Abstract
Linear languages can be characterized by regular-like expressions (linear expressions) according to a previous work. In this paper, we consider some equivalence properties of linear expressions in order to obtain a characterization of reversal and Kolmogorov complexity of linear languages. First, we introduce the relationship between regular expressions equivalence properties and linear expressions equivalence properties. Then, we define permutation and compression equi- valence properties in order to handle linear expressions to obtain shorter equivalent ones. The study of reversal and Kolmogorov complexities associated to linear grammars is performed in the rest of the paper. We obtain a speed-up theorem for reversal complexity. Finally, we define a Kolmogorov- like complexity associated to linear grammars and we deduce upper bounds for such complexity measure.
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