Subword Complexities of Various Classes of Deterministic Developmental Languages without Interactions

Lee has shown that ifL is aDOL language, then πink(L) <C · k2 for some constantC, where πink(L) denotes the number of subwords of lengthk inL. We show that the result does not hold forDIL languages. It is also shown that each everywhere growing (uniform)DIL language is the image under a coding of an everywhere growing (uniform)DOL language. A similar result holds for languages generated by systems with tables. These enable us to solve the subword complexity problems for developmental languages with interactions.