Related papers: Semidefinite programming bounds for error-correcti…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
Epistemic protocol specifications allow programs, for settings in which multiple agents act with incomplete information, to be described in terms of how actions are related to what the agents know. They are a variant of the knowledge-based…
For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a…
We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
Code completion has become a common practice for programmers during their daily programming activities. It aims at automatically predicting the next tokens or lines that the programmers tend to use. A good code completion tool can…
For a strongly connected category $\mathcal C$ with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of ${\sf lim} : \mathrm{Ab}^{\mathcal C}\to…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality…
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…
An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
In recent papers, Margolis, Rhodes and Schilling proved that the complexity of a finite semigroup is computable. This solved a problem that had been open for more than 50 years. The purpose of this paper is to survey the basic results of…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
This PhD thesis is concerned with SDP bounds for codes: upper bounds for (non)-binary error correcting codes and lower bounds for (non)-binary covering codes. The methods are based on the method of Schrijver that uses triple distances in…