Testing the Equivalence of Regular Languages

@article{Almeida2009TestingTE,
  title={Testing the Equivalence of Regular Languages},
  author={Marco Almeida and Nelma Moreira and Rog{\'e}rio Reis},
  journal={J. Autom. Lang. Comb.},
  year={2009},
  volume={15},
  pages={7-25}
}
The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp pro- posed an almost linear algorithm for testing the equivalence of two de- terministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algo- rithm to non… 
View PDF on arXiv
22 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
6

Tables from this paper

22 Citations

Deciding Regular Expressions (In-)Equivalence in Coq

This work presents a mechanically verified implementation of an algorithm for deciding regular expression (in-)equivalence within the Coq proof assistant through an iterated process of testing the equivalence of their partial derivatives and also does not construct the underlying automata.

On the Equivalence of Automata for KAT-expressions

A decision procedure is obtained where the extra burden of dealing with boolean expressions avoids the explicit use of all possible assignments to the boolean variables, and the decision procedure for testing KAT expressions equivalence without explicitly constructing the automata is specialization.

Formalization of closure properties for context-free grammars

The results obtained so far include the representation of context-free grammars, the description of algorithms for some operations on them and the proof of related theorems (e.g. the correctness of these algorithms).

Partial Derivative Automata Formalized in Coq

A computer assisted proof of the correctness of a partial derivative automata construction from a regular expression within the Coq proof assistant is presented.

Brief Announcement: Regular and Dyck Languages in MPC

This paper gives a regular language testing algorithm, which succeeds with high probability using Õ(1 over ε) queries to the input string, and gives a simple dynamic programming solution for regular language recognition.

Optimizing Regular Expressions via Rewrite-Guided Synthesis

This work investigates automatically transforming regular expressions to remove inefficiencies, and presents a new approach called rewrite-guided synthesis (ReGiS), in which a unique interplay between SyGuS and equality saturation-based rewriting helps to overcome these problems, resulting in an efficient, scalable framework for expression optimization.

Formalization of simplification for context-free grammars

This paper presents a formalization, using the Coq proof assistant, of the fact that general context-free grammars generate languages that can be also generated by simpler and equivalent context- Free Grammars.

On solving cycle-free context-free grammar equivalence problem using numerical analysis

ReGiS: Regular Expression Simplification via Rewrite-Guided Synthesis

This work presents a new approach called rewrite-guided synthesis (ReGiS), in which a unique interplay between SyGuS and equality saturation-based rewriting helps to overcome problems, resulting in an efficient, scalable framework for expression simplification.

The Open-Source LearnLib - A Framework for Active Automata Learning

The current, open-source version of LearnLib was completely rewritten from scratch, incorporating the lessons learned from the decade-spanning development process of the previous versions oflearnLib.

24 References

On the Representation of Finite Automata

An unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFA’s) with n states over an alphabet of k symbols is given and how its enumeration provides an alternative way to obtain the exact number of ICDFA”s is shown.

Automata and Computability

    D. Kozen
    Computer Science
    Undergraduate Texts in Computer Science
  • 1997
This introduction to the basic theoretical models of computability develops their rich and varied structure and culminates in discussions of effective computability, decidability, and Godel's incompleteness theorems.

Enumeration and generation with a string automata representation

Antimirov and Mosses's Rewrite System Revisited

A functional approach to Antimirov and Mosses's rewrite system for deciding the equivalence of two (extended) regular expressions is presented, and it is concluded that these methods are feasible and, generally, faster than the classical methods.

Behavioural differential equations: a coinductive calculus of streams, automata, and power series

An Introduction to Automata Theory

Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines Parallel and serial…

A Linear Algorithm for Testing Equivalence of Finite Automata.

Abstract : An algorithm is given for determining if two finite automata with start states are equivalent. The asymptotic running time of the algorithm is bounded by a constant times the product of…

Partial Derivatives of Regular Expressions and Finite Automaton Constructions

On the performance of automata minimization algorithms

This paper compares the running time of four minimization algorithms based on experimental results and applies these algorithms to both deterministic and nondeterministic random automata.

Derivatives of Regular Expressions

In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed and this leads, in a very natural way, to the construction of a state diagram from a regularexpression containing any number of logical operators.