Proof Complexity of Pigeonhole Principles
نویسنده
چکیده
The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m > n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studied combinatorial principle. In this survey we try to summarize what is known about its proof complexity, and what we would still like to prove. We also mention some applications of the pigeonhole principle to the study of efficient provability of major open problems in computational complexity, as well as some of its generalizations in the form of general matching principles.
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