Related papers: Matrix Code
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
In this paper, by using matrix product codes, several classes of new quantum codes are obtained. Moreover, some of them have better parameters than the previous quantum codes available.
We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object…
Quantum computing provides computational advantages in various domains. To benefit from these advantages complex hybrid quantum applications must be built, which comprise both quantum and classical programs. Engineering these applications…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
Programming is a powerful and ubiquitous problem-solving tool. Developing systems that can assist programmers or even generate programs independently could make programming more productive and accessible, yet so far incorporating…
Reasoning is a fundamental component of language understanding. Recent prompting techniques, such as chain of thought, have consistently improved LLMs' performance on various reasoning tasks. Nevertheless, there is still little…
Traditionally, computer programming has been the prerogative of professional developers using textual programming languages such as C, Java, or Python. Low-code programming promises an alternative: letting citizen developers create programs…
A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
We define a compilation scheme for a constructor-based, strongly-sequential, graph rewriting system which shortcuts some needed steps. The object code is another constructor-based graph rewriting system. This system is normalizing for the…
Artificial intelligence (AI) tools based on large language models have acheived human-level performance on some computer programming tasks. We report several experiments using GPT-4 to generate computer code. These experiments demonstrate…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
We present an algorithm for tests generation tools based on symbolic execution. The algorithm is supposed to help in situations, when a tool is repeatedly failing to cover some code by tests. The algorithm then provides the tool a necessary…
Quantum computers have the potential to solve certain problems faster than classical computers by exploiting quantum mechanical effects such as superposition. However, building high-quality quantum software is challenging due to the…
Code execution is a fundamental aspect of programming language semantics that reflects the exact behavior of the code. However, most pre-trained models for code intelligence ignore the execution trace and only rely on source code and…