Date of Award
Thesis open access
A recently revisited question in finite automata theory considers the possible numbers n and d for which there exists an n-state minimal NFA with a minimal equivalent DFA of d states. We present a new class of finite automata, the NFA En of n states, which in a sense contains half of the state hierarchy [n, 2n]; that is, by making small modifications to En, we can create a minimal equivalent DFA of d states for any d ∈ (2n−1, 2n]. Although this is not stronger than the most recent of work that has been done on the problem, the value of this result lies in the systematic and intuitive method by which we, given the parameter d, construct the appropriate NFA from En. Specifically, the construction from En is a direct reflection of the binary representation of 2n−d, each 1-bit of which indicates a single modification to make to En. We conclude the thesis with a discussion of computational results to suggest that these methods can be extended to reach the entire state hierarchy, that is, to answer the question for any d ∈ [n, 2n].
Maly, Matthew, "On the State Hierarchy of Exploding Automata" (2010). Computer Science Honors Theses. 19.