Showing papers on "Formal language published in 1972"
TL;DR: Developed is a stochastic context-free language for use in pattern classification of chromosome images based on statistical decision theory with the probability of occurrence of each pattern computed from the stochastically context- free grammar.
Abstract: A procedure is described for stochastic syntax analysis of context-free languages. The parsing algorithm utilizes a bottom-up technique used in precedence languages. All decisions encountered in the algorithm ate determined statistically. The stochastic choice is computed from the a priori probability distribution of the language. Also developed is a stochastic context-free language for use in pattern classification of chromosome images. Classification is based on statistical decision theory with the probability of occurrence of each pattern computed from the stochastic context-free grammar.
49 citations
15 citations
TL;DR: A new data base is introduced by generalizing the notion of concatenation in representing patterns with a relationship matrix and it is shown that this data base will allow us to remove many of the present restrictions placed on the types of patterns that can be handled by syntax-directed systems.
Abstract: The problem of developing an appropriate data base for syntax-directed pattern analysis and recognition is considered. A new data base is introduced by generalizing the notion of concatenation in representing patterns with a relationship matrix. The characteristics of relationship matrix are demonstrated in teh context of formal language theory. It is shown that this data base will allow us to remove many of the present restrictions placed on the types of patterns that can be handled by syntax-directed systems. Problems in pattern analysis (description and generation) as well as in pattern recognition are discussed and examples are given to illustrate the potential application of this data base in both of these areas.
6 citations
14 Jun 1972
TL;DR: In this article, it was shown that a grammar such that in each noncontext-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side is context-free.
Abstract: If G is a grammar such that in each noncontext-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side; then the language generated by G is context-free Six previous results follow as simple corollaries of this theorem
3 citations
Journal Article•
3 citations
TL;DR: There will be no disqjretment that the AI&&L 68 authors intended to include such constructs, that the above example is fairly described, or that the following is the intended s,vr?+actic justification for the inclusion of tie particular construct.
2 citations
TL;DR: This paper studies translations between schemes and related equivalence problems, i.e., problems of determining whether two schemes in a given class are equivalent, and presents four methods: applying the theory of formal languages, programming, measuring the complexity of a computation, and “cutting and pasting”.
Abstract: Here and in a further paper [2] we study translations between schemes and related equivalence problems, i.e., problems of determining whether two schemes in a given class are equivalent. In particular, we are concerned with the question of developing methods for attacking these problems. It seems to us that some “general methods” ought to exist or, at least, a general form ought to be given to the existing “tricks”. In these papers we present four methods: applying the theory of formal languages, programming, measuring the complexity of a computation, and “cutting and pasting” (roughly speaking, the application of a method due to Rabin and Scott [8] to bound the search necessary to determine if two schemes will behave differently).Although a few of the results are true for some general notion of scheme, we have nearly always had in mind, for the sake of illustration, just three specific classes of schemes: program schemes, program schemes augmented with counters, and recursively defined schemes. The greater part of the study is restricted to monadic schemes (i.e., schemes containing only functions and predicates of a single argument), and in the case of recursively defined schemes, we are concerned almost exclusively with the single variable monadic recursion schemes introduced by de Bakker and Scott in [1].
1 citations
25 Sep 1972
TL;DR: A property of polynomial complete languages is extended in order to better compare various classes of formal languages defined by time- or tape-bounded turing machines.
Abstract: A property of polynomial complete languages is extended in order to better compare various classes of formal languages defined by time- or tape-bounded turing machines.
1 citations
01 Jan 1972
TL;DR: A procedure is described forstochastic syntax analysis of context-free languages, where the parsing algorithm utilizes abottom-up technique used in precedence languages and the choice of language is computed from theriori probability distribution of the language.
Abstract: A procedure isdescribed forstochastic syntax analysis ofcontext-free languages. Theparsing algorithm utilizes abottom-up technique usedinprecedence languages. Alldecisions encountered in thealgorithm atedetermined statistically. Thestochastic choice is computed fromtheapriori probability distribution ofthelanguage. Alsodeveloped isastochastic context-free language foruseinpat- ternclassification ofchromosome images. Classification isbasedon statistical decision theory withtheprobability ofoccurrence ofeach pattern computed fromthestochastic context-free grammar. IndexTerms-Bottom-up parsing, context-free languages, formal languages, linguistic pattern recognition, picture classification, stochastic compiler, stochastic context-free languages, stochastic linguistic pattern recognition, stochastic parsing, stochastic syntax analysis, syntax-directed compiler.
TL;DR: This paper answers a question of Marcus about the language L, a language composed of strings a"1a"2...a"n of elements of V such that for some k, if a"i@eS"k then a" i"+"1@e S"k" +"1" then Where does L fall in the standard hierarchy of formal languages?