Re-describing an algorithm by Hopcroft
Theoretical Computer Science
Theoretical Computer Science
Hopcroft's Algorithm and Cyclic Automata
Language and Automata Theory and Applications
Continuant polynomials and worst-case behavior of Hopcroft's minimization algorithm
Theoretical Computer Science
Circular sturmian words and Hopcroft's algorithm
Theoretical Computer Science
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
On the complexity of hopcroft’s state minimization algorithm
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
On extremal cases of Hopcroft's algorithm
Theoretical Computer Science
The average complexity of Moore's state minimization algorithm is O(n log log n)
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Average complexity of Moore's and Hopcroft's algorithms
Theoretical Computer Science
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In this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft's algorithm. Hopcroft's algorithm has several degrees of freedom, so there can exist different sequences of refinements of the set of the states that lead to the final partition. We find an infinite family of binary automata for which such a process is unique. Some recent papers (cf. [3,7,1]) have been devoted to find families of automata for which Hopcroft's algorithm has its worst execution time. They are unary automata associated to circular words. However, automata minimization can be achieved also in linear time when the alphabet has only one letter (cf. [14]), so in this paper we face the tightness of the algorithm when the alphabet contains more than one letter. In particular we define an infinite family of binary automata representing the worst case of Hopcroft's algorithm. They are automata associated to particular trees and we deepen the connection between the refinement process of Hopcroft's algorithm and the combinatorial properties of such trees.