Minimizing finite state automata

Computer science is a strange mix of engineering, science, and math. This is captured well by the historic roots of deterministic finite state automata (DFAs). The first ideas that can be recognized as a precursor to DFAs can be found with Gilberth & Gilberth (1921) introducing flow process charts into mechanical and industrial engineering. Independently, McCullock & Pitts (1943) used nerve-nets as a model of neural activity. This preceded Turing’s 1948 entry into brain science with B-type neural networks, and Rosenblatt’s perceptrons (1957). Unlike Turing and Rosenblatt, McCullock & Pitts model did not incorporate learning. However, the nerve nets went on to have a more profound effect on ratiocination because — as Kleene (1951) recognized — they became the modern form of DFAs. Although DFAs are now in less vogue than they were a few decades ago, they are an essential part of a standard computer science curriculum due to their centrality in computer science. Yesterday, I had the privilege of familiarizing students with the importance of DFAs by giving a lecture of Prakash Panangaden’s COMP 330 course. Since Prakash already introduced the students to the theory of DFAs, regular expressions, and languages, I was tasked with explaining the more practical task of DFA minimization.

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