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Maximum Matching and Linear Programming in Fixed-Point Logic with Counting
[article]
2013
arXiv
pre-print
We establish the expressibility in fixed-point logic with counting (FPC) of a number of natural polynomial-time problems. In particular, we show that the size of a maximum matching in a graph is definable in FPC. This settles an open problem first posed by Blass, Gurevich and Shelah, who asked whether the existence of perfect matchings in general graphs could be determined in the more powerful formalism of choiceless polynomial time with counting. Our result is established by showing that the
arXiv:1304.6870v1
fatcat:jp4v3sxrvfb6rolqnpkpumrsei