Implementation and analysis of NFAs with adjustable deterministic blow-up

Non-deterministic and deterministic automata both have the expressive power to recognize regular languages; thus, for any non-deterministic automaton there exists an equivalent deterministic automaton that recognizes the same regular language (and vice versa). Depending on the regular language recognized, however , the number of states in minimal NFAs and DFAs recognizing the language may differ significantly; an n-state NFA can be equivalent to an DFA with as few as n and as many as 2 n states. This project explores the question of whether there always exists an n-state minimal NFA such that the equivalent minimal DFA has n ≤ d ≤ 2 n states. Past research has shown several methods to construct an n-state minimal NFA for a given (n, d) pair over varying alphabet sizes; this report presents several of those constructions and proves their correctness. In addition, some of the constructions are implemented using Java, allowing the NFAs for a particular (n, d) pair to be quickly constructed, visualized, and converted to DFA or regular expressions representations.