相关论文: Using Automata to obtain Regular Expressions for I…
The basic method of rewriting for words in a free monoid given a monoid presentation is extended to rewriting for paths in a free category given a `Kan extension presentation'. This is related to work of Carmody-Walters on the Todd-Coxeter…
Kan extensions provide a natural general framework for a variety of combinatorial problems. We have developed rewriting procedures for Kan extensions (over the category of sets) and this enables one program to address a wide range of…
Regular languages are closed under a wealth of formal language operators. Incorporating such operators in regular expressions leads to concise language specifications, but the transformation of such enhanced regular expressions to finite…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
It is shown how to use a small finite state automaton in two variables in order to carry out the Knuth-Bendix process for rewriting words in a group in shortlex order. The two-variable automaton can be used to store an infinite set of rules…
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton.…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automata-theoretic approach may be applied to answer…
It is shown how to use a small finite state automaton in two variables in order to carry out part of the Knuth--Bendix process for rewriting words in a group. The main objective is to provide a substitute for the most space-demanding module…
Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present…
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…
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…
In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the…
We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational…
The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on…
Relating formal re nement techniques with commercial object oriented software development methods is important to achieve enhancement of the power and exibility of these software development methods and tools. We will present an automata…
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…
Reconfiguration paths express sequences of successive reconfiguration operations within a component-based approach allowing dynamic reconfigurations. We use constructs from regular expressions-pin particular, alternatives-to introduce…
Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these…