Minimisation of acyclic deterministic automata in linear time
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
An O(n log n) implementation of the standard method for minimizing n-state finite automata
Information Processing Letters
Re-describing an algorithm by Hopcroft
Theoretical Computer Science
Concrete Math
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Description and analysis of a bottom-up DFA minimization algorithm
Information Processing Letters
Circular sturmian words and Hopcroft's algorithm
Theoretical Computer Science
A first investigation of Sturmian trees
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
On extremal cases of Hopcroft's algorithm
Theoretical Computer Science
A challenging family of automata for classical minimization algorithms
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
The tractability frontier for NFA minimization
Journal of Computer and System Sciences
Average complexity of Moore's and Hopcroft's algorithms
Theoretical Computer Science
A graph theoretic approach to automata minimality
Theoretical Computer Science
Nondeterministic Moore automata and Brzozowski's minimization algorithm
Theoretical Computer Science
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This paper is concerned with the analysis of the worst case behavior of Hopcroft's algorithm for minimizing deterministic finite state automata. We extend a result of Castiglione, Restivo and Sciortino. They show that Hopcroft's algorithm has a worst case behavior for the automata recognizing Fibonacci words. In a previous paper, we have proved that this holds for all standard Sturmian words having an ultimately periodic directive sequence (the directive sequence for Fibonacci words is (1,1,...)). We prove here that the same conclusion holds for all standard Sturmian words having a directive sequence with bounded elements. More precisely, we obtain in fact a characterization of those directive sequences for which Hopcroft's algorithm has worst case running time. These are the directive sequences (d"1,d"2,d"3,...) for which the sequence of geometric means (d"1d"2...d"n)^1^/^n is bounded. As a consequence, we easily show that there exist directive sequences for which the worst case for the running time is not attained.