Overlays and Limited Memory Communication

Papakonstantinou, Periklis A.; Scheder, Dominik; Song, Hao

doi:10.1109/ccc.2014.37

Cited by 10 publications

(21 citation statements)

References 19 publications

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“…Papakonstantinou, Scheder, and Song [25, Open Problem 1] asked whether the product method can yield a tight P NP communication lower bound for every function. This is especially relevant in light of the fact that all existing lower bounds against P NPcc (proved in [18,25]) have used the product method (except those lower bounds that hold against an even stronger model: unbounded error randomized communication complexity, UPP cc [26]). We show that the product method can fail exponentially badly, even for total functions.…”

Section: Applicationmentioning

confidence: 99%

“…Rectangle DLs. A communication complexity variant of decision lists was introduced by Papakonstantinou, Scheder, and Song [25] (they called them rectangle overlays). A rectangle decision list of cost k is a sequence (R 1 , 1 ), .…”

Section: Fact 4 For Allmentioning

confidence: 99%

“…We define the rectangle decision list complexity of F , denoted DL cc (F ), as the minimum k such that F can be computed by a cost-k rectangle decision list. We again have a quadratic relationship [25,Theorem 3] (for details, see full version of this paper [12]).…”

Section: Fact 4 For Allmentioning

confidence: 99%

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Query-to-Communication Lifting for PNP

et al. 2018

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We prove that the P NP -type query complexity (alternatively, decision list width) of any boolean function f is quadratically related to the P NP -type communication complexity of a lifted version of f . As an application, we show that a certain "product" lower bound method of Impagliazzo and Williams (CCC 2010) fails to capture P NP communication complexity up to polynomial factors, which answers a question of Papakonstantinou, Scheder, and Song (CCC 2014).

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Section: Applicationmentioning

confidence: 99%

Section: Fact 4 For Allmentioning

confidence: 99%

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Query-to-Communication Lifting for PNP

et al. 2018

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“…Another motivation comes from the algebrization framework [1,28], which converts communication lower bounds (such as for AM) into barriers to proving relations among classical, time-bounded complexity classes. The absence of and need for nontrivial AM communication lower bounds has been explicitly pointed out in [46,45,48,42,40].…”

Section: Introductionmentioning

confidence: 97%

“…Other powerful subclasses of the polynomial hierarchy for which communication lower bounds are known include SBP (which lies between MA and AM) [24] and P NP [29,48].…”

Section: Introductionmentioning

confidence: 99%

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

Göös

Pitassi

Watson

2015

Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science

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We study whether information complexity can be used to attack the long-standing open problem of proving lower bounds against Arthur-Merlin (AM) communication protocols. Our starting point is to show that-in contrast to plain randomized communication complexity-every boolean function admits an AM communication protocol where on each yesinput, the distribution of Merlin's proof leaks no information about the input and moreover, this proof is unique for each outcome of Arthur's randomness. We posit that these two properties of zero information leakage and unambiguity on yes-inputs are interesting in their own right and worthy of investigation as new avenues toward AM.• Zero-information protocols (ZAM). Our basic ZAM protocol uses exponential communication for some functions, and this raises the question of whether more efficient protocols exist. We prove that all functions in the classical space-bounded complexity classes NL and ⊕L have polynomial-communication ZAM protocols. We also prove that ZAM complexity is lower bounded by conondeterministic communication complexity.• Unambiguous protocols (UAM). Our most technically substantial result is a Ω(n) lower bound on the UAM complexity of the NP-complete set-intersection function; the proof uses information complexity arguments in a new, indirect way and overcomes the "zero-information barrier" described above. We also prove that in general, UAM complexity is lower bounded by the classic discrepancy bound, and we give evidence that it is not generally lower bounded by the classic corruption bound. * All proofs appear in the full version of this work [23].

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The Landscape of Communication Complexity Classes

2018

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We prove several results which, together with prior work, provide a nearly-complete picture of the relationships among classical communication complexity classes between P and PSPACE, short of proving lower bounds against classes for which no explicit lower bounds were already known. Our article also serves as an up-to-date survey on the state of structural communication complexity.Among our new results we show that MA ⊆ ZPP NP [1] , that is, Merlin-Arthur proof systems cannot be simulated by zero-sided error randomized protocols with one NP query. Here the class ZPP NP[1] has the property that generalizing it in the slightest ways would make it contain AM ∩ coAM, for which it is notoriously open to prove any explicit lower bounds. We also prove that US ⊆ ZPP NP[1] , where US is the class whose canonically complete problem is the variant of set-disjointness where yes-instances are uniquely intersecting. We also prove that US ⊆ coDP, where DP is the class of differences of two NP sets. Finally, we explore an intriguing open issue: are rank-1 matrices inherently more powerful than rectangles in communication complexity? We prove a new separation concerning PP that sheds light on this issue and strengthens some previously known separations.

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Overlays and Limited Memory Communication

Cited by 10 publications

References 19 publications

Query-to-Communication Lifting for PNP

Query-to-Communication Lifting for PNP

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

The Landscape of Communication Complexity Classes

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