Logical Methods in Computer Science (Feb 2010)

Guarded Second-Order Logic, Spanning Trees, and Network Flows

  • Achim Blumensath

DOI
https://doi.org/10.2168/LMCS-6(1:4)2010
Journal volume & issue
Vol. Volume 6, Issue 1

Abstract

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According to a theorem of Courcelle monadic second-order logic and guarded second-order logic (where one can also quantify over sets of edges) have the same expressive power over the class of all countable $k$-sparse hypergraphs. In the first part of the present paper we extend this result to hypergraphs of arbitrary cardinality. In the second part, we present a generalisation dealing with methods to encode sets of vertices by single vertices.

Keywords