Minimisation of acyclic deterministic automata in linear time
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Re-describing an algorithm by Hopcroft
Theoretical Computer Science
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Average State Complexity of Operations on Unary Automata
MFCS '99 Proceedings of the 24th 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
An n log n algorithm for minimizing states in a finite automaton
An n log n algorithm for minimizing states in a finite automaton
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Enumeration and random generation of accessible automata
Theoretical Computer Science
Hopcroft's Algorithm and Cyclic Automata
Language and Automata Theory and Applications
Analytic Combinatorics
Continuant polynomials and worst-case behavior of Hopcroft's minimization algorithm
Theoretical Computer Science
On Extremal Cases of Hopcroft's Algorithm
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
REGAL: a library to randomly and exhaustively generate automata
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
On the complexity of hopcroft’s state minimization algorithm
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
| Hi-index | 5.24 |
In this paper we prove that for the uniform distribution on complete deterministic automata, the average time complexity of Moore's state minimization algorithm is O(nloglogn), where n is the number of states in the input automata and the number of letters in the alphabet is fixed. Then, an unusual family of implementations of Hopcroft's algorithm is characterized, for which the algorithm will be proved to be always faster than Moore's algorithm. Finally, we present experimental results on the usual implementations of Hopcroft's algorithm.