The Myhill-Nerode Theorem and DFA Minimization
نویسنده
چکیده
The DFA model of computation has explicit state names for every possible state that a machine might be in. Nevertheless, when writing programs, although we do think about the different states that a program might be in, we do not explicitly label them. We now consider how to identify machine states associated with a language L merely by identifying a particular relationship between strings in L rather than discussing explicit labels. The payoff for such an abstract notion of state is great. We will be able to articulate a new characterization of regular languages that will be useful for determining whether or not a language is regular. Further, we will also be able to define and compute a canonical minimal DFA — a DFA with the fewest possible states. Section 2 introduces the relationship between strings and concludes with a theorem characterizing regular languages. Section 3 extends the ideas in section 2 and develops an algorithm for minimizing DFAs.
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تاریخ انتشار 2015