On protocols for monotone feasible interpolation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00574198" target="_blank" >RIV/67985840:_____/23:00574198 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/23:10467112

Výsledek na webu

<a href="https://doi.org/10.1145/3583754" target="_blank" >https://doi.org/10.1145/3583754</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3583754" target="_blank" >10.1145/3583754</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On protocols for monotone feasible interpolation

Popis výsledku v původním jazyce

Dag-like communication protocols, a generalization of the classical tree-like communication protocols, are useful objects in the realm of proof complexity (most importantly for monotone feasible interpolation) and circuit complexity. We consider three kinds of protocols in this article (d is the degree of a protocol): - IEQ-d-dags: feasible sets of these protocols are described by inequality which means that the feasible sets are combinatorial triangles, these protocols are also called triangle-dags in the literature, - EQ-d-dags: feasible sets are described by equality, and - c-IEQ-d-dags: feasible sets are described by a conjunction of c inequalities.Garg, Göös, Kamath, and Sokolov (Theory of Computing, 2020) mentioned all these protocols, and they noted that EQ-d-dags are a special case of c-IEQ-d-dags. The exact relationship between these types of protocols is unclear. As our main contribution, we prove the following statement: EQ-2-dags can efficiently simulate c-IEQ-d-dags when c and d are constants. This implies that EQ-2-dags are at least as strong as IEQ-d-dags and that EQ-2-dags have the same strength as c-IEQ-d-dags for c ≥ 2 (because 2-IEQ-2-dags can trivially simulate EQ-2-dags).Hrubeš and Pudlák (Information Processing Letters, 2018) proved that IEQ-d-dags over the monotone Karchmer-Wigderson relation are equivalent to monotone real circuits which implies that we have exponential lower bounds for these protocols. Lower bounds for EQ-2-dags would directly imply lower bounds for the proof system R(LIN).

Název v anglickém jazyce

On protocols for monotone feasible interpolation

Popis výsledku anglicky

Dag-like communication protocols, a generalization of the classical tree-like communication protocols, are useful objects in the realm of proof complexity (most importantly for monotone feasible interpolation) and circuit complexity. We consider three kinds of protocols in this article (d is the degree of a protocol): - IEQ-d-dags: feasible sets of these protocols are described by inequality which means that the feasible sets are combinatorial triangles, these protocols are also called triangle-dags in the literature, - EQ-d-dags: feasible sets are described by equality, and - c-IEQ-d-dags: feasible sets are described by a conjunction of c inequalities.Garg, Göös, Kamath, and Sokolov (Theory of Computing, 2020) mentioned all these protocols, and they noted that EQ-d-dags are a special case of c-IEQ-d-dags. The exact relationship between these types of protocols is unclear. As our main contribution, we prove the following statement: EQ-2-dags can efficiently simulate c-IEQ-d-dags when c and d are constants. This implies that EQ-2-dags are at least as strong as IEQ-d-dags and that EQ-2-dags have the same strength as c-IEQ-d-dags for c ≥ 2 (because 2-IEQ-2-dags can trivially simulate EQ-2-dags).Hrubeš and Pudlák (Information Processing Letters, 2018) proved that IEQ-d-dags over the monotone Karchmer-Wigderson relation are equivalent to monotone real circuits which implies that we have exponential lower bounds for these protocols. Lower bounds for EQ-2-dags would directly imply lower bounds for the proof system R(LIN).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ACM Transactions on Computation Theory

ISSN

1942-3454

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

2

Kód UT WoS článku

001020428600002

EID výsledku v databázi Scopus

2-s2.0-85164243386