Adventures in Monotone Complexity and TFNP

Göös, Mika; Kamath, Pritish; Robere, Robert; Sokolov, Dmitry

doi:10.4230/lipics.itcs.2019.38

Cited by 15 publications

(12 citation statements)

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“…Another interesting application of Theorem 3.7, observed in a follow-up work [GKRS18], is that it improves this separation to an exponential separation between NC 2 and mon-P. This is done by considering the monotone function 3Xor-Sat n , which receives as input an indicator vector for a set of 3Xor constraints over n variables and outputs 1 if the set is unsatisfiable and 0 otherwise.…”

Section: Theorem 37 ([Ggks20]mentioning

confidence: 99%

“…Then PLS dt is defined as consisting of all query search problems that can be reduced, via shallow decision-tree reductions, to the query-Iteration problem. (See [GKRS18] for a more formal definition.) What is striking is that in some cases the query analogue of a TFNP class can be captured by a natural propositional proof system, and the communication analogue can be captured by a natural circuit model (via the KW game).…”

Section: Query/communication Tfnpmentioning

confidence: 99%

“…It has turned out to be fruitful to place these total search problems on center stage when trying to understand proof systems and circuit models. In fact, recent research has shown that the classical (Turing machine) theory of total search problems (TFNP) can serve as a general "organizing principle" for proof systems and circuit classes in this way [GKRS18].…”

Section: Introductionmentioning

confidence: 99%

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Proofs, Circuits, and Communication

Rezende¹,

Göös²,

Robere³

2022

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Section: Theorem 37 ([Ggks20]mentioning

confidence: 99%

Section: Query/communication Tfnpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proofs, Circuits, and Communication

Rezende¹,

Göös²,

Robere³

2022

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“…(The paper [HY20] initially defined a more restricted "metered" version of this problem, but we use the formulation from [FGMS20], which they prove is equivalent to the one from [HY20].) It is also natural to define a sink-only version of EOPL as suggested by [GKRS18].…”

Section: Introductionmentioning

confidence: 99%

Further Collapses in TFNP

Göös¹,

Hollender²,

Jain³

et al. 2022

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We show EOPL = PLS ∩ PPAD. Here the class EOPL consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubáček and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result yields a new simpler proof of the breakthrough collapse CLS = PLS ∩ PPAD by Fearnley et al. (STOC 2021). We also prove a companion result SOPL = PLS ∩ PPADS, where SOPL is the class associated with the Sink-of-Potential-Line problem.

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“…Some known natural complete problems for TFNP subclasses are: the PPADcompleteness of NashEquilibrium [DGP09], the PPA-completeness of ConsensusHalving, NecklaceSplitting and HamSandwich problems [FG18,FG19] and the PPP-completeness of natural problems related to lattice-based cryptography [SZZ18]. Finally, the theory of total search problems has found connections beyond its original scope to areas like communication complexity and circuit lower bounds [GKRS19], cryptography [BPR15, KNY19, CHK + 19] and the Sum-of-Squares hierarchy [KM18].…”

mentioning

confidence: 99%

On the Complexity of Modulo-q Arguments and the Chevalley-Warning Theorem

Göös,

Kamath,

Sotiraki

et al. 2019

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We study the search problem class PPA q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA p for prime p.Our main result is to establish that an explicit version of a search problem associated to the Chevalley-Warning theorem is complete for PPA p for prime p. This problem is natural in that it does not explicitly involve circuits as part of the input. It is the first such complete problem for PPA p when p ≥ 3.Finally we discuss connections between Chevalley-Warning theorem and the well-studied short integer solution problem and survey the structural properties of PPA q .

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Adventures in Monotone Complexity and TFNP

Cited by 15 publications

References 0 publications

Proofs, Circuits, and Communication

Proofs, Circuits, and Communication

Further Collapses in TFNP

On the Complexity of Modulo-q Arguments and the Chevalley-Warning Theorem

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