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Vulnerability identification is crucial for cyber security in the software-related industry. Early identification methods require significant manual efforts in crafting features or annotating vulnerable code. Although the recent pre-trained…
Statistical language modeling techniques have successfully been applied to source code, yielding a variety of new software development tools, such as tools for code suggestion and improving readability. A major issue with these techniques…
We study variable-length codes for point-to-point discrete memoryless channels with noiseless unlimited-rate feedback that occurs in $L$ bursts. We term such codes variable-length bursty-feedback (VLBF) codes. Unlike classical codes with…
System relevant embedded software needs to be reliable and, therefore, well tested, especially for aerospace systems. A common technique to verify programs is the analysis of their abstract syntax tree (AST). Tree structures can be…
One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$.…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding…
A novel learnable dictionary encoding layer is proposed in this paper for end-to-end language identification. It is inline with the conventional GMM i-vector approach both theoretically and practically. We imitate the mechanism of…
In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
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…
A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of…
Large Language Models (LLMs) have achieved remarkable success in source code understanding, yet as software systems grow in scale, computational efficiency has become a critical bottleneck. Currently, these models rely on a text-based…
Optimal zero-delay coding (quantization) of $\mathbb{R}^d$-valued linearly generated Markov sources is studied under quadratic distortion. The structure and existence of deterministic and stationary coding policies that are optimal for the…
In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…
Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$,…
A coding scheme for write once memory (WOM) using polar codes is presented. It is shown that the scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted. The encoding and decoding…
This study investigates the fundamental limits of variable-length compression in which prefix-free constraints are not imposed (i.e., one-to-one codes are studied) and non-vanishing error probabilities are permitted. Due in part to a…
We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…