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"Semantic Atlas" is a mathematic and statistic model to visualise word senses according to relations between words. The model, that has been applied to proximity relations from a corpus, has shown its ability to distinguish word senses as…
The Longest Common Subsequence (LCS) is a fundamental string similarity measure, and computing the LCS of two strings is a classic algorithms question. A textbook dynamic programming algorithm gives an exact algorithm in quadratic time, and…
A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…
Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…
The correlation dimension of natural language is measured by applying the Grassberger-Procaccia algorithm to high-dimensional sequences produced by a large-scale language model. This method, previously studied only in a Euclidean space, is…
The paper considers various formalisms based on Automata, Temporal Logic and Regular Expressions for specifying queries over sequences. Unlike traditional binary semantics, the paper presents a similarity based semantics for thse…
Keeping in mind the necessity of intelligent system in educational sector, this paper proposes a text analysis based automated approach for automatic evaluation of the descriptive answers in an examination. In particular, the research…
A pseudo-Anosov surface automorphism $\phi$ has associated to it an algebraic unit $\lambda_\phi$ called the dilatation of $\phi$. It is known that in many cases $\lambda_\phi$ appears as the spectral radius of a Perron-Frobenius matrix…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
Large language models (LLMs) are advanced artificial intelligence (AI) systems that can perform a variety of tasks commonly found in human intelligence tests, such as defining words, performing calculations, and engaging in verbal…
We study languages and formal power series associated to (variants of) Hammersley's process. We show that the ordinary Hammersley process yields a regular language and the Hammersley tree process yields deterministic context-free (but…
One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…
We demonstrate the ability of large language models (LLMs) to perform iterative self-improvement of robot policies. An important insight of this paper is that LLMs have a built-in ability to perform (stochastic) numerical optimization and…
A surprising property of word vectors is that word analogies can often be solved with vector arithmetic. However, it is unclear why arithmetic operators correspond to non-linear embedding models such as skip-gram with negative sampling…
Consider a compact metric space $X$, and let $\mathcal{F}=\{f_1,\,f_2,\ldots,\, f_k\}$ be a set of contracting and continuous self maps on $X$. Let $\Sigma$ be a sub-shift on $k$ symbols, and let $\Sigma_k$ be the full shift. Define…
The study of the theory of operators over modal pseudocomplemented De Morgan algebras was begun in the papers [15] and [16]. In this paper, we introduce and study the class of modal pseudocomplemented De Morgan algebras enriched by an…
Consider a Leibniz superalgebra $\mathfrak L$ additionally graded by an arbitrary set $I$ (set grading). We show that $\mathfrak L$ decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Lexical iconicity, a direct relation between a word's meaning and its form, is an important aspect of every natural language, most commonly manifesting through sound-meaning associations. Since Large language models' (LLMs') access to both…