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Reachability is harder for directed than for undirected finite graphs

Published online by Cambridge University Press:  12 March 2014

Miklos Ajtai  and
Ronald Fagin
Miklos Ajtai
Affiliation:
IBM Almaden Research Center, San Jose, California 95120
Ronald Fagin
Affiliation:
IBM Almaden Research Center, San Jose, California 95120
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Abstract

Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic second-order sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain “built-in” relations, such as the successor relation). The proof makes use of Ehrenfeucht-Fraïssé games, along with probabilistic arguments. However, we show that for directed finite graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 1 , March 1990 , pp. 113 - 150
Copyright
Copyright © Association for Symbolic Logic 1990

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