Formal language theory/Parallel replacement systems

Parallel replacement systemsEdit

A foray into the language theoretic aspects of Lindenmayer systems. For D0L systems, we have followed the presentation in Salomaa's book[1].

A D0L (deterministic, zero context) system   over an alphabet   consists of a start string   and a single replacement rule given by a homomorphism  . These systems have perhaps surprising properties.

Question: What happens when   for some string  ?


HierachiesEdit

0L: instead of a homomorphism, there is a finite substitution

Question: Find a language that is in 0L but not in D0L. (this is not hard)

DTOL: instead of a single homomorphism, there is a table   of homomorphisms

Question: Find a language that is in DT0L but not in D0L or 0L.


Further ReadingEdit

BooksEdit

[2]

  1. Arto Salomaa, Jewels in Formal Language Theory, Computer Science Press 1981
  2. Rozenberg and Salomaa, The Mathematical Theory of L Systems