Related papers: Generating Synchronizing Automata with Large Reset…
In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
We revisit, beyond the uniform case, some aspects of the convergence of the cumulative shape of the RSK Young diagrams associated with random words, obtaining rates of convergence in Kolmogorov's distance. Since the length of the top row of…
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
We describe a novel algorithm for random sampling of freely reduced words equal to the identity in a finitely presented group. The algorithm is based on Metropolis Monte Carlo sampling. The algorithm samples from a stretched Boltzmann…
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…
This paper provides several optimizations of the rank-based approach for complementing B\"{u}chi automata. We start with Schewe's theoretically optimal construction and develop a set of techniques for pruning its state space that are key to…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
We exhibit new conditions under which a primitive automaton is synchronizing. In particular, we show that the primitivity of an automaton forces its synchronizability whenever the automaton has either a letter of defect 1 or a word of rank…
Sentence Simplification aims to rephrase complex sentences into simpler sentences while retaining original meaning. Large Language models (LLMs) have demonstrated the ability to perform a variety of natural language processing tasks.…
We develop a new algorithm to compute determinants of all possible Hankel matrices made up from a given finite length sequence over a finite field. Our algorithm fits within the dynamic programming paradigm by exploiting new recursive…
In the computational-mechanics structural analysis of one-dimensional cellular automata the following automata-theoretic analogue of the \emph{change-point problem} from time series analysis arises: \emph{Given a string $\sigma$ and a…
The success of a text simplification system heavily depends on the quality and quantity of complex-simple sentence pairs in the training corpus, which are extracted by aligning sentences between parallel articles. To evaluate and improve…
Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that \v{C}erny's conjecture holds true, if and only if, it holds true for planar automata. In this paper we have…
The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups…