Describing Graphs a First Order Approach to Graph Canonization
نویسندگان
چکیده
In this paper we ask the question What must be added to rst order logic plus least xed point to obtain exactly the polynomial time properties of unordered graphs We consider the languages Lk consisting of rst order logic restricted to k variables and Ck consisting of Lk plus counting quanti ers We give e cient canonization algorithms for graphs characterized by Ck or Lk It follows from known results that all trees and almost all graphs are characterized by C This paper appeared in Complexity Theory Retrospective Alan Selman ed Springer Verlag
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