Non-Self-Embedding Grammars, Constant-Height Pushdown Automata, And Limited Automata

Non-self-embedding grammars are a restriction of contextfree grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and 1-limited automata to deterministic finite automata. Constant-height pushdown automata and 1limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height push-down automata are polynomially related in size. Furthermore, a polynomial size simulation by 1-limited automata is presented. However, the converse transformation is proved to cost exponential.