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  - https://doi.org/10.1016/j.ic.2010.11.008
SN  - 0890-5401
VL  - 209
IS  - 3
SP  - 344
EP  - 352
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Bordihn, Henning
A1  - Kutrib, Martin
A1  - Malcher, Andreas
T1  - Undecidability and hierarchy results for parallel communicating finite automata
JF  - International journal of foundations of computer science
N2  - Parallel communicating finite automata (PCFAs) are systems of several finite state automata which process a common input string in a parallel way and are able to communicate by sending their states upon request. We consider deterministic and nondeterministic variants and distinguish four working modes. It is known that these systems in the most general mode are as powerful as one-way multi-head finite automata. It is additionally known that the number of heads corresponds to the number of automata in PCFAs in a constructive way. Thus, undecidability results as well as results on the hierarchies induced by the number of heads carry over from multi-head finite automata to PCFAs in the most general mode. Here, we complement these undecidability and hierarchy results also for the remaining working modes. In particular, we show that classical decidability questions are not semi-decidable for any type of PCFAs under consideration. Moreover, it is proven that the number of automata in the system induces infinite hierarchies for deterministic and nondeterministic PCFAs in three working modes.
KW  - Automata systems
KW  - cooperating systems
KW  - formal languages
KW  - decidability questions
Y1  - 2011
U6  - https://doi.org/10.1142/S0129054111008891
SN  - 0129-0541
VL  - 22
IS  - 7
SP  - 1577
EP  - 1592
PB  - World Scientific
CY  - Singapore
ER  -