Related papers: Closures in Formal Languages: Concatenation, Separ…
Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite…
Sequential programming and work-flow programming are two useful, but radically different, ways of describing computational processing. Of the two, it is sequential programming that we teach all programmers and support by programming…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
Human languages expand vocabularies by combining existing morphemes rather than inventing arbitrary forms. Communicative efficiency shapes lexical systems at multiple levels (Gibson et al., 2019), yet morphological composition -- combining…
Recent advancements in large language models have demonstrated remarkable capabilities across various NLP tasks. But many questions remain, including whether open-source models match closed ones, why these models excel or struggle with…
According to a previous result by S. V. Avgustinovich and the author, each factorial language admits a unique canonical decomposition to a catenation of factorial languages. In this paper, we analyze the appearance of the canonical…
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…
We present an approach to simultaneously perform semantic segmentation and prepositional phrase attachment resolution for captioned images. Some ambiguities in language cannot be resolved without simultaneously reasoning about an associated…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
The problem of \emph{regular separability} asks, given two languages $K$ and $L$, whether there exists a regular language $S$ with $K\subseteq S$ and $S\cap L=\emptyset$. This problem has recently been studied for various classes of…
We in this paper show that omega regular languages are not closed under infinite union and intersection. As an attempt, we propose to add step variables and quantifiers to temporal logics to enhance the expressiveness of the underlying…
Locally finite omega languages were introduced by Ressayre in [Journal of Symbolic Logic, Volume 53, No. 4, p.1009-1026]. They generalize omega languages accepted by finite automata or defined by monadic second order sentences. We study…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their…
Words can be represented by composing the representations of subword units such as word segments, characters, and/or character n-grams. While such representations are effective and may capture the morphological regularities of words, they…
We study the problem of disentangling locked processes via code refactoring. We identify and characterise a class of processes that is not lock-free; then we formalise an algorithm that statically detects potential locks and propose…
In a consistent text, many words and phrases are repeatedly used in more than one sentence. When an identical phrase (a set of consecutive words) is repeated in different sentences, the constituent words of those sentences tend to be…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…