Abstract
Finite languages are an important sub-regular language family, which were intensively studied during the last two decades in particular from a descriptional complexity perspective. An important contribution to the theory of finite languages are the deterministic and the recently introduced nondeterministic finite cover automata (DFCAs and NFCAs, respectively) as an alternative representation of finite languages by ordinary finite automata. We compare these two types of cover automata from a descriptional complexity point of view, showing that these devices have a lot in common with ordinary finite automata. In particular, we study how to adapt lower bound techniques for nondeterministic finite automata to NFCAs such as, e.g., the biclique edge cover technique, solving an open problem from the literature. Moreover, the trade-off of conversions between DFCAs and NFCAs as well as between finite cover automata and ordinary finite automata are investigated. Finally, we present some results on the average size of finite cover automata.
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Part of the work was done while the first author was at Institut für Informatik, Ludwig-Maximilians-Universität München, Oettingenstraße 67, 80538 München, Germany and the second author was at Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany.
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Notes
- 1.
For a language \(L\subseteq \varSigma ^*\) define the Myhill-Nerode relation \(\equiv _L\) on words as follows: for \(u,v\in \varSigma ^*\) let \(u\equiv _Lv\) if and only if \(uw\in L\iff vw\in L\), for all \(w\in \varSigma ^*\).
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Gruber, H., Holzer, M., Jakobi, S. (2015). More on Deterministic and Nondeterministic Finite Cover Automata. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_10
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