Abstract
This article estimates the worst-case running time complexity for traversing and printing all successful paths of a normalized trim acyclic automaton. First, we show that the worst-case structure is a festoon with distribution of arcs on states as uniform as possible. Then, we prove that the complexity is maximum when we have a distribution of e (Napier constant) outgoing arcs per state on average, and that it can be exponential in the number of arcs.
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References
Berstel, J. 1989. Finite Automata and Rational Languages. An Introduction, in Formal Properties of Finite Automata and Applications. In J.-E. Pin, editor, Lecture Notes in Computer Science, number 386. Verlag, 1989 edition, pages 2–14.
Caron, P. and D. Ziadi. 2000. Characterization of Glushkov automata. Theoret. Comput. Sci., 233(1–2):75–90.
Eilenberg, S. 1974. Automata, Languages, and Machines, volume A. Academic Press, San Diego, CA, USA.
Giammarresi, D., J.-L. Ponty, and D. Wood. 2001. Thompson digraphs: A characterization, in WIA’99. Lecture Notes in Computer Science, 2214:91–100.
Hopcroft, J. E, R. Motwani, and J. D Ullman. 2001. Introduction to Automata Theory, Languages and Computation. Low Price Edition. Addison Wesley Longman, Inc, Reading, Mass., USA, 2 edition.
Nicaud, C. 2000. Étude du comportement en moyenne des automates finis et des languages rationnels. Thesis, University of Paris 7.
Perrin, D. 1990. Finite automata. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science: Volume B: Formal Models and Semantics. Elsevier, Amsterdam, pages 1–57.
Yu, S., Q. Zhuang, and K. Salomaa. 1994. The state complexities of some basic operations on regular languages. Theoret. Comput. Sci., 125(2):315–328.
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© 2003 Springer-Verlag Berlin Heidelberg
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Guingne, F., Kempe, A., Nicart, F. (2003). Running Time Complexity of Printing an Acyclic Automaton. In: Ibarra, O.H., Dang, Z. (eds) Implementation and Application of Automata. CIAA 2003. Lecture Notes in Computer Science, vol 2759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45089-0_13
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DOI: https://doi.org/10.1007/3-540-45089-0_13
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