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Nondeterministic Finite Automata—Recent Results on the Descriptional and Computational Complexity

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Implementation and Applications of Automata (CIAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5148))

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Abstract

Nondeterministic finite automata (NFAs) were introduced in [67], where their equivalence to deterministic finite automata was shown. Over the last 50 years, a vast literature documenting the importance of finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss recent developments relevant to NFAs related problems like, for example, (i) simulation of and by several types of finite automata, (ii) minimization and approximation, (iii) size estimation of minimal NFAs, and (iv) state complexity of language operations. We thus come across descriptional and computational complexity issues of nondeterministic finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.

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  1. Institut für Informatik, Technische Universität München, Boltzmannstr. 3, 85748, Garching bei München, Germany

    Markus Holzer

  2. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib

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  1. Markus Holzer
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Oscar H. Ibarra Bala Ravikumar

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Holzer, M., Kutrib, M. (2008). Nondeterministic Finite Automata—Recent Results on the Descriptional and Computational Complexity. In: Ibarra, O.H., Ravikumar, B. (eds) Implementation and Applications of Automata. CIAA 2008. Lecture Notes in Computer Science, vol 5148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70844-5_1

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