequence of related investigations in finite model theory [KV92, DH95, KV96, DLW96] Moreover, the following special case...
.... deterministic Turing machines in time 2 O(n) There is a special case of the conjecture, singled out by Gurevich, Immerman, and Shelah [15], that is of particular interest. Namely, it is unknown whether LFP collapses to FO on the class of all finite structures of the form...
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BibTeX entry: (Update)
Y. Gurevich, N. Immerman, and S. Shelah. Mccolm's conjecture. In Proc. 7th IEEE Symp. on Logic in Comp. Sci., pages 10-- 19, 1994. http://citeseer.ist.psu.edu/article/gurevich94mccolms.html More
@inproceedings{ gurevich94mccolms,
author = "Yuri Gurevich and Neil Immerman and Saharon Shelah",
title = "McColm's Conjecture",
booktitle = "Logic in Computer Science",
pages = "10-19",
year = "1994",
url = "citeseer.ist.psu.edu/article/gurevich94mccolms.html" }
Citations (may not include all citations):379 Complexity of Relational Query Languages (context) - Vardi - 1982
149 Logic and the Challenge of Computer Science (context) - Gurevich - 1988
114 Generic Computation And Its Complexity (context) - Abiteboul, Vianu - 1991
98 An Optimal Lower Bound on the Number of Variables for Graph .. - Cai, Furer et al. - 1992
85 Upper and Lower Bounds for First Order Expressibility (context) - Immerman - 1982
78 On Moschovakis Closure Ordinals (context) - Barwise - 1977
66 Describing Graphs: A First-Order Approach to Graph Canonizat.. - Immerman, Lander - 1990
61 Descriptive and Computational Complexity - Immerman - 1989
37 Feasible Computation Through Model Theory - Dawar - 1993
18 On Uniformity Within NC 1 (context) - Barrington, Immerman et al. - 1990
1 When is Arithmetic Possible (context) - McColm - 1990
1 Fixpoint Logic vs. Infinitary Logic in Finite-Model Theory (context) - Kolaitis, Vardi - 1992
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