Related papers: Power Circuits, Exponential Algebra, and Time Comp…

Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…

We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…

Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…

In arXiv:1710.08163 a generalization of Boolean circuits to arbitrary finite algebras had been introduced and applied to sketch P versus NP-complete borderline for circuits satisfiability over algebras from congruence modular varieties.…

Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…

We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…

We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…

We consider the theory of algebraically closed fields of characteristic zero with multivalued operations $x\mapsto x^r$ (raising to powers). It is in fact the theory of equations in exponential sums. In an earlier paper we have described…

We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which…

An efficient randomized polynomial identity test for noncommutative polynomials given by noncommutative arithmetic circuits remains an open problem. The main bottleneck to applying known techniques is that a noncommutative circuit of size…

The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…

We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…

The motivation for this paper is to study the complexity of constant-width arithmetic circuits. Our main results are the following. 1. For every k > 1, we provide an explicit polynomial that can be computed by a linear-sized monotone…

We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…

We show that a circuit walk from a given feasible point of a given linear program to an optimal point can be computed in polynomial time using only linear algebra operations and the solution of the single given linear program. We also show…

This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…

An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms containing exponentiation. All constants occuring in the term are…

Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic…