Turn-Bounded Grammars and Their Relation to Ultralinear Languages

We define a mapping from the context-free grammars to the class of one-state pushdown acceptors. A turn-bounded grammar is a cfg for which its corresponding one-state pda is finite-turn. From S. Ginsburg and E. H. Spanier it follows that this class of grammars generates the ultralinear languages. Our main result is that every turn-bounded grammar is equivalent to a turn-bounded grammar in Greibach form, a property not shared by the ultralinear grammars. Since Greibach's construction does not preserve turnboundedness an alternate construction is required to obtain our result. As a corollary we have that every Ȩ -free ultralinear language is accepted by a onestate finite-turn pda that reads an input symbol on every move.