The sequence equivalence problem for primitive D0L systems

The D0L sequence equivalence problem consists of deciding, given two morphisms g:X⁎→X⁎g:X⁎→X⁎, h:X⁎→X⁎h:X⁎→X⁎ and a word w∈X⁎w∈X⁎, whether or not gi(w)=hi(w)gi(w)=hi(w) for all i⩾0i⩾0. We show that in case of primitive morphisms, to decide the D0L sequence equivalence problem, it suffices to consider the terms of the sequences with i<7n3nlogn, where n is the cardinality of X. A smaller bound is obtained for primitive looping morphisms.

► We study the D0L sequence equivalence problem. ► We give a new bound for the sequence equivalence problem for primitive D0L systems. ► Our bound is polynomial and depends only on the size of the alphabet.