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Unformatted text preview: Sep. 8, 2010 (Wednesday) Chapter 1: Regular Languages 5 Minimum State Finite Automata Theorem: For a regular language, there exists a unique (up to isomorphism) minimum state finite automaton recognizing it. • Definition: A language is a regular language, if there exists some finite automaton recognizing it. • Definition: Two finite automata are isomorphic, if they are structurally identical (i.e. they differ only in their state names). For example, the following two finite automata are isomorphic, since if we replace A , B , and C with X , Y , and Z , respectively, then M 5 is the same as M 6. M6 A B C X Z Y 1 1 1 1 1 1 M5 • That is, no matter which method we use to design a finite automaton for a given language, we should always get the same finite automaton (except the name difference) after minimizing the number of states. In today’s class, we will study a method to minimize a finite automaton. Basic Idea: If we can partition all states of a finite automaton into several groups, and every group satisfies the following conditions, • all states in the same group are either all final states or all non-final states. • all states in the same group go to the same next group for each input symbol, then each group can be combined into a single state. If all states in a group are final states, then the combined state is a final state. If all states in a group are non-final states, then the combined state is a non-final state. 7 Algorithm: based on lecture notes at http://www.cs.uky.edu/ lewis/essays/compilers/min-fa.html • step 1: partition all states into two groups – Group G1 contains all final states...
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This note was uploaded on 09/30/2010 for the course CSE 434sd taught by Professor Csczdxc during the Spring '10 term at Harding.
- Spring '10