Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The combinatorial matching principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching beten them. Therefore, it follows from recent lor bounds for the pigeonhole principle that the matching principle requires exponential-size bounded-depth Frege proofs. M. Ajtai (1990) previously shod that the matching principle does not have polynomial-size bounded-depth Frege proofs even with the pigeonhole principle as an axiom schema. His proof utilizes nonstandard model theory and is nonconstructive.  improve Ajtai's lor bound from barely superpolynomial to exponential, and eliminate the nonstandard model theory. Our lor bound is also related to the inherent complexity of particular search classes. In particular, oracle separations beten the complexity classes PPA and PPAD and beten PPA and PPP follow from our techniques. >
['Paul Beame', 'Toniann Pitassi']
I am writing a research paper on a idea An exponential separation between the matching principle and the pigeonhole principle
[{"from": "human", "value": "I am writing a research paper on a idea An exponential separation between the matching principle and the pigeonhole principle"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The combinatorial matching principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching beten them. Therefore, it follows from recent lor bounds for the pigeonhole principle that the matching principle requires exponential-size bounded-depth Frege proofs. M. Ajtai (1990) previously shod that the matching principle does not have polynomial-size bounded-depth Frege proofs even with the pigeonhole principle as an axiom schema. His proof utilizes nonstandard model theory and is nonconstructive.  improve Ajtai's lor bound from barely superpolynomial to exponential, and eliminate the nonstandard model theory. Our lor bound is also related to the inherent complexity of particular search classes. In particular, oracle separations beten the complexity classes PPA and PPAD and beten PPA and PPP follow from our techniques. >"}]