A note on proofs with graphs

Authors:
Renata de Freitas;Petrucio Viana
Affiliations:
Institute of Mathematics, Fluminense Federal University, Brazil;Institute of Mathematics, Fluminense Federal University, Brazil
Venue:
Science of Computer Programming
Year:
2008

Citing 9
Cited 1

Proofs with graphs

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Algebra of programming

Algebra of programming
Linear-time computability of combinatorial problems on series-parallel graphs

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Electronic Notes in Theoretical Computer Science (ENTCS)

A calculus for graphs with complement

Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference

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Abstract

Curtis and Lowe (S. Curtis, G. Lowe, Proofs with graphs, Sci. Comput. Program. 26 (1996) 197-216) presented a graphical calculus to prove inclusions between relations, leaving completeness of the system as an open question. Here we recast their system, excluding complementation and union, by presenting a low complexity decision algorithm to decide its valid inclusions. Completeness follows as a corollary.