Hopcroft’s Algorithm and Tree-like Automata
- Authors: Castiglione, G.; Restivo, A.; Sciortino, M.
- Publication year: 2009
- Type: Altro
- Key words: Automata minimization, Hoprcroft's algorithm, trees.
- OA Link: http://hdl.handle.net/10447/40016
In order to analyze some extremal cases of Hopcroft’s algorithm we deepened the relationship between combinatorial properties of circular words and the ex- ecution of the algorithm on cyclic automata associated to such words.In this paper we highlight the notion of word tree and in particular, we char- acterize the word trees for which Hopcroft’s algorithm on the associated tree-like automata has a unique refinement process. Moreover, we show the relationship between the time complexity of the refinements process of the Hopcroft’s algo- rithm on unary cyclic automata and binary tree-like automata. Such a result allows to exhibit a family of tree-like automata representing the worst case of the algorithm.