T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In Proceedings of the 33rd annual ACM Symposium on Theory Of Computing, pages 347--355, 2001. Home/Search Document Details and Download
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A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
....to compute with depth d circuits of bottom fan in k. Because resolution may be viewed as Res(1) our results for Res(k) generalize known results for resolution. The weak pigeonhole principle (for any number of pigeons) is known to require an exponential number of steps to refute in resolution [31, 20, 32, 12, 6, 16, 26, 28, 29], and we generalize these lower bounds for the case of the cn to n pigeonhole principle. Resolution refutations of randomly chosen sets of clauses are also known to require exponential size [14, 6, 5, 9] We extend these results to general Res(k) systems, although as k increases, so does the width ....
T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In ACM Symposium on Theory of Computing (STOC), 2001.
Size Space tradeoffs for Resolution - Ben-Sasson (2002) (Correct)
.... years, several size lower bounds have been obtained for various families of CNF formulas, starting with the lower bound of Tseitin for regular resolution presented in 1968 [34] and followed by the lower bound of Haken in 1985 [24] that eventually let the way to many other such bounds (e.g. [35, 20, 6, 14, 30, 31] and many others) A second complexity measure, closely related to the size is the minimal width, measured as the maximal size of a clause in the proof. This measure, introduced by [14] is actually a space measure, as it counts the maximal space a single clause will occupy in a proof. ....
T. Pitassi, R. Raz. Regular Resolution lower bounds for the Weak Pigeonhole Principle. In Proceedings of the 33rd ACM STOC, 2001.
Lower Bounds for the Weak Pigeonhole Principle and.. - Atserias, Bonet, Esteban (2002) (1 citation) (Correct)
....allowing the number of pigeons to be greater than n 1. We call this principle weak pigeonhole principle, or PHP m n , when the number of pigeons m is at least 2n. This simple principle is central to many mathematical arguments but quite often, it occurs implicitely only. See the introductions in [14, 16] for a nice discussion on this. The proof techniques of Haken where extended in [9] to prove that PHP n 2 Gammaffl n requires exponential size proofs in Resolution. A very intriguing and often studied open problem is to prove exponential size lower bounds for Resolution proofs of PHP m n for ....
T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. to appear in STOC'
Proof Complexity of Pigeonhole Principles - Razborov (2001) (3 citations) (Correct)
....A resolution proof is called regular if along every path in this proof every literal is resolved at most once. Proofs in every one of the two subsystems of Resolution considered in [24] are in fact regular. The following result by Pitassi and Raz made a major improvement on [24] Theorem 14 ([25]) Every regular resolution proof of FPHP n 2 n must have size exp(n= log n) O(1) Shortly after Raz [26] came up with a complete solution for the basic version PHP m n . By Theorem 11, this immediately extends to the onto version. Theorem 15 ( 26] SR (onto PHP n 2 n ) exp(n= log ....
....all of them were originally stated in this form) Theorem 18 ( 24] Every rectangular calculus proof of FPHP 1 n must have size exp( n 1=2 ) Theorems 17 and 18 determine the rectangular calculus complexity of the very weak pigeonhole principle up to a logarithmic factor. Theorem 19 ([25]) Every regular resolution proof of FPHP 1 n must have size exp(n (1) Theorem 20 ( 26] SR (onto PHP 1 n ) exp(n (1) 26] also estimates the constant assumed in the expression n (1) above as between 1=10 and 1=8. Theorem 21 ( 27 29] SR (onto FPHP 1 n ) exp( n 1=3 ....
Pitassi, T., Raz, R.: Regular resolution lower bounds for the weak pigeonhole principle. In: Proceedings of the 33rd ACM Symposium on the Theory of Computing. (2001) 347-355
P != NP , Propositional Proof Complexity, and Resolution Lower.. - Raz (2002) Self-citation (Raz) (Correct)
....Resolution failed to give lower bounds for the weak pigeonhole principle. In particular, for m n , no non trivial lower bound was known until very recently. In the last two years, these problems were completely solved. An exponential lower bound for any Regular Resolution proof was proved in [8], and an exponential lower bound for any Resolution proof was nally proved in [9] More precisely, it was proved in [9] that for any m, any Resolution proof for the weak pigeonhole principle WPHP n is of length ) where 0 is some global constant ( 1=8) The lower bound was further ....
....[15] in fact, this was one of the main motivations to consider the onto functional case) Otherwise, the proof seems to be quite robust in the way the Boolean circuit is encoded. Acknowledgement I would like to thank Toni Pitassi for very enjoying collaboration that lead to the results in [8, 9]. ....
Pitassi, T., and Raz, R., \Regular resolution lower bounds for the weak pigeonhole principle," Symposium on Theory of Computing, 2001, pp. 347-355.
Resolution Lower Bounds for the Weak Pigeonhole Principle - Raz (2001) (21 citations) Self-citation (Raz) (Correct)
....was known. A partial progress was made by Razborov, Wigderson and Yao, who proved exponential lower bounds for Regular Resolution proofs, but only when the Regular Resolution proof is of a certain restricted form [RWY] An exponential lower bound for any Regular Resolution proof was proved in [PR]. In this paper, we prove an exponential lower bound for any Resolution proof. More precisely, we prove that for any m, any Resolution proof for the weak pigeon hole principle, WPHP n , is of ) where ffl 0 is some global constant) 1.1 Lower Bounds for NP 6ae P=poly As mentioned above, ....
Pitassi, T., and Raz, R., "Regular resolution lower bounds for the weak pigeonhole principle," Symposium on Theory of Computing, 2001.
On Resolution Complexity of Matching Principles - Dantchev (2002) (Correct)
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T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In Proceedings of the 33rd annual ACM Symposium on Theory Of Computing, pages 347--355, 2001.
Resolution Lower Bounds for Perfect Matching Principles - Razborov (2004) (14 citations) (Correct)
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T. Pitassi, R. Raz, Regular resolution lower bounds for the weak pigeonhole principle, in: Proceedings of the 33rd ACM Symposium on the Theory of Computing, 2001, pp. 347--355.
Resolution Lower Bounds for the Weak Functional Pigeonhole.. - Razborov (2002) (3 citations) (Correct)
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T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In Proceedings of the 33rd ACM Symposium on the Theory of Computing, pages 347-355, 2001.
A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
No context found.
T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In ACM Symposium on Theory of Computing (STOC), 2001.
The Complexity of Resource-Bounded Propositional Proofs - Atserias (2001) (Correct)
No context found.
T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In 33rd Annual ACM Symposium on the Theory of Computing, pages 347--355, 2001.
A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
No context found.
T. Pitassi and R. Raz. Regular resolution lower bounds for the weak pigeonhole principle. In Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing, pages 347--355, 2001.
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