Related papers: Notes on Lynch-Morawska Systems

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The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…

Large Language Models (LLMs) bring transformative benefits alongside unique challenges, including intellectual property (IP) and ethical concerns. This position paper explores a novel angle to mitigate these risks, drawing parallels between…

The Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that…

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The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of…

The landscape of Large Language Models (LLMs) shifts rapidly towards dynamic, multi-agent systems. This introduces a fundamental challenge in establishing computational trust, specifically how one agent can verify that another's output was…

Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…

Query rewrite, which aims to generate more efficient queries by altering a SQL query's structure without changing the query result, has been an important research problem. In order to maintain equivalence between the rewritten query and the…

Schema matching is a crucial task in data integration, involving the alignment of a source schema with a target schema to establish correspondence between their elements. This task is challenging due to textual and semantic heterogeneity,…

Large Language Models (LLMs), combined with program-based solving techniques, are increasingly demonstrating proficiency in mathematical reasoning. For example, closed-source models such as OpenAI GPT-4 and Claude show excellent results in…

Large Language Models (LLMs) have achieved remarkable progress in code-related tasks. Despite their advancement, empirical evidence reveals that they still struggle with \emph{deductive code reasoning}, the ability to reason about the…

We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…

Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…

The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…

Large language models (LLMs) have demonstrated great potential for domain-specific applications, such as the law domain. However, recent disputes over GPT-4's law evaluation raise questions concerning their performance in real-world legal…

We consider a general class of decision problems concerning formal languages, called ``(one-dimensional) unboundedness predicates'', for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces…

This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…

Leftist grammars [Motwani et al., STOC 2000] are special semi-Thue systems where symbols can only insert or erase to their left. We develop a theory of leftist grammars seen as word transformers as a tool toward rigorous analyses of their…