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On Parallel Processing in Formal Models: Jumping Automata and Normal Forms
Kocman, Radim ; Černá, Ivana (oponent) ; Janoušek, Jan (oponent) ; Meduna, Alexandr (vedoucí práce)
The present thesis introduces and studies new possibilities of parallel processing in formal models. More specifically, it focuses its attention on parallel versions of jumping finite automata and on normal forms of grammars with interesting parallel properties. In the first part of this thesis, we give an initial motivation for studying parallel processing in formal models. We briefly introduce jumping models and normal forms of grammars and grammar systems. Finally, we state the precise focus and goals of our research. The second part of this thesis is focused on new results on jumping finite automata. First, we introduce n-parallel jumping finite automata that enhance the original jumping finite automaton model with multiple reading heads. The rest of the chapter then studies the accepting power of the model under two different jumping modes. Second, we introduce double-jumping finite automata and explore advanced jumping modes utilizing two heads. We study the accepting power of the models and also the closure properties of the related language families. Lastly, we introduce jumping 5'->3' Watson-Crick finite automata that combine the jumping behavior with the biology-inspired Watson-Crick finite automata that process double-stranded DNA sequences. The rest of this chapter then studies the accepting power of the model under unrestricted and various restricted conditions. The third part of this thesis is focused on new results on CD grammar systems. We introduce two types of transformations that turn arbitrary general grammars into equivalent two-component general CD grammar systems of very reduced and simplified forms. Apart from the reduction and simplification, we describe several other useful properties concerning these systems and the way they work. In the last part, we mention possible application perspectives for the introduced models and normal forms, and we conclude the thesis with the final summary and the description of theoretical perspectives for the achieved results.
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