Related papers: Automata and rational expressions
Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree…
Robotic Process Automation (RPA) is the automation of rule-based routine processes to increase efficiency and to reduce costs. Due to the utmost importance of process automation in industry, RPA attracts increasing attention in the…
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
This is my working paper on a proposed logical framework for the practice of mathematics, which is paralleled by philosophical considerations and a computer implementation (a variant of Automath). Updated 10/27/2016 with a version from…
Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blow-up in the…
Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…
This paper corrects the characterisation of biautomatic groups presented in Lemma 2.5.5 in the book Word Processing in Groups by Epstein et al. We present a counterexample to the lemma, and we reformulate the lemma to give a valid…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
This survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. Consequently,…
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.
Autonomous systems control many tasks in our daily lives. To increase trust in those systems and safety of the interaction between humans and autonomous systems, the system behaviour and reasons for autonomous decision should be explained…
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of rational subsets of groups, with particular emphasis on the automata-theoretic approach to finitely generated subgroups of free groups. Indeed, Stallings'…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
The increasing incorporation of Artificial Intelligence in the form of automated systems into decision-making procedures highlights not only the importance of decision theory for automated systems but also the need for these decision…
We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but…
In our recent publication we obtained a series expansion of the arctangent function involving complex numbers. In this work we show that this formula can also be expressed as a real rational function.
In this work we aim at applying automata techniques to problems studied in Dynamic Epistemic Logic, such as epistemic planning. To do so, we first remark that repeatedly executing ad infinitum a propositional event model from an initial…
This paper is devoted to finite state automata, regular expression matching, pattern recognition, and the exponential blow-up problem, which is the growing complexity of automata exponentially depending on regular expression length. This…
Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and…