Related papers: A Quantum Unique Games Conjecture
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a…
We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
Tablut is a complete-knowledge, deterministic, and asymmetric board game, which has not been solved nor properly studied yet. In this work, its rules and characteristics are presented, then a study on its complexity is reported. An upper…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA$_1$-complete…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
In this work, we introduce a new toolkit for analyzing cloning games, a notion that captures stronger and more quantitative versions of the celebrated quantum no-cloning theorem. This framework allows us to analyze a new cloning game based…
The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…
We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant…
Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we…
A constraint satisfaction problem (CSP) is said to be \emph{approximation resistant} if it is hard to approximate better than the trivial algorithm which picks a uniformly random assignment. Assuming the Unique Games Conjecture, we give a…
Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…
We propose an analytical framework for studying parallel repetition, a basic product operation for one-round two-player games. In this framework, we consider a relaxation of the value of a game, $\mathrm{val}_+$, and prove that for…
A working definition of the term \quantum game" is developed in an attempt to gain insights into aspects of quantum mechanics via game theory.
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…
Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…
The extension of a conflict control problem with infinite horizon is constructed. This extension is the projective limit of restricted games. Relations between "sensitivity to target set" and the existence of the optimal control are…