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Efficient Approaches to Subset Construction
, 1995
"... This thesis addresses important issues in the conversion of nondeterministic finite automata into deterministic finite automata: the development of the conversion process, the behavior of the conversion process with respect to input automata, and the relationship of output automata to input automata ..."
Abstract
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This thesis addresses important issues in the conversion of nondeterministic finite automata into deterministic finite automata: the development of the conversion process, the behavior of the conversion process with respect to input automata, and the relationship of output automata to input automata. In developing a robust, efficient, and modular conversion program, it is necessary to analyze searching and sorting routines, abstract data types, and other issues in order to determine appropriate routines and structures for use with automata and their manipulation. Subset construction is a well-known procedure for converting a nondeterministic finite automaton into a deterministic finite automaton. A large part of this thesis explains the improvements made to an existing, inefficient, implementation of subset construction based on a pseudo-code specification. The testing phase of this project led to a study of the behavior of the conversion process with respect to different types of automata. Very few automata were available for testing, therefore, methods to generate test automata were examined. Some interesting behavior in the output automata, with respect to the input automata, prompted concurrent study in this area. A conjecture based on the density of automata enables us to estimate the cost of subset construction prior to actually performing the construction. In conclusion, recommended implementations of subset construction are suggested based upon information about the input automaton.

