Abstract
In this paper we ask the question, “What must be added to first-order logic plus least-fixed point to obtain exactly the polynomial-time properties of unordered graphs?” We consider the languages L k consisting of first-order logic restricted to k variables and C k consisting of L k plus “counting quantifiers”. We give efficient canonization algorithms for graphs characterized by C k or L k . It follows from known results that all trees and almost all graphs are characterized by C 2.
Research supported by NSF grants DCR-8603346 and CCR-8806308. Part of this work was done in the Fall of 1985 while this author was visiting the Mathematical Sciences Research Institute, Berkeley, CA.
Research supported by grants from the National Science Foundation (DCB-8611317) and from the System Development Foundation (G612).
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Immerman, N., Lander, E. (1990). Describing Graphs: A First-Order Approach to Graph Canonization. In: Selman, A.L. (eds) Complexity Theory Retrospective. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4478-3_5
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DOI: https://doi.org/10.1007/978-1-4612-4478-3_5
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