An automata-theoretic characterization of the OI-hierarchy

Abstract

Though is was “obvious” to “insiders”, that the level-n pds — which circulated in unformalized versions prior to the knowledge of Maslov's papers — just had to be the automata model fitting to level-n languages, the complexity of the encodings in both directions shows, how far apart both concepts are. We hope that the technics develloped in establishing

$$\frac{{5.1{\text{}}Theorem}}{{\forall \Omega {\text{ }} \geqslant {\text{ }}1}}{\text{ }}n - L_{OI} {\text{ (}}\sum {\text{) = n}} - \mathcal{P}\mathcal{D}\mathcal{A}{\text{ (}}\sum {\text{)}}$$

will turn out to be useful in further applications, e.g. reducing the equivalence problem of level-n schemes [Da 1] to that of deterministic n-pda's (c.f. [Cou], [Gal] for the case n=1).