Three partition refinement algorithms
SIAM Journal on Computing
From regular expressions to deterministic automata
Theoretical Computer Science
Regular expressions into finite 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)
Programming Techniques: Regular expression search algorithm
Communications of the ACM
Data Structures and Algorithms
Data Structures and Algorithms
Computing epsilon-Free NFA from Regular Expressions in O(n log²(n)) Time
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Translating Regular Expressions into Small epsilon-Free Nondeterministic Finite Automata
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
A New Quadratic Algorithm to Convert a Regular Expression into an Automaton
WIA '96 Revised Papers from the First International Workshop on Implementing Automata
From Regular Expressions to DFA's Using Compressed NFA's
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Algorithms for Computing Small NFAs
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Derivation of Rational Expressions with Multiplicity
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Brzozowski's Derivatives Extended to Multiplicities
CIAA '01 Revised Papers from the 6th International Conference on Implementation and Application of Automata
Computing the Equation Automaton of a Regular Expression in Space and Time
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Constructing NFA s by Optimal Use of Positions in Regular Expressions
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Construction of fuzzy automata from fuzzy regular expressions
Fuzzy Sets and Systems
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Two classical constructions to convert a regular expression into a finite non-deterministic automaton provide complementary advantages: the notion of position of a symbol in an expression, introduced by Glushkov and McNaugthon-Yamada, leads to an efficient computation of the position automaton (there exist quadratic space and time implementations w.r.t. the size of the expression), whereas the notion of derivative of an expression w.r.t. a word, due to Brzozowski, and generalized by Antimirov, yields a small automaton. The number of states of this automaton, called the equation automaton, is less than or equal to the number of states of the position automaton, and in practice it is generally much smaller. So far, algorithms to build the equation automaton, such as Mirkin's or Antimirov's ones, have a high space and time complexity. The aim of this paper is to present new theoretical results allowing to compute the equation automaton in quadratic space and time, improving by a cubic factor Antimirov's construction. These results lay on the computation of a new kind of derivative, called canonical derivative, which makes it possible to connect the notion of continuation in a linear expression due to Berry and Sethi, and the notion of partial derivative of a regular expression due to Antimirov. A main interest of the notion of canonical derivative is that it leads to an efficient computation of the equation automaton via a specific reduction of the position automaton.