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We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for…
A locally threshold testable language L is a language with the property that for some non negative integers k and l and for some word u from L, a word v belongs to L if and only if (1) the prefixes [suffixes] of length k-1 of words u and v…
Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning. However, their ability to perform exact, deterministic computation remains unclear. In this work, we systematically evaluate…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
This thesis is devoted to studying estimates of the least common multiple of some integer sequences. Our study focuses on effective bounding of the $\mathrm{lcm}$ of some class of quadratic sequences, as well as arithmetic progressions and…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining…
Large language models (LLMs) are increasingly used for automated code refactoring tasks. Although these models can quickly refactor code, the quality may exhibit inconsistencies and unpredictable behavior. In this article, we systematically…
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
Local grammars can be represented in a very convenient way by automata. This paper describes and illustrates an efficient algorithm for the application of local grammars put in this form to lemmatized texts.
LLMs can be unpredictable, as even slight alterations to the prompt can cause the output to change in unexpected ways. Thus, the ability of models to accurately explain their behavior is critical, especially in high-stakes settings. One…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
Large language models (LLMs) have demonstrated remarkable capabilities for medical question answering and programming, but their potential for generating interpretable computable phenotypes (CPs) is under-explored. In this work, we…
We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator $G^p$ expressing that on a path, certain formula holds with at least a given frequency p, thus relaxing the…
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less…
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…
The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the most practical lattice reduction algorithm in digital communications. In this paper, several variants of the LLL algorithm with either lower theoretic complexity or fixed-complexity…
The rapid advancement of natural language processing (NLP) technologies, such as instruction-tuned large language models (LLMs), urges the development of modern evaluation protocols with human and machine feedback. We introduce Evalica, an…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.