Generating similar images using bag context picture grammars

A Dissertation submitted to the Faculty of Science in partial fulfilment of the requirements for the degree of Master of Science University of the Witwatersrand, Johannesburg, February 2018Formal language theory was born in the middle of the 20th century as a tool for modeling and investigating syntax of natural languages. It was developed in connection with the handling of programming languages. Bag context grammars are a fairly new grammar class where bag context tree grammars have been defined. Bag context is used to regulate rewriting in tree grammars. In this dissertation we use bag context to regulate rewriting in picture grammars and thus to generate similar pictures. This work is exploratory work since bag context picture grammars have not been defined. We use examples to show how bag context picture grammars can be used to generate pictures. In this work bag context picture grammars are defined and used to generate similar pictures. Pictures generated by random context picture grammars and three of their sub-classes are selected and bag context picture grammars are used to generate the same pictures to those selected. A lemma is defined that is used to convert the class of random context picture grammars and three of their sub-classes into equivalent bag context picture grammars. For each grammar selected, an equivalent bag context picture grammar is created and used to generate several pictures that are similar to each other. Similarity is defined by noting small differences that are seen in pictures that belong to the same gallery. In this work we generate similar pictures with bag context picture grammars and thus make the discovery that bag context gives a certain level of control in terms of rules applied in a grammar.XL201

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We introduce new possibilities to control the application of rules based on the preceding application of rules which can be de ned for a general model of sequential grammars and we show some similarities to other control mechanisms as graph-controlled grammars and matrix grammars with and without applicability checking as well as gram- mars with random context conditions and ordered grammars. Using both activation and blocking of rules, in the string and in the multiset case we can show computational com- pleteness of context-free grammars equipped with the control mechanism of activation and blocking of rules even when using only two nonterminal symbols

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Accepting networks of evolutionary picture processors

We extend the study of networks of evolutionary processors accepting words to a similar model, processing rectangular pictures. To this aim, we introduce accepting networks of evolutionary picture processors and investigate their computational power. We show that these networks can accept the complement of any local picture language as well as picture languages that are not recognizable. Some open problems regarding decidability issues and closure properties are finally discussed

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Regulated rewriting in formal language theory

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2008.Context-free grammars are well-studied and well-behaved in terms of decidability, but many real-world problems cannot be described with context-free grammars. Grammars with regulated rewriting are grammars with mechanisms to regulate the applications of rules, so that certain derivations are avoided. Thus, with context-free rules and regulated rewriting mechanisms, one can often generate languages that are not context-free. In this thesis we study grammars with regulated rewriting mechanisms. We consider problems in which context-free grammars are insufficient and in which more descriptive grammars are required. We compare bag context grammars with other well-known classes of grammars with regulated rewriting mechanisms. We also discuss the relation between bag context grammars and recognizing devices such as counter automata and Petri net automata. We show that regular bag context grammars can generate any recursively enumerable language. We reformulate the pumping lemma for random permitting context languages with context-free rules, as introduced by Ewert and Van der Walt, by using the concept of a string homomorphism. We conclude the thesis with decidability and complexity properties of grammars with regulated rewriting