相关论文: Gap-preserving reductions and RE-completeness of i…
The class $\mathsf{MIP}^*$ is the set of languages decidable by multiprover interactive proofs with quantum entangled provers. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that $\mathsf{MIP}^*$ is equal to $\mathsf{RE}$,…
In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…
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 show that the value of a general two-prover quantum game cannot be computed by a semi-definite program ofvpolynomial size (unless P=NP), a method that has been successful in more restricted quantum games. More precisely, we show that…
The concept of nimbers--a.k.a. Grundy-values or nim-values--is fundamental to combinatorial game theory. Nimbers provide a complete characterization of strategic interactions among impartial games in their disjunctive sums as well as the…
Robust self-testing in non-local games allows a classical referee to certify that two untrustworthy players are able to perform a specific quantum strategy up to high precision. Proving robust self-testing results becomes significantly…
A value of a CSP instance is typically defined as a fraction of constraints that can be simultaneously met. We propose an alternative definition of a value of an instance and show that, for purely combinatorial reasons, a value of an…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to…
In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…
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…
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…
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…
We address the problem of solving parity games with imperfect information on finite graphs of bounded structural complexity. It is a major open problem whether parity games with perfect information can be solved in PTIME. Restricting the…
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…
Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…
First, we consider the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent…
This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class…
This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that…