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

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

2009-10-16

arxiv.org/abs/0910.3085v2

LMCS 6 (1:4) 2010

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-6(1:4)2010

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.

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