Guarded Second-Order Logic, Spanning Trees, and Network Flows
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 hyperg...
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2010-02-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/1207/pdf |
| Summary: | 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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| ISSN: | 1860-5974 |