A. Atserias, M.L. Bonet, J.L. Esteban. Lower bounds for the weak pigeonhole principle beyond Resolution. Inform. and Comput. 176 (2) pp. 136--152, 2002. Home/Search Document Details and Download
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A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
....also extends previous research on the Res(k) system. The complexity of Res(k) refutations was first studied by Krajcek [24] who was motivated by the connection between Res(polylog(n) and the provability of combinatorial statements in the arithmetic theory T 2 (#) Atserias, Bonet and Esteban [3] gave exponential lower bounds for Res(2) refutations of the 2n to n weak pigeonhole principle and of random 3CNFs. They also proved a quasi polynomial separation between Res(2) and resolution; this separation was later strengthened to almost exponential by Atserias and Bonet [2] Esteban, Galesi ....
.... to almost exponential by Atserias and Bonet [2] Esteban, Galesi and Messner [17] showed that that there is an exponential separation between treelike Res(k) and treelike Res(k 1) The lower bounds for Res(k) refutations of the weak pigeonhole principle given by Atserias, Bonet and Esteban [3] apply only for k = 2; our lower bound works for non constant k, up to log n log log n. On the other hand, Maciel, Pitassi and Woods [25] give quasipolynomial size refutations in Res(polylog(n) Therefore, among depth two, quasi polynomial size refutations of the weak pigeonhole principle, ....
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A. Atserias, M. L. Bonet, and J. L. Esteban. Lower bounds for the weak pigeonhole principle beyond resolution. Lecture Notes in Computer Science, 2076.
Bounded-depth Frege lower bounds for weaker pigeonhole.. - Buresh-Oppenheim.. (Correct)
....lower bounds for the weak pigeonhole principle are out of the question. In fact, this upper bound is provable in a very restricted form of bounded depth Frege where all lines in the proof are disjunctions of polylog n sized conjunctions, a proof system known as Res(polylog n) On the other hand, [2] shows exponential lower bounds for weak pigeonhole principles in Res(2) a proof system which allows lines to be disjunctions of size 2 conjunctions. In this paper we prove quasi polynomial lower bounds for the weak pigeonhole principle whenever m n n=polylog n. More precisely, we show that ....
.... Res(polylog n) proofs of the weak pigeonhole principle which would match the upper bounds in [14] It is conceivable that this could be achieved by proving lower bounds for Res(k) proofs of the weak pigeonhole principle for larger and larger k, extending the exponential lower bound for Res(2) in [2]; but new techniques seem to be needed. Acknowledgments We are very grateful to Alan Woods for suggesting this problem a while back and for the many valuable comments and insights that he shared with us. We also want to thank Mike Molloy for some helpful discussions. Finally, we are grateful to ....
A. Atserias, M. L. Bonet, and J. Esteban. Lower bounds for the weak pigeonhole principle beyond resolution. In J. Orejas, P. G. Spirakis, and J. van Leeuwen, editors, Automata, Languages, and Programming: 28th International Colloquium, volume 2076.
Proof Complexity of Pigeonhole Principles - Razborov (2001) (3 citations) (Correct)
....the gap between R = R(1) and F 1:5 = R(polylog) All our intuition from complexity theory and mathematical logic strongly suggests that the distance between 2 and polylog should be much shorter than between 2 and 1. The last mysterious result (in Section 4. 2 ) due to Atserias, Bonet and Esteban [22] indicates that for the pigeonhole principle the situation is exactly the opposite. Theorem 10 ( 22] SR(2) onto FPHP 2n n ) exp(n= log n) O(1) The case of R(3) is still open. 4.3 Weak PHP m n : m = n 2 (mystery becomes hard labour) The most remarkable thing that happens at this ....
....logic strongly suggests that the distance between 2 and polylog should be much shorter than between 2 and 1. The last mysterious result (in Section 4.2 ) due to Atserias, Bonet and Esteban [22] indicates that for the pigeonhole principle the situation is exactly the opposite. Theorem 10 ([22]) SR(2) onto FPHP 2n n ) exp(n= log n) O(1) The case of R(3) is still open. 4.3 Weak PHP m n : m = n 2 (mystery becomes hard labour) The most remarkable thing that happens at this stop is that the proof method of Theorems 2, 8 also completely breaks down. The question on ....
Atserias, A., Bonet, M.L., Esteban, J.L.: Lower bounds for the weak pigeonhole principle beyond resolution. To appear in Information and Computation (2000)
On the Complexity of Resolution with Bounded Conjunctions - Esteban, Galesi, Messner (2004) (5 citations) Self-citation (Esteban) (Correct)
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A. Atserias, M.L. Bonet, J.L. Esteban. Lower bounds for the weak pigeonhole principle beyond Resolution. Inform. and Comput. 176 (2) pp. 136--152, 2002.
A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
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A. Atserias, M. L. Bonet, and J. L. Esteban. Lower bounds for the weak pigeonhole principle beyond resolution. Lecture Notes in Computer Science, 2076.
An Optimal Lower Bound for Resolution with - Conjunctions Jan Johannsen (Correct)
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A. Atserias, M. L. Bonet, and J. L. Esteban. Lower bounds for the weak pigeonhole principle beyond resolution, 2002.
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