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Abstract: We consider infinitary logic with two variable symbols and counting quantifiers, C , and its intersection with Ptime on finite relational structures. In particular we exhibit a Ptime canonization procedure for finite relational structures which provides unique representatives up to equivalence in C . As a consequence we obtain a recursive presentation for the class of all those queries on arbitrary finite relational structures which are both Ptime and definable in C . The proof renders ... (Update)
Context of citations to this paper: More
...all L k equivalence relations is precisely equivalence in first order logic, which is the same as isomorphism on finite structures. Martin Otto [14] proved that L 2 equivalence admits P canonization and thus that there is a logic capturing L 2 ( equivalence) invariant P. Our...
...first structure A with respect to of size at most g(jI j) with I k (f(I) I if such a structure exists, and arbitrary otherwise. Otto [62] proved that for k = 2 the answer to Questions 1 and 2 is yes . Actually, he proved more: Theorem 5.1 (Otto [62] For each vocabulary...
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BibTeX entry: (Update)
M. Otto. Ptime canonization for two variables with counting. In Proceedings of the 10th IEEE Symposium on Logic in Computer Science, pages 342--352, 1995. http://citeseer.ist.psu.edu/otto95ptime.html More
@inproceedings{ otto95ptime,
author = "Martin Otto",
title = "Ptime Canonization for Two Variables with Counting",
booktitle = "Logic in Computer Science",
pages = "342-352",
year = "1995",
url = "citeseer.ist.psu.edu/otto95ptime.html" }
Citations (may not include all citations):379 Complexity of Relational Query Languages (context) - Vardi - 1982
245 Relational Queries Computable in Polynomial Time - Immerman - 1986 ACM DBLP
149 Logic and the Challenge of Computer Science (context) - Gurevich - 1988
85 Upper and Lower Bounds for First-Order Expressibility (context) - Immerman - 1982
78 On Moschovakis Closure Ordinals (context) - Barwise - 1977 DBLP
66 Describing Graphs: A First Order Approach to Graph Canonizat.. - Immerman, Lander - 1990
57 Infinitary Logic and Inductive Definability over Finite Stru.. - Dawar, Lindell et al. - 1991 ACM DBLP
37 Feasible Computation through Model Theory - Dawar - 1993 ACM
33 A Decision Method for Validity of Sentences in Two Variables (context) - Scott - 1962
33 Information and Computation (context) - Kolaitis, Vardi et al. - 1992 DBLP
29 Deux ou trois choses que je sais de Ln (context) - Poizat - 1982
28 Zeitschrift fur mathematische Logik und Grundlagen der Mathe.. (context) - Mortimer, with et al. - 1975
26 Inductive Definability with Counting on Finite Structures - Gradel, Otto - 1993 ACM DBLP
18 The Expressive Power of Fixed-Point Logic with Counting (context) - Otto - 1994 DBLP
11 Canonical Labellings of Graphs in Linear Average Time (context) - Babai, Kucera - 1980
5 rd ACM Symp (context) - Abiteboul, Vianu et al. - 1991
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