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Further oracles separating conjectures about incompleteness in the finite domain
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-09-22 , DOI: 10.1016/j.tcs.2020.09.040
Titus Dose

Pudlák [14] lists several major complexity theoretic conjectures relevant to proof complexity and asks for oracles that separate pairs of corresponding relativized conjectures. Among these conjectures are:

CON and SAT: coNP (resp., NP) does not contain many-one complete sets that have P-optimal proof systems.

NPcoNP: NPcoNP does not have many-one complete problems.

PNP.

We construct two of the oracles that Pudlak asks for:

Relative to the first oracle, NPcoNP holds and CON does not hold.

Relative the second oracle, PNP holds and both CON and SAT do not hold. This separates PNP from another conjecture by Pudlák, namely the conjecture CONSAT.



中文翻译:

关于有限域中不完全性的猜想的进一步预言

Pudlák[14]列出了与证明复杂性相关的几个主要的复杂性理论猜想,并要求预言家将成对的相应相对论猜想分开。这些猜想包括:

骗子SAT考试:coNP(resp。,NP)不包含具有P最优证明系统的多套完整集。

NP核蛋白NP核蛋白 没有很多完整的问题。

PNP

我们构造了Pudlak要求的两个预言:

相对于第一个神谕, NP核蛋白 持有并 骗子 不成立。

相对于第二个神谕, PNP 两者兼而有之 骗子SAT考试不举行。这分开PNP 来自普德拉克的另一个猜想,即猜想 骗子SAT考试

更新日期:2020-11-04
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