On Patterns and Graphs by Brian Mayoh
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Abstract:
As graph grammars are used in many areas of computer science, it is not surprising that many different kinds of graph grammars have been introduced. As there are many practical and theoretical advantages of contextfreedom, characterisation of "contextfree " in [Co87]. However the practical and theoretical advantages of contextfreedom are not lost if one moves to the more expressive pattern version of a contextfree grammar. In this paper we have 3 aims:. to explain what the pattern version of a contextfree grammar is and why the advantages of contextfreedom are preserved,. to give the pattern version of several popular graph and hypergraph grammars,. by giving striking examples to show that the extra expressive power of patterns is worth having. #1 Patterns: what and why? In formal language theory the idea of patterns seems to have appeared first in the contextual grammars of Marcus[Ma69] and Paun[Pa82,Pa94]. Then those interested in language learning started using patterns [An80], and now the formal linguists are reinvigorating the idea [DPS93]. In the string world one can define a pattern as a word W on terminal and nonterminal letters together with a partition of the occurrences of the nonterminals in W. If all occurrences of the same nonterminal are equivalent, then the pattern is fractal; if all occurrences of nonterminals are equivalent only to themselves, then the pattern is discrete. Thus a discrete fractal pattern has at most one occurrence of each nonterminal. When displaying patterns we display the partitition using the convention:. l is the empty pattern. nonterminals with the same adornment are equivalent,. unadorned nonterminals are only equivalent to themselves. Thus a b S c b T a c S ' b b T ' is a pattern where the last two nonterminals are equivalent to each other and the first two are only equivalent to themselves. If W1 (W2, W3) are terminal words derivable from S (T, both S and T), then one can substitute in the pattern to get the terminal word: a b W1 c b W2 a c W3 b b W3 Def.1. A string pattern multigrammar G consists of S a terminal alphabet, D a nonterminal alphabet, and for each S in D a set
