Ch8 - Chapter 8 Turing Machine(TMs Turing Machines s s s s...

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Chapter 8 Turing Machine (TMs)

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2 Turing Machines Accepts the languages that can be generated by unrestricted ( phrase-structured ) grammars No computational machine (i.e., computational language recognition system) is more powerful than the class of TMs due to the language processing power, i.e., the generative power of grammars , its unlimited memory , and time of computations Proposed by Alan Turing in 1936 as a result of studying algorithmic processes by means of a computational model TMs are similar to FAs since they both consist of i) a control mechanism , and ii) an input tape In addition, TMs can i) move their tape head back and forth , and ii) write on, as well as read from, their tapes.
3 Turing Machines Defn. 8.1.1 A TM is a quintuple M = ( Q , , Γ , δ , q 0 ), where Q is a finite set of states Γ is a finite set called the tape alphabet which contains B , a special symbol that represents a blank Γ - { B }, is the input alphabet δ : Q × Γ Q × Γ × { L, R }, a transition function , which is a partial function q 0 Q , is the start state

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4 Turing Machines Machine Operations: Write operation - replaces a symbol on the tape with another (not necessarily distant) symbol Move operation - moves the tape head one cell to the right (left, respectively) and then shift to a new (or current) state Halt operation - halts when the TM encounters a < state , input symbol > pair for which no transition is defined
5 Turing Machines Machine Operations . TMs are designed to perform computations on strings from the input alphabet Example 8.1.2 . A TM produces a copy of input string over { a , b } with input BuB and terminates with tape BuBuB , where u ( a b )* q 1 q 0 q 2 q 3 q 4 q 6 q 5 q 7 B/B R B/B R B/B R a/a R a/a R a/a R a/a R b/Y R b/b R b/b R b/b R b/b R B/B L B/B L b/b L a/a L B/a L B/b L a/X R X/X R X/a L Y/b L Y/Y R >

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6 TMs Transitions of TMs: uq i vB xq j yB denotes that xq j yB is obtained from uq i vB by a single transition of M uq i vB xq j yB denotes that xq j yB is obtained from uq i vB by zero or more transitions of M . TMs as Language Acceptors TMs can be designed to accept languages besides computing functions , and accepting a string does not require the entire input string to be read. Defn. 8.2.1 Let M = ( Q , , Γ , δ , q 0 , F ) be a TM. A string u * is accepted by final state if the computation of M with input u halts in a final state. m
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This note was uploaded on 03/02/2012 for the course C S 252 taught by Professor Dennisng during the Winter '12 term at BYU.

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Ch8 - Chapter 8 Turing Machine(TMs Turing Machines s s s s...

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