EDT0L grammars with only one variable have tractable generating functions

Abstract

We introduce new counting techniques for computing the growth of EDT0L languages based on generalized Parikh vectors. The structure generating function S(z) for any language formed from an unambiguous EDT0L system with one variable and m tables is tractable in the sense that its Taylor polynomial SN(z) can be constructed in time O(N2+log2m). We illustrate by example that this result is not necessarily true for systems with several variables. The dichotomy between one variable and several variables is partially explained using matrix algebra.