相关论文: MuPAD codes which implement limit-computable funct…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

We explore several concepts for analyzing the intuitive notion of computational irreducibility and we propose a robust formal definition, first in the field of cellular automata and then in the general field of any computable function f…

For all natural numbers a,b and d > 0, we consider the function f_{a,b,d} which associates n/d to any integer n when it is a multiple of d, and an + b otherwise; in particular f_{3,1,2} is the Collatz function. Coding in base a > 1 with b <…

We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…

A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum…

Subshifts are sets of colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissible completions. Since soficity of $\mathbb{Z}$ subshifts is…

We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…

For a finite binary string $x$ its logical depth $d$ for significance $b$ is the shortest running time of a program for $x$ of length $K(x)+b$. There is another definition of logical depth. We give a new proof that the two versions are…

We present an approach to parameterized reachability for communicating finite-state threads that formulates the analysis as a satisfiability problem. In addition to the unbounded number of threads, the main challenge for SAT/SMT-based…

Multiphase ranking functions (M$\Phi$RFs) are tuples $\langle f_1,\ldots,f_d \rangle$ of linear functions that are often used to prove termination of loops in which the computation progresses through a number of "phases". Our work provides…

In this paper, we continue the study of Maximally Recoverable (MR) Grid Codes initiated by Gopalan et al. [SODA 2017]. More precisely, we study codes over an $m \times n$ grid topology with one parity check per row and column of the grid…

We consider models of quantum computation that involve operations performed on some fixed resourceful quantum state. Examples that fit this paradigm include magic state injection and measurement-based approaches. We introduce a framework…

The submodular function maximization is an attractive optimization model that appears in many real applications. Although a variety of greedy algorithms quickly find good feasible solutions for many instances while guaranteeing…

Let $n, m, k$ be positive integers with $k=n-m+1$. We establish an abstract Morse-Sard-type theorem which allows us to deduce, on the one hand, a previous result of De Pascale's for Sobolev $W^{k,p}_{\textrm{loc}}(\mathbb{R}^n,…

We consider the following combinatorial question. Let $$ S_0 \subset S_1 \subset S_2 \subset ...\subset S_m $$ be nested sets, where #$(S_i) = i$. A move consists of altering one of the sets $S_i$, $1 \le i \le m-1$, in a manner so that the…

We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…

Motivated by the established notion of storage codes, we consider sets of infinite sequences over a finite alphabet such that every $k$-tuple of consecutive entries is uniquely recoverable from its $l$-neighborhood in the sequence. We…

Neural networks are capable of superposition -- representing more features than there are dimensions. Recent work considers the analogous concept for computation instead of storage, proposing theoretical constructions. But there has been…

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…

For a bilinear map $*:\mathbb R^d\times \mathbb R^d\to \mathbb R^d$ of nonnegative coefficients and a vector $s\in \mathbb R^d$ of positive entries, among an exponentially number of ways combining $n$ instances of $s$ using $n-1$…