Abstract
We investigate here the descriptional and the computational complexity of parallel communicating grammar systems (PCGS). A new descriptional complexity measure — the communication structure of the PCGS — is introduced and related to the communication complexity (the number of communications). Several hierarchies resulting from these complexity measures and some relations between the measures are established. The results are obtained due to the development of two lower-bound proof techniques for PCGS. The first one is a generalization of pumping lemmas from formal language theory and the second one reduces the lower bound problem for some PCGS to the proof of lower bounds on the number of reversals of certain sequential computing models.
The study of hierarchies on the number of grammars for PCGS with other communication structures (planar graphs, hypercubes, etc) remains open.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
K.Culik, J.Gruska, A.Salomaa. Systolic trellis automata. International Journal of Computer Mathematics 15 and 16 (1984).
P.Duris, J.Hromkovic: Zerotesting bounded multicounter machines. Kybernetika 23(1987), No.1, 13–18.
S.Ginsburg: Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland Publ.Comp., Amsterdam 1975.
C.A.R.Hoare. Communicating sequential processes. Comm. ACM 21 vol. 8 (1978).
J.Hromkovic: Hierarchy of reversal bounded one-way multicounter machines. Kybernetica 22(1986), No.2, 200–206.
J. Kari. Decision problems concerning cellular automata. University of Turku, PhD Thesis (1990).
D.Pardubska. The communication hierarchies of parallel communicating systems. Proceedings of IMYCS'92, to appear.
Gh.Paun. On the power of synchronization in parallel communicating grammar systems. Stud. Cerc. Matem. 41 vol.3 (1989).
Gh.Paun. Parallel communicating grammar systems: the context-free case. Found. Control Engineering 14 vol.1 (1989).
Gh. Paun. On the syntactic complexity of parallel communicating grammar systems. Kybernetika, 28(1992), 155–166.
Gh.Paun, L.Santean. Further remarks on parallel communicating grammar systems. International Journal of Computer Mathematics 35 (1990).
Gh.Paun, L.Santean. Parallel communicating grammar systems: the regular case. Ann. Univ. Buc. Ser. Mat.-Inform. 37 vol.2 (1989).
A.Salomaa. Formal Languages. Academic Press New York London (1973).
L. Santean, J.Kari: The impact of the number of cooperating grammars on the generative power, Theoretical Computer Science, 98, 2(1992), 249–263.
D. Wierzchula: Systeme von parallellen Grammatiken (in German). Diploma thesis, Dept. of Mathematics and Computer Science, University of Paderborn, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hromkovic, J., Kari, J., Kari, L. (1993). Some hierarchies for the communication complexity measures of cooperating grammar systems. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_41
Download citation
DOI: https://doi.org/10.1007/3-540-57182-5_41
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57182-7
Online ISBN: 978-3-540-47927-7
eBook Packages: Springer Book Archive