Abstract
A regular language is k-block deterministic if it is specified by a k-block deterministic regular expression. This subclass of regular languages has been introduced by Giammarresi et al. as a possible extension of one-unambiguous regular languages defined and characterized by Brüggemann-Klein and Wood. We first show that each k-block deterministic regular language is the alphabetic image of some one-unambiguous regular language. Moreover, we show that the conversion from a minimal DFA of a k-block deterministic regular language to a k-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in k-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in k-block deterministic regular languages.
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Caron, P., Mignot, L., Miklarz, C. (2015). On the Hierarchy of Block Deterministic Languages. 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_6
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DOI: https://doi.org/10.1007/978-3-319-22360-5_6
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