Three partition refinement algorithms
SIAM Journal on Computing
From regular expressions to deterministic automata
Theoretical Computer Science
Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
Handbook of formal languages, vol. 1
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Data Structures and Algorithms
Data Structures and Algorithms
From Mirkin's Prebases to Antimirov's Word Partial Derivatives
Fundamenta Informaticae
Brzozowski's Derivatives Extended to Multiplicities
CIAA '01 Revised Papers from the 6th International Conference on Implementation and Application of Automata
Derivatives of rational expressions and related theorems
Theoretical Computer Science - Implementation and application automata
Theoretical Computer Science - Implementation and application of automata
Derivatives of rational expressions with multiplicity
Theoretical Computer Science
Description and analysis of a bottom-up DFA minimization algorithm
Information Processing Letters
Fast equation automaton computation
Journal of Discrete Algorithms
Construction of Tree Automata from Regular Expressions
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
An Efficient Computation of the Equation K-automaton of a Regular K-expression
Fundamenta Informaticae
Language operations with regular expressions of polynomial size
Theoretical Computer Science
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
An efficient computation of the equation K-automaton of a regular K-expression
DLT'07 Proceedings of the 11th international conference on Developments in language theory
On the average number of states of partial derivative automata
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Partial derivatives of an extended regular expression
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Note: From regular expressions to smaller NFAs
Theoretical Computer Science
The average transition complexity of Glushkov and partial derivative automata
DLT'11 Proceedings of the 15th international conference on Developments in language theory
The language, the expression, and the (small) automaton
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
Derivatives of regular expressions and an application
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Construction of fuzzy automata from fuzzy regular expressions
Fuzzy Sets and Systems
An Efficient Computation of the Equation K-automaton of a Regular K-expression
Fundamenta Informaticae
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
On the average size of glushkov and equation automata for KAT expressions
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Hi-index | 5.23 |
Let E be a regular expression. Our aim is to establish a theoretical relation between two well-known automata recognizing the language of E, namely the position automaton PE constructed by Glushkov or McNaughton and Yamada, and the equation automaton EE constructed by Mirkin or Antimirov. We define the notion of c-derivative (for canonical derivative) of a regular expression E and show that if E is linear then two Brzozowski's derivatives of E are aci-similar if and only if the corresponding c-derivatives are identical. It allows us to represent the Berry-Sethi's set of continuations of a position by a unique c-derivative, called the c-continuation of the position. Hence the definition of CE, the c-continuation automaton of E, whose states are pairs made of a position of E and of the associated c-continuation. If states are viewed as positions, CE is isomorphic to PE. On the other hand, a partial derivative, as defined by Antimirov, is a class of c-derivatives for some equivalence relation, thus CE reduces to EE. Finally CE makes it possible to go from PE to EE, while this cannot be achieved directly (from the state graphs). These theoretical results lead to an O(|E|2) space and time algorithm to compute the equation automaton, where |E| is the size of the expression. This is the complexity of the most efficient constructions yielding the position automaton, while the size of the equation automaton is not greater and generally much smaller than the size of the position automaton.