A PROOF COMPLEXITY CONJECTURE AND THE INCOMPLETENESS THEOREM

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509694" target="_blank" >RIV/00216208:11320/25:10509694 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=iM-iy_xn1O" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=iM-iy_xn1O</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2023.69" target="_blank" >10.1017/jsl.2023.69</a>

Result language
angličtina
Original language name
A PROOF COMPLEXITY CONJECTURE AND THE INCOMPLETENESS THEOREM
Original language description
Given a sound first-order p-time theory T capable of formalizing syntax of first-order logicwe define a p-time function gT that stretches all inputs by one bit and we use its properties to show thatT must be incomplete. We leave it as an open problem whether for some T the range of gT intersects allinfinite NP sets (i.e., whether it is a proof complexity generator hard for all proof systems).A propositional version of the construction shows that at least one of the following three statements istrue:1. There is no p-optimal propositional proof system (this is equivalent to the non-existence of a timeoptimal propositional proof search algorithm).2. E ⊆ P/poly.3. There exists function h that stretches all inputs by one bit, is computable in sub-exponential time,and its range Rng(h) intersects all infinite NP sets
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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