Related papers: Linear Programming Bounds
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
In the past years, deep learning models have been successfully applied in several cognitive tasks. Originally inspired by neuroscience, these models are specific examples of differentiable programs. In this paper we define and motivate…
An extremely simple, description of Karmarkar's algorithm with very few technical terms is given.
A new system of library code is proposed and initiated. It is emphasized that the same terminologies as we find in our textbooks should be used for class names in the library code. The language C# invented by Microsoft is adopted in this…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
Predictive coding is an influential theory of cortical function which posits that the principal computation the brain performs, which underlies both perception and learning, is the minimization of prediction errors. While motivated by…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the…
Compilers are used to run programs that are written in a range of designs from text to executable formats. With the advent of the internet, studies related to the development of cloud based compilers are being carried out. There is a…
This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as…
In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be…
This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic…
The first objective of this paper is to present and discuss various types of models of program understanding. They are discussed in relation to models of text understanding. The second objective of this paper is to assess the effect of…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…