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Controlled finite automata

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Abstract

This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.

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Acknowledgments

This work was supported by the following grants: MŠMT CZ1.1.00/02.0070 and TAČR TE01010415. The authors thank the anonymous referee for useful comments regarding the first version of this paper.

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Authors and Affiliations

  1. Department of Information Systems, Faculty of Information Technology, IT4Innovations Centre of Excellence, Brno University of Technology, Božetěchova 1/2, 612 66 , Brno, Czech Republic

    Alexander Meduna & Petr Zemek

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  1. Alexander Meduna
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  2. Petr Zemek
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Correspondence to Petr Zemek.

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Meduna, A., Zemek, P. Controlled finite automata. Acta Informatica 51, 327–337 (2014). https://doi.org/10.1007/s00236-014-0199-5

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