. "103" . "RIV/67985840:_____/11:00369680!RIV12-AV0-67985840" . . . . . "Proceedings of the London Mathematical Society" . "We give combinatorial principles GI(k), based on k-turn games, which are complete for the class of NP search problems provably total at the kth level T(2)(k) of the bounded arithmetic hierarchy and hence characterize the for all Sigma(b)(1) consequences of T(2)(k). Our argument uses a translation of first-order proofs into large, uniform propositional proofs in a system in which the soundness of the rules can be witnessed by polynomial time reductions between games. We show that for all(Sigma) over cap (b)(1)(alpha) conservativity of T(2)(i+1) (alpha) over T(2)(i)(alpha) already implies. for all(Sigma) over cap (b)(1)(a) conservativity of T(2)(alpha) over T(2)(i)(alpha). We translate this into propositional form and give a polylogarithmic width CNF (GI(3)) over bar such that if (GI(3)) over bar has small R(log) refutations then so does any polylogarithmic width CNF which has small constant depth refutations. We prove a resolution lower bound for (GI(3)) over bar."@en . "The provably total search problems of bounded arithmetic"@en . . "1"^^ . "1" . "Pigeonhole principle; polynomial hierarchy; local search"@en . . "RIV/67985840:_____/11:00369680" . "2"^^ . "[AE30141C4A16]" . . "0024-6115" . . . "The provably total search problems of bounded arithmetic" . . "000292311700004" . . "The provably total search problems of bounded arithmetic"@en . "Skelley, A." . "10.1112/plms/pdq044" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "33"^^ . . "P(LC505), Z(AV0Z10190503)" . . . "The provably total search problems of bounded arithmetic" . . . "224926" . . "We give combinatorial principles GI(k), based on k-turn games, which are complete for the class of NP search problems provably total at the kth level T(2)(k) of the bounded arithmetic hierarchy and hence characterize the for all Sigma(b)(1) consequences of T(2)(k). Our argument uses a translation of first-order proofs into large, uniform propositional proofs in a system in which the soundness of the rules can be witnessed by polynomial time reductions between games. We show that for all(Sigma) over cap (b)(1)(alpha) conservativity of T(2)(i+1) (alpha) over T(2)(i)(alpha) already implies. for all(Sigma) over cap (b)(1)(a) conservativity of T(2)(alpha) over T(2)(i)(alpha). We translate this into propositional form and give a polylogarithmic width CNF (GI(3)) over bar such that if (GI(3)) over bar has small R(log) refutations then so does any polylogarithmic width CNF which has small constant depth refutations. We prove a resolution lower bound for (GI(3)) over bar." . "Thapen, Neil" .