FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2963930882> ?p ?o ?g. }

• W2963930882 endingPage "1462" @default.
• W2963930882 startingPage "1424" @default.
• W2963930882 abstract "Does every Boolean tautology have a short propositional-calculus proof? Here, a propositional-calculus (i.e., Frege) proof is any proof starting from a set of axioms and deriving new Boolean formulas using a fixed set of sound derivation rules. Establishing any superpolynomial-size lower bound on Frege proofs (in terms of the size of the formula proved) is a major open problem in proof complexity and among a handful of fundamental hardness questions in complexity theory. Noncommutative algebraic formulas, on the other hand, constitute a quite weak computational model, for which exponential-size lower bounds were shown back in 1991 by Nisan [Proceedings of STOC, 1991, pp. 410--418], using a particularly transparent argument. In this work we show that Frege lower bounds in fact follow from size lower bounds on noncommutative formulas computing certain families of polynomials (and that such lower bounds on noncommutative formulas must exist, unless (NP=coNP). More precisely, we demonstrate a natural association between tautologies $T$ to families of noncommutative polynomials $P$ such that if $T$ has a polynomial-size Frege proof, then some noncommutative polynomial in $P$ can be computed by a polynomial-size noncommutative algebraic formula, and conversely, when $T$ is a formula in disjunctive normal form, if some polynomial in $P$ has a polynomial-size noncommutative algebraic formula over $GF(2)$, then $T$ has a Frege proof of quasi-polynomial size. The argument is a characterization of Frege proofs as noncommutative formulas: we show that the Frege system is (quasi-) polynomially equivalent to a noncommutative ideal proof system(IPS), following the recent work of Grochow and Pitassi [Proceedings of FOCS, 2014, pp. 110--119] that introduced a propositional proof system in which proofs are algebraic circuits and the work in [I. Tzameret, Inform. Comput., 209 (2011), pp. 1269--1292] that considered adding the commutator as an axiom in algebraic propositional proof systems. This also gives a characterization of propositional Frege proofs in terms of (noncommutative) algebraic formulas that is tighter than (the formula version of IPS) in Grochow and Pitassi [Proceedings of FOCS, 2014, pp. 110--119]." @default.
• W2963930882 created "2019-07-30" @default.
• W2963930882 creator A5019424035 @default.
• W2963930882 creator A5066962007 @default.
• W2963930882 creator A5080958670 @default.
• W2963930882 date "2018-01-01" @default.
• W2963930882 modified "2023-09-26" @default.
• W2963930882 title "Characterizing Propositional Proofs as Noncommutative Formulas" @default.
• W2963930882 cites W1964394232 @default.
• W2963930882 cites W1968655942 @default.
• W2963930882 cites W1982672583 @default.
• W2963930882 cites W1988083342 @default.
• W2963930882 cites W1988738948 @default.
• W2963930882 cites W1999069928 @default.
• W2963930882 cites W2009994177 @default.
• W2963930882 cites W2029390834 @default.
• W2963930882 cites W2034804004 @default.
• W2963930882 cites W2044632231 @default.
• W2963930882 cites W2062310247 @default.
• W2963930882 cites W2074020517 @default.
• W2963930882 cites W2080132708 @default.
• W2963930882 cites W2090449431 @default.
• W2963930882 cites W2091628344 @default.
• W2963930882 cites W2110206454 @default.
• W2963930882 cites W2114400329 @default.
• W2963930882 cites W2121894367 @default.
• W2963930882 cites W2130566259 @default.
• W2963930882 cites W2158912767 @default.
• W2963930882 cites W2166026605 @default.
• W2963930882 cites W2167115661 @default.
• W2963930882 cites W2169713712 @default.
• W2963930882 cites W2323554188 @default.
• W2963930882 cites W2460222798 @default.
• W2963930882 cites W4212786702 @default.
• W2963930882 doi "https://doi.org/10.1137/16m1107632" @default.
• W2963930882 hasPublicationYear "2018" @default.
• W2963930882 type Work @default.
• W2963930882 sameAs 2963930882 @default.
• W2963930882 citedByCount "4" @default.
• W2963930882 countsByYear W29639308822019 @default.
• W2963930882 countsByYear W29639308822021 @default.
• W2963930882 countsByYear W29639308822022 @default.
• W2963930882 crossrefType "journal-article" @default.
• W2963930882 hasAuthorship W2963930882A5019424035 @default.
• W2963930882 hasAuthorship W2963930882A5066962007 @default.
• W2963930882 hasAuthorship W2963930882A5080958670 @default.
• W2963930882 hasBestOaLocation W29639308822 @default.
• W2963930882 hasConcept C105605280 @default.
• W2963930882 hasConcept C108710211 @default.
• W2963930882 hasConcept C114614502 @default.
• W2963930882 hasConcept C118615104 @default.
• W2963930882 hasConcept C134306372 @default.
• W2963930882 hasConcept C202444582 @default.
• W2963930882 hasConcept C2524010 @default.
• W2963930882 hasConcept C33923547 @default.
• W2963930882 hasConcept C68797384 @default.
• W2963930882 hasConcept C90119067 @default.
• W2963930882 hasConcept C9376300 @default.
• W2963930882 hasConceptScore W2963930882C105605280 @default.
• W2963930882 hasConceptScore W2963930882C108710211 @default.
• W2963930882 hasConceptScore W2963930882C114614502 @default.
• W2963930882 hasConceptScore W2963930882C118615104 @default.
• W2963930882 hasConceptScore W2963930882C134306372 @default.
• W2963930882 hasConceptScore W2963930882C202444582 @default.
• W2963930882 hasConceptScore W2963930882C2524010 @default.
• W2963930882 hasConceptScore W2963930882C33923547 @default.
• W2963930882 hasConceptScore W2963930882C68797384 @default.
• W2963930882 hasConceptScore W2963930882C90119067 @default.
• W2963930882 hasConceptScore W2963930882C9376300 @default.
• W2963930882 hasFunder F4320321001 @default.
• W2963930882 hasIssue "4" @default.
• W2963930882 hasLocation W29639308821 @default.
• W2963930882 hasLocation W29639308822 @default.
• W2963930882 hasOpenAccess W2963930882 @default.
• W2963930882 hasPrimaryLocation W29639308821 @default.
• W2963930882 hasRelatedWork W2020855749 @default.
• W2963930882 hasRelatedWork W2461309715 @default.
• W2963930882 hasRelatedWork W2461509449 @default.
• W2963930882 hasRelatedWork W2471400301 @default.
• W2963930882 hasRelatedWork W2573730213 @default.
• W2963930882 hasRelatedWork W2962731772 @default.
• W2963930882 hasRelatedWork W2962908760 @default.
• W2963930882 hasRelatedWork W2989887679 @default.
• W2963930882 hasRelatedWork W3035076537 @default.
• W2963930882 hasRelatedWork W4213091458 @default.
• W2963930882 hasVolume "47" @default.
• W2963930882 isParatext "false" @default.
• W2963930882 isRetracted "false" @default.
• W2963930882 magId "2963930882" @default.
• W2963930882 workType "article" @default.