: .
NFORMATION AND CONTROL 54, 155--s) can be generated (syntac-
tically described) by graph grammars, see, ., Rosenfeld and Milgram
(1972), Mylopoulos (1972), and Pfalz (1972). Quite often, however, one
does not have to use general graphs to describe patterns and it suffices to use
strings as follows. Primitives are given names which are letters from some
155
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fixed alphabet and then patterns can be represented as strings over the given
alphabet (which is sometimes extended to include the names of operators
acting as subpatterns). A string describing a given pattern corresponds to a
traversal of this pattern "through" its component subpatterns, see, .,
Kirsch (1964), Knoke and Wiley (1967), Shaw (1969), and Winkler (1978).
Such an approach of describing languages consisting of multidimensional
objects by string languages has the potential advantage of the use of a
considerably rich body of knowledge about string grammars and languages
(see, ., Ginsburg, 1966; Harrison, 1978; and Salomaa, 1973) to study
languages consisting of structures more complicated than strings.
In this paper we will be concerned with (languages of) patterns, the
building blocks of which (their primitives) are unit lines in the two-
dimensional Cartesian grid. Such patterns, referred to as pictures are
particularly suitable for the description by strings because each point in the
Cartesian plane has four neighbours. Moving to a neighbour of a given point
(or, in other words, adding a li
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