Related papers: Merlin-Arthur Games and Stoquastic Complexity
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
In this paper, we consider constrained optimization problems with convex, smooth objective and constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class…
Modern Internet-scale storage systems often provide weak consistency in exchange for better performance and resilience. An important weak consistency property is k-atomicity, which bounds the staleness of values returned by read operations.…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
The $k$-QSAT problem is a quantum analog of the famous $k$-SAT constraint satisfaction problem. We must determine the zero energy ground states of a Hamiltonian of $N$ qubits consisting of a sum of $M$ random $k$-local rank-one projectors.…
The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a…
Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In…
We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability…
This paper contributes to the study of a new and remarkable family of stochastic processes that we will term class $\Sigma^{r}(H)$. This class is potentially interesting because it unifies the study of two known classes: the class…
When combined properly, search techniques can reveal the full potential of sophisticated branching heuristics. We demonstrate this observation on the well-known class of random 3-SAT formulae. First, a new branching heuristic is presented,…
The Metropolis algorithm (MA) is a classic stochastic local search heuristic. It avoids getting stuck in local optima by occasionally accepting inferior solutions. To better and in a rigorous manner understand this ability, we conduct a…
This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has…
Heuristic methods for solution of problems in the NP-Complete class of decision problems often reach exact solutions, but fail badly at "phase boundaries", across which the decision to be reached changes from almost always having one value…
We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic…
Simulated annealing (SA) attracts more attention among classical heuristic algorithms because the solution of the combinatorial optimization problem can be naturally mapped to the ground state of the Ising Hamiltonian. However, in practical…
We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of…
The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…
The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex…
In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…