Dag-Like Communication and Its Applications

Sokolov, Dmitry

doi:10.1007/978-3-319-58747-9_26

Cited by 17 publications

(21 citation statements)

References 12 publications

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“…Strong computability essentially (but not completely) coincides with the notion of computability that Sokolov gave in [14] for general relations. Strong computability implies more intuitive notion of computability that we gave in the Preliminaries.…”

Section: Effective Versionmentioning

confidence: 72%

“…However, to capture the circuit size in our results we consider not only standard tree-like protocols, but also dag-like protocols. This notion was considered by Sokolov in [14]. We use slightly different variant of this notion, arguably more intuitive one.…”

Section: Preliminariesmentioning

confidence: 99%

“…A lot of circuit depth lower bounds as well as formula size lower bounds rely on this discovery [10,13,5,7,4]. Karchmer -Wigderson games have been used also in adjacent areas like Proof Complexity (see, e.g., [14]).…”

Section: Introductionmentioning

confidence: 99%

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Multiparty Karchmer-Wigderson Games and Threshold Circuits

Kozachinskiy¹,

Podolskii²

2020

Preprint

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We suggest a generalization of Karchmer -Wigderson communication games to the multiparty setting. Our generalization turns out to be tightly connected to circuits consisting of threshold gates. This allows us to obtain new explicit constructions of such circuits for several functions. In particular, we provide an explicit (polynomial-time computable) log-depth monotone formula for Majority function, consisting only of 3-bit majority gates and variables. This resolves a conjecture of Cohen et al. (CRYPTO 2013).

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Section: Effective Versionmentioning

confidence: 72%

Section: Preliminariesmentioning

confidence: 99%

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Multiparty Karchmer-Wigderson Games and Threshold Circuits

Kozachinskiy¹,

Podolskii²

2020

Preprint

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“…DAG-like communication protocols [46,40,52], generalizing the usual notion of tree-like communication protocols [35,31,41], provide a useful abstraction to study two kinds of objects in complexity theory:…”

Section: Appetizermentioning

confidence: 99%

“…In circuit complexity, a straightforward generalization of the Karchmer-Wigderson depth characterization [32] shows that the monotone circuit complexity of any monotone function f equals rect-DAG(S f ); see [40,52].…”

Section: Resolve Xmentioning

confidence: 99%