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We consider approximating the minmax value of a multi-player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of epsilon log n digits (for any constant epsilon>0 is…

Computer Science and Game Theory · Computer Science 2008-12-18 Kristoffer Arnsfelt Hansen , Thomas Dueholm Hansen , Peter Bro Miltersen , Troels Bjerre Sørensen

We continue the line of work initiated by Kalai et al. (STOC '23), studying "compiled" nonlocal games played between a classical verifier and a single quantum prover, with cryptography simulating the spatial separation between the players.…

Quantum Physics · Physics 2025-07-24 David Cui , Chirag Falor , Anand Natarajan , Tina Zhang

We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…

Computer Science and Game Theory · Computer Science 2014-11-04 Krishnendu Chatterjee , Laurent Doyen , Mickael Randour , Jean-François Raskin

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

Computer Science and Game Theory · Computer Science 2015-07-15 Thomas Brihaye , Gilles Geeraerts , Axel Haddad , Benjamin Monmege

We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to…

Quantum Physics · Physics 2015-05-28 Zhengfeng Ji

Non-local games are an important part of quantum information processing. Recently there has been an increased interest in generalizing non-local games beyond the basic setup by considering games with multiple parties and/or with large…

Quantum Physics · Physics 2016-09-09 Matej Pivoluska , Marcin Pawlowski , Martin Plesch

We study the complexity of computing the commuting-operator value $\omega^*$ of entangled XOR games with any number of players. We introduce necessary and sufficient criteria for an XOR game to have $\omega^* = 1$, and use these criteria to…

Quantum Physics · Physics 2019-02-12 Adam Bene Watts , Aram W. Harrow , Gurtej Kanwar , Anand Natarajan

We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to…

Quantum Physics · Physics 2025-07-17 Julius A. Zeiss , Gereon Koßmann , Omar Fawzi , Mario Berta

The quantum PCP (QPCP) conjecture states that all problems in QMA, the quantum analogue of NP, admit quantum verifiers that only act on a constant number of qubits of a polynomial size quantum proof and have a constant gap between…

Quantum Physics · Physics 2016-03-09 Alex B. Grilo , Iordanis Kerenidis , Attila Pereszlényi

We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying…

Optimization and Control · Mathematics 2023-05-05 Marianne Akian , Stéphane Gaubert , Ulysse Naepels , Basile Terver

Gradient-based algorithms have shown great promise in solving large (two-player) zero-sum games. However, their success has been mostly confined to the low-precision regime since the number of iterations grows polynomially in $1/\epsilon$,…

Computer Science and Game Theory · Computer Science 2024-10-30 Ioannis Anagnostides , Tuomas Sandholm

Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…

Computer Science and Game Theory · Computer Science 2012-03-02 Kristoffer Arnsfelt Hansen , Rasmus Ibsen-Jensen , Peter Bro Miltersen

Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…

Computational Complexity · Computer Science 2016-08-31 Massimo Cairo , Romeo Rizzi

In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we…

Quantum Physics · Physics 2019-05-28 Alex B. Grilo , William Slofstra , Henry Yuen

The recent MIP*=RE theorem of Ji, Natarajan, Vidick, Wright, and Yuen shows that the complexity class MIP* of multiprover proof systems with entangled provers contains all recursively enumerable languages. Prior work of Grilo, Slofstra, and…

Quantum Physics · Physics 2024-07-31 Kieran Mastel , William Slofstra

The complexity of free games with two or more classical players was essentially settled by Aaronson, Impagliazzo, and Moshkovitz (CCC'14). There are two complexity classes that can be considered quantum analogues of classical free games:…

Quantum Physics · Physics 2023-02-10 Anand Natarajan , Tina Zhang

There are few explicit examples of two player nonlocal games with a large gap between classical and quantum value. One of the reasons is that estimating the classical value is usually a hard computational task. This paper is devoted to…

Quantum Physics · Physics 2024-11-07 M. Rosicka , S. Szarek , A. Rutkowski , P. Gnaciński , M. Horodecki

One of the major outstanding foundational problems about boolean functions is the sensitivity conjecture, which (in one of its many forms) asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial that…

Computational Complexity · Computer Science 2015-11-25 Justin Gilmer , Michal Koucký , Michael Saks

We study quantum communication protocols, in which the players' storage starts out in a state where one qubit is in a pure state, and all other qubits are totally mixed (i.e. in a random state), and no other storage is available (for…

Quantum Physics · Physics 2020-01-01 Hartmut Klauck , Debbie Lim

We bound separations between the entangled and classical values for several classes of nonlocal $t$-player games. Our motivating question is whether there is a family of $t$-player XOR games for which the entangled bias is $1$ but for which…

Quantum Physics · Physics 2018-11-28 Tom Bannink , Jop Briët , Harry Buhrman , Farrokh Labib , Troy Lee