Cellular automata and
attributed parallel array grammars
Rudolf FREUND
Technische Universität Wien, Institut für Computersprachen
Resselgasse 3, A-1040 Wien, Austria
email: freund@csafl.tuwien.ac.at
Fritz TAFILL
Technische Universität Wien, Institut für Elektrotechnik und
Elektronik,
Arbeitsgruppe für Neuronale Elekronik
Gußhausstraße 25 -- 29, A-1040 Wien, Austria
email: fritz@synapse.iaee.tuwien.ac.at
ABSTRACT. The concept of n-dimensional parallel array grammars
(e.g. see [1])
is a useful means for the formal syntactic description of
n-dimensional cellular automata ([7]); for the two-dimensional
case, a survey of possible applications of array automata like picture
recognition is given in [5]. As n-dimensional parallel
array grammars are a more general model than n-dimensional cellular
automata, they also allow for simpler solutions of complex problems.
Attributed parallel array grammars have been shown to be a useful tool for
the formal description of the static and dynamic characteristics of neural
networks; because of the underlying grid structure, Kohonen's model of
self-organizing feature maps (e.g. see [6]) is especially
well suited for being represented by n-dimensional parallel array grammars
(e.g. see [3], [4]). Using the concept
of different levels of scaling like in [2], even hierarchical
networks can be modelled by attributed parallel array grammars.
REFERENCES
- R. Freund, ``Aspects of n-dimensional Lindenmayer
systems'', Developments in Language Theory, Turku, Finland, 1993.
- R. Freund, ``Multi-level eco-array grammars'', Artificial
Life -- Grammatical Models (Gh. Paun, ed., Black Sea University
Press, Bucure\c sti, 1995), pp. 166 -- 174.
- R. Freund, F. Tafill, ``Modelling Kohonen networks
by attributed parallel array systems'', SPIE'93, Innsbruck, Austria,
1993.
- R. Freund, F. Tafill, ``Formal representation of
neural networks'', ICANN'94, Sorrento, Italy, 1994.
- K. Inoue, I. Takanami, ``A survey of
two-dimensional automata theory'', Information Sciences
{\bf 55} (1991), pp. 99 -- 121.
- H. Ritter, K. Schulten, T. Martinetz, Neuronale
Netze (Addison-Wesley, Deutschland, 1990).
- S. Wolfram (ed.), Theory and applications of
cellular automata (World Scientific Publ., Singapore, 1986).