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Chase-like decoding algorithms are a popular choice for soft-input decoding of algebraic codes. In this paper, we evaluate the performance of different test pattern sets using three methods. For test pattern sets with a certain structure…

We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…

Automatic code completion helps improve developers' productivity in their programming tasks. A program contains instructions expressed via code statements, which are considered as the basic units of program execution. In this paper, we…

In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a…

Code generation has largely improved development efficiency in the era of large language models (LLMs). With the ability to follow instructions, current LLMs can be prompted to generate code solutions given detailed descriptions in natural…

Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…

Competitive programming has emerged as a critical benchmark for evaluating the reasoning and coding capabilities of Large Language Models (LLMs). Despite impressive progress on existing benchmarks, we argue that current evaluations…

To assess the quality of a test suite, one can rely on mutation testing, which computes whether the overall test cases are adequately exercising the covered lines. However, this high level of granularity may overshadow the quality of…

Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…

Software testing is a critical aspect of software development, yet generating test cases remains a routine task for engineers. This paper presents a benchmark, CLOVER, to evaluate models' capabilities in generating and completing test cases…

Code generation systems have been extensively developed in recent years to generate source code based on natural language instructions. However, despite their advancements, these systems still face robustness issues where even slightly…

Today, AI technology is showing its strengths in almost every industry and walks of life. From text generation, text summarization, chatbots, NLP is being used widely. One such paradigm is automatic code generation. An AI could be…

We prove that the exact crossing number of a graph can be efficiently computed for simple graphs having bounded vertex cover. In more precise words, Crossing Number is in FPT when parameterized by the vertex cover size. This is a notable…

By interpreting the well-known, qualitative criteria for the existence of quantum error correction (QEC) codes by Knill and Laflamme from a quantitative perspective, we propose a figure of merit for assessing a QEC scheme based on the…

In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal…

This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that…

During software evolution, developers commonly face the problem of mapping a specific code region from one commit to another. For example, they may want to determine how the condition of an if-statement, a specific line in a configuration…

AI-based code generation is increasingly prevalent, with GitHub Copilot estimated to generate 46% of the code on GitHub. Accurately evaluating how well generated code aligns with developer intent remains a critical challenge. Traditional…

Gallager-type error-correcting codes that nearly saturate Shannon's bound are constructed using insight gained from mapping the problem onto that of an Ising spin system. The performance of the suggested codes is evaluated for different…