Breadth and Depth Grammars and Deque Automata

Abstract

We introduce BD (Breadth-Depth) grammars which extend context-free grammars by allowing breadth-first derivations. Their languages are recognized by Deque (double ended queue) automata having a single state. BD languages also include languages recognized by monostatic queue automata. It is shown that the commutative image of BD languages is semilinear, that they have a periodicity (pumping) property, and can be homomorphically characterized as h(DAD∩R), where DAD is the Dyck-AntiDyck language, and R a regular set. Non-autoinclusive BD grammars coincide in power with breadth-first grammars with regular right parts.

Multi-Push-Down Languages and Grammars

“…. .hK (2) ; p 0 k ; p 0 which has form (8). The new con guration of the automaton is now hq 2 ; x; A (2) B (2) .…”

“…to the con guration (8), which obviously has the form (hA (j) ; q 1 ; q 2 ihB (j) ; q 2 ; s 0 3 i . .…”