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Formal Definition● an alphabet● a set of states ○ one denoted as a "starting state" ○ one or more denoted as "accepting states"● a transition function ○ takes a symbol and a state and returns a new state
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Formal Definition● an alphabet● a set of states ○ one denoted as a "starting state" ○ one or more denoted as "accepting states"● a transition function ○ takes a symbol and a state and returns zero or more states
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Formal Definition (slightly simplified)● two alphabets ○ one for reading, the input alphabet ○ one for writing, the output (or tape) alphabet● a set of states ○ one starting state ○ one accepting state ○ one rejecting state● a transition function takes a symbol and a state and returns a new state, a symbol to write, and Left or Right
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Example TMLets call it MIt accepts strings whose length is a power of 2Accepted strings: "0", "00", "0000"Rejected strings: "", "000", "000000"
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A description of M Attribution: Sipser, Figure 3.8
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Wrapping upWhy do we care about Turing machines?
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ReferencesDeterministic finite automaton. (2012, March 11). Retrieved from http://en.wikipedia.org/wiki/Deterministic_finite_automatonNondeterministic finite automaton. (2012, April 20). Retrieved from http://en.wikipedia.org/wiki/Nondeterministic_finite_automatonPetzold, C. (2008). The annotated turing. Indianapolis: Wiley Publishing, Inc.Sipser, M. (2006). Introduction to the theory of computation. (2nd ed.). Boston:Thompson Course Technology.Turing machine. (2012, April 17). Retrieved from http://en.wikipedia.org/wiki/Turing_machine
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