TY - JOUR
A1 - Bordihn, Henning
A1 - Holzer, Markus
A1 - Kutrib, Martin
T1 - Decidability of operation problems for TOL languages and subclasses
JF - Information and computation
N2 - We investigate the decidability of the operation problem for TOL languages and subclasses. Fix an operation on formal languages. Given languages from the family considered (OL languages, TOL languages, or their propagating variants), is the application of this operation to the given languages still a language that belongs to the same language family? Observe, that all the Lindenmayer language families in question are anti-AFLs, that is, they are not closed under homomorphisms, inverse homomorphisms, intersection with regular languages, union, concatenation, and Kleene closure. Besides these classical operations we also consider intersection and substitution, since the language families under consideration are not closed under these operations, too. We show that for all of the above mentioned language operations, except for the Kleene closure, the corresponding operation problems of OL and TOL languages and their propagating variants are not even semidecidable. The situation changes for unary OL languages. In this case we prove that the operation problems with respect to Kleene star, complementation, and intersection with regular sets are decidable.
KW - L systems
KW - Operation problem
KW - Decidability
KW - Unary languages
Y1 - 2011
U6 - http://dx.doi.org/10.1016/j.ic.2010.11.008
SN - 0890-5401 (print)
VL - 209
IS - 3
SP - 344
EP - 352
PB - Elsevier
CY - San Diego
ER -