On the Hierarchy of Block Deterministic Languages
Pascal Caron, Ludovic Mignot, Cl\'ement Miklarz

TL;DR
This paper investigates the hierarchy and relationships between $k$-lookahead and $k$-block deterministic regular languages, correcting previous misconceptions and establishing proper inclusion relations among these language classes.
Contribution
It clarifies the hierarchy of $k$-block and $k$-lookahead deterministic languages, correcting earlier proofs and establishing proper inclusions through new constructions and properties.
Findings
Each $k$-block deterministic language is an alphabetic image of a one-unambiguous language.
The conversion from minimal DFA to $k$-block deterministic automaton involves state elimination.
The hierarchy in $k$-block deterministic languages is proper, and $k$-block is strictly included in $k$-lookahead deterministic languages.
Abstract
A regular language is -lookahead deterministic (resp. -block deterministic) if it is specified by a -lookahead deterministic (resp. -block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood (-lookahead determinism) and by Giammarresi et al. (-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each -block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a -block deterministic regular language to a -block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper…
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Advanced Algebra and Logic
