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Electronic Colloquium on Computational Complexity

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Reports tagged with TFNP:
TR12-100 | 23rd July 2012
Tomas Jirotka

NP Search Problems

The thesis summarizes known results in the field of NP search problems. We discuss the complexity of integer factoring in detail, and we propose new results which place the problem in known classes and aim to separate it from PLS in some sense. Furthermore, we define several new search problems.

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TR16-063 | 18th April 2016
Pavel Hubacek, Eylon Yogev

Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds

Revisions: 1

Local search proved to be an extremely useful tool when facing hard optimization problems (e.g. via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts the optimization ... more >>>

TR16-199 | 15th December 2016
Pavel Hubacek, Moni Naor, Eylon Yogev

The Journey from NP to TFNP Hardness

The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one ... more >>>

TR17-015 | 4th February 2017
Ilan Komargodski, Moni Naor, Eylon Yogev

White-Box vs. Black-Box Complexity of Search Problems: Ramsey and Graph Property Testing

Revisions: 1

Ramsey theory assures us that in any graph there is a clique or independent set of a certain size, roughly logarithmic in the graph size. But how difficult is it to find the clique or independent set? If the graph is given explicitly, then it is possible to do so ... more >>>

TR17-056 | 7th April 2017
Paul Goldberg, Christos Papadimitriou

Towards a Unified Complexity Theory of Total Functions

Revisions: 1

The complexity class TFNP is the set of {\em total function} problems that belong to NP: every input has at least one output and outputs are easy to check for validity, but it may be hard to find an output. TFNP is not believed to have complete problems, but it ... more >>>

TR18-120 | 21st June 2018
Alexandros Hollender, Paul Goldberg

The Complexity of Multi-source Variants of the End-of-Line Problem, and the Concise Mutilated Chessboard

The complexity class PPAD is usually defined in terms of the END-OF-LINE problem, in which we are given a concise representation of a large directed graph having indegree and outdegree at most 1, and a known source, and we seek some other degree-1 vertex. We show that variants where we ... more >>>

TR19-074 | 22nd May 2019
Arka Rai Choudhuri, Pavel Hubacek, Chethan Kamath, Krzysztof Pietrzak, Alon Rosen, Guy Rothblum

Finding a Nash Equilibrium Is No Easier Than Breaking Fiat-Shamir

The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography.

We show that ... more >>>

TR19-125 | 27th August 2019
Elazar Goldenberg, Karthik C. S.

Hardness Amplification of Optimization Problems

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.

We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently aggregate any $k$ instances of $\Pi$ and form one large instance ... more >>>

TR20-153 | 6th October 2020
Robert Kleinberg, Daniel Mitropolsky, Christos Papadimitriou

Total Functions in the Polynomial Hierarchy

We identify several genres of search problems beyond NP for which existence of solutions is guaranteed. One class that seems especially rich in such problems is PEPP (for "polynomial empty pigeonhole principle"), which includes problems related to existence theorems proved through the union bound, such as finding a bit string ... more >>>

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