Related papers: On the Computing Power of $+$, $-$, and $\times$
We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location.…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…
For any two arithmetic functions $f,g$ let $\bullet$ be the commutative and associative arithmetic convolution $(f\bullet g)(k):=\sum_{m=0}^k \left( \begin{array}{c} k m \end{array} \right)f(m)g(k-m)$ and for any $n\in\mathbb{N},$…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals (PCR/$\mathbb{Q}$). We show that there is a set of polynomial constraints $Q_n$…
We consider the quadratic optimization problem $\max_{x \in C}\ x^T Q x + q^T x$, where $C\subseteq\mathbb{R}^n$ is a box and $r := \mathrm{rank}(Q)$ is assumed to be $\mathcal{O}(1)$ (i.e., fixed). We show that this case can be solved in…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
We use a variety of computational tools to obtain a degree-$\binom{m + n - 2}{m - 1}$ polynomial equation conjecturally satisfied by the top-left entry of the Sinkhorn limit of a positive $m \times n$ matrix. The degree of this equation has…
Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…
Let $\R$ be a real closed field, $ {\mathcal Q} \subset \R[Y_1,...,Y_\ell,X_1,...,X_k], $ with $ \deg_{Y}(Q) \leq 2, \deg_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m$, and $ {\mathcal P} \subset \R[X_1,...,X_k] $ with $\deg_{X}(P)…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…
We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…
In this article choiceless polynomial time (CPT) is extended using non-determini\-stic Abstract State Machines (ASMs), which are restricted by three conditions: (1) choice is restricted to choice among atoms; (2) update sets in a state must…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…