相关论文: VPSPACE and a transfer theorem over the complex fi…
In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP($\mathcal{C}$,-), in which the goal is, given a relational structure $\mathbf{A}$ from a class $\mathcal{C}$ of structures and an…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
Constraint Satisfaction Problems (CSPs) form a broad class of combinatorial problems, which can be formulated as homomorphism problems between relational structures. The CSP dichotomy theorem classifies all such problems over finite domains…
Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few…
In this paper we explore the possibility of defining p-local finite groups in terms of transfer properties of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be…
We study the verification of distributed systems where processes are finite automata with access to a shared pool of locks. We consider objectives that are boolean combinations of local regular constraints. We show that the problem,…
The polynomial cluster value problem replaces the role of the continuous linear functionals in the original cluster value problem for the continuous polynomials to describe the corresponding cluster sets and fibers. We prove several…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
In the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, we formulate a local conjecture (arithmetic transfer) in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary…
A topological invariant of a polynomial map $p:X\to B$ from a complex surface containing a curve $C\subset X$ to a one-dimensional base is given by a rational second homology class in the compactification of the moduli space of genus $g$…
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…
We define a theory of parameterized algebraic complexity classes in analogy to parameterized Boolean counting classes. We define the classes VFPT and VW[t], which mirror the Boolean counting classes #FPT and #W[t], and define appropriate…
It is known that for any class C closed under union and intersection, the Boolean closure of C, the Boolean hierarchy over C, and the symmetric difference hierarchy over C all are equal. We prove that these equalities hold for any…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
Arithmetic circuit complexity studies the complexity of computing polynomials using only arithmetic operations such as addition, multiplication, subtraction, and division. Polynomials over rings of integers model counting problems.…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
The central open question of algebraic complexity is whether VP is unequal to VNP, which is saying that the permanent cannot be represented by families of polynomial-size algebraic circuits. For symmetric algebraic circuits, this has been…
Rosenbrock's theorem on polynomial system matrices is a classical result in linear systems theory that relates the Smith-McMillan form of a rational matrix $G$ with the Smith forms of an irreducible polynomial system matrix $P$ giving rise…
Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most…