1 research outputs found
Deque languages, automata and planar graphs
The memory of a deque (double ended queue) automaton is more general than a
queue or two stacks; to avoid overgeneralization, we consider quasi-real-time
operation. Normal forms of such automata are given. Deque languages form an AFL
but not a full one. We define the characteristic deque language, CDL, which
combines Dyck and AntiDyck (or FIFO) languages, and homomorphically
characterizes the deque languages. The notion of deque graph, from graph
theory, well represents deque computation by means of a planar hamiltonian
graph on a cylinder, with edges visualizing producer-consumer relations for
deque symbols. We give equivalent definitions of CDL by labelled deque graphs,
by cancellation rules, and by means of shuffle and intersection of simpler
languages. The labeled deque graph of a sentence generalizes traditional syntax
trees. The layout of deque computations on a cylinder is remindful of 3D models
used in theoretical (bio)chemistry