Issue |
RAIRO-Theor. Inf. Appl.
Volume 45, Number 1, January-March 2011
ICTCS 09
|
|
---|---|---|
Page(s) | 59 - 75 | |
DOI | https://doi.org/10.1051/ita/2011011 | |
Published online | 15 March 2011 |
Hopcroft's algorithm and tree-like automata
Università di Palermo, Dipartimento di Matematica e
Applicazioni, via Archirafi, 34, 90123 Palermo, Italy; giusi@math.unipa.it
Received:
22
January
2010
Accepted:
18
November
2010
Minimizing a deterministic finite automata (DFA) is a very important problem in theory of automata and formal languages. Hopcroft's algorithm represents the fastest known solution to the such a problem. In this paper we analyze the behavior of this algorithm on a family binary automata, called tree-like automata, associated to binary labeled trees constructed by words. We prove that all the executions of the algorithm on tree-like automata associated to trees, constructed by standard words, have running time with the same asymptotic growth rate. In particular, we provide a lower and upper bound for the running time of the algorithm expressed in terms of combinatorial properties of the trees. We consider also tree-like automata associated to trees constructed by de Brujin words, and we prove that a queue implementation of the waiting set gives a Θ(n log n) execution while a stack implementation produces a linear execution. Such a result confirms the conjecture given in [A. Paun, M. Paun and A. Rodríguez-Patón. Theoret. Comput. Sci. 410 (2009) 2424–2430.] formulated for a family of unary automata and, in addition, gives a positive answer also for the binary case.
Mathematics Subject Classification: 68Q45 / 68Q25
Key words: Automata minimization / Hopcroft's algorithm / word trees
© EDP Sciences, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.