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 …

For several classical nonnegative integer functions we investigate if they are members of the
counting complexity class# P or not. We prove# P membership in surprising cases, and in …

We resolve the computational complexity of two problems known as Necklace Splitting and
Discrete Ham Sandwich, showing that they are PPA-complete. For Necklace Splitting, this …

We show that the computational problem Consensus Halving is PPA-Complete, the first PPA-
Completeness result for a problem whose definition does not involve an explicit circuit. We …

In the ε-Consensus-Halvingproblem, a fundamental problem in fair division, there are n
agents with valuations over the interval [0, 1], and the goal is to divide the interval into pieces …

Computing a Fixed Point of Contraction Maps in Polynomial Queries Page 1 Computing a
Fixed Point of Contraction Maps in Polynomial Queries ** Chen Columbia University New York …

Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound
connections to the complexity of the fundamental cryptographic primitives: collision-resistant …

We study the problem of finding an exact solution to the Consensus Halving problem. While
recent work has shown that the approximate version of this problem is PPA-complete …

We study the search problem class $\mathrm {PPA} _q $ defined as a modulo-$ q $ analog
of the well-known $\textit {polynomial parity argument} $ class $\mathrm {PPA} $ introduced …

We resolve the complexity of n-dimensional Octahedral Tucker (a special case of the
celebrated Tucker problem), a classical statement from algebraic topology, by proving it …