Related papers: Semidefinite programming bounds for error-correcti…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…
Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…
Let $A(n,d)$ be the maximum number of $0,1$ words of length $n$, any two having Hamming distance at least $d$. We prove $A(20,8)=256$, which implies that the quadruply shortened Golay code is optimal. Moreover, we show $A(18,6)\leq 673$,…
Let $A(n,d)$ (respectively $A(n,d,w)$) be the maximum possible number of codewords in a binary code (respectively binary constant-weight $w$ code) of length $n$ and minimum Hamming distance at least $d$. By adding new linear constraints to…
This paper extends the foundational work of Dollma \emph{et al}. on codes for ordered composite DNA sequences. We consider the general setting with an alphabet of size $q$ and a resolution parameter $k$, moving beyond the binary ($q=2$)…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
We discuss here constraint programming (CP) by using a proof-theoretic perspective. To this end we identify three levels of abstraction. Each level sheds light on the essence of CP. In particular, the highest level allows us to bring CP…
This is a shortened version of "The Limits of Mathematics--Course Outline & Software" (IBM Research Report RC 19324, December 1993) in which all Mathematica code has either been deleted or, if absolutely necessary, replaced by C code. The…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
Data profiling is critical in machine learning for generating descriptive statistics, supporting both deeper understanding and downstream tasks like data valuation and curation. This work addresses profiling specifically in the context of…
In this paper, we develop a method for computing controlled invariant sets using Semidefinite Programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets. The task is reduced to a…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
This is a book about large language models. As indicated by the title, it primarily focuses on foundational concepts rather than comprehensive coverage of all cutting-edge technologies. The book is structured into five main chapters, each…
This article is the first of an intended series of works on the model theory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core…
Program correctness used to be the main concern of computer software in the early days when formal semantics was a hot topic. But, the word "correct" was afterwards replaced by reliable, robust and trustworthy etc., a tradeoff situation…
While a large number of pre-trained models of source code have been successfully developed and applied to a variety of software engineering (SE) tasks in recent years, our understanding of these pre-trained models is arguably fairly…
Instruction tuning plays a pivotal role in Code Large Language Models (Code LLMs) for the task of program synthesis. Presently, two dominant paradigms for collecting tuning data are natural-instruct (human-written) and self-instruct…