AbstractWe show that every resolution proof of the functional version FPHPnm of the pigeonhole principle (in which one pigeon may not split between several holes) must have size exp(Ω(n/(logm)2)). This implies an exp(Ω(n1/3)) bound when the number of pigeons m is arbitrary
AbstractWe show that the known bounded-depth proofs of the Weak Pigeonhole Principle PHPn2n in size ...
We see that the version of the pigeon-hole principle in which every hole is forced to receive a pi...
AbstractWe work with an extension of Resolution, called Res(2), that allows clauses with conjunction...
Abstract The relativized weak pigeonhole principle states that if at least 2n out of n 2 pigeons fly...
We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower ...
The relativized weak pigeonhole principle states that if at least 2n out of n2 pigeons fly into n ho...
The relativized weak pigeonhole principle states that if at least 2n out of n2 pigeons fly into n ho...
Despite the fact that the resolution proof system has been extensively studied for decades, a full u...
Despite the fact that the resolution proof system has been extensively studied for decades, a full u...
The relativized weak pigeonhole principle states that if at least 2n out of n(2) pigeons fly into n ...
AbstractWe work with an extension of Resolution, called Res(2), that allows clauses with conjunction...
We extend results of A. Haken to give an exponential lower bound on the size of resolution proofs f...
AbstractWe extend results of Haken to give an exponential lower bound on the size of resolution proo...
We work with an extension of Resolution, called Res(2), that allows clauses with conjunc-tions of tw...
AbstractWe extend results of Haken to give an exponential lower bound on the size of resolution proo...
AbstractWe show that the known bounded-depth proofs of the Weak Pigeonhole Principle PHPn2n in size ...
We see that the version of the pigeon-hole principle in which every hole is forced to receive a pi...
AbstractWe work with an extension of Resolution, called Res(2), that allows clauses with conjunction...
Abstract The relativized weak pigeonhole principle states that if at least 2n out of n 2 pigeons fly...
We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower ...
The relativized weak pigeonhole principle states that if at least 2n out of n2 pigeons fly into n ho...
The relativized weak pigeonhole principle states that if at least 2n out of n2 pigeons fly into n ho...
Despite the fact that the resolution proof system has been extensively studied for decades, a full u...
Despite the fact that the resolution proof system has been extensively studied for decades, a full u...
The relativized weak pigeonhole principle states that if at least 2n out of n(2) pigeons fly into n ...
AbstractWe work with an extension of Resolution, called Res(2), that allows clauses with conjunction...
We extend results of A. Haken to give an exponential lower bound on the size of resolution proofs f...
AbstractWe extend results of Haken to give an exponential lower bound on the size of resolution proo...
We work with an extension of Resolution, called Res(2), that allows clauses with conjunc-tions of tw...
AbstractWe extend results of Haken to give an exponential lower bound on the size of resolution proo...
AbstractWe show that the known bounded-depth proofs of the Weak Pigeonhole Principle PHPn2n in size ...
We see that the version of the pigeon-hole principle in which every hole is forced to receive a pi...
AbstractWe work with an extension of Resolution, called Res(2), that allows clauses with conjunction...
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