Showing papers on "Grammar systems theory published in 1971"
13 Oct 1971
380 citations
IBM1
TL;DR: A method for the description of the hierarchical structure of two-dimensional pictures is proposed, and a picture analysis program is described that accepts picture-processing grammar in tabular form and processes pictures using that grammar.
53 citations
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TL;DR: This chapter describes a grammar for maps whose sentences are not strings of symbols, but rather sets of symbols that can be interconnected in more general ways, are of importance in connection with the formal theory of picture processing and description.
Abstract: Publisher Summary This chapter describes a grammar for maps. Grammars whose sentences are not strings of symbols, but rather sets of symbols that can be interconnected in more general ways, are of importance in connection with the formal theory of picture processing and description. One of the most general formalisms of this kind deals with sentences, which are labeled directed graphs, that is, webs. Webs arise naturally in connection with descriptions of pictures; a description can present the relations among objects or regions in the given picture, so that it can be represented by a web whose vertices represent regions and whose edges indicate related pairs of regions. As pictures are planar, the webs that arise in this way can mostly be planar. When a graph is used to represent the adjacency relation between regions in the plane, not all of the topological information about the regions is preserved.
26 citations
TL;DR: It is shown that in some cases one can obtain unambiguity only by increasing complexity, and in any complexity class there are unambiguous languages, all simplest grammars of which are ambiguous.
Abstract: Four of the criteria of complexity of the description of context-free languages by context-free grammars are considered. The unsolvability of the basic problems is proved for each of these criteria. For instance, it is unsolvable to determine the complexity of the language generated by a given grammar, or to find out the simplest grammar, or to decide whether a given grammar is the simplest one and so on. Next, it is shown that in some cases one can obtain unambiguity only by increasing complexity. Namely, for each of the four criteria, in any complexity class there are unambiguous languages, all simplest grammars of which are ambiguous. As one would expect, it is unsolvable whether for an arbitrary grammar G there are unambiguous grammars within the simplest grammars for the language generated by G.
24 citations
01 Jan 1971
5 citations
16 Nov 1971
TL;DR: There are certain aspects of language theory that have had, or can have, significant impact on the design and implementation of compilers that are, principally, the subjects of context free grammars and syntax directed translations.
Abstract: There are certain aspects of language theory that have had, or can have, significant impact on the design and implementation of compilers. These areas are, principally, the subjects of context free grammars and syntax directed translations. It is perhaps to be expected that the deep and interesting theorems of language theory do not usually find application. Rather, it is the definitions of formal constructs and their elementary properties that find use.
4 citations