Graph automata for linear graph languages

Abstract

We introduce graph automata as devices for the recognition of linear graph languages. A graph automaton is the canonical extension of a finite state automaton recognizing a set of connected labeled graphs. It consists of a finite state control and a collection of heads, which search the input graph. In a move the graph automaton reads a new subgraph, checks some consistency conditions, changes states and moves some of its heads beyond the read subgraph. It proceeds such that the set of currently visited edges is an edge-separator between the visited and the yet undiscovered part of the input graph. Hence, the graph automaton realizes a graph searching strategy. Our main result states that finite graph automata recognize exactly the set of graph languages generated by connected linear NCE graph grammars.