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Lecture 35

# Lecture 35 - ECE52 Spring 11 Lecture 35 Interim project...

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1 ECE52 Spring 11 Lecture 35 4/11/11 Interim project progress reports due Friday 4/15/11 Viewed some of http://aturingmachine.com/ in class

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2 A FSM with infinite memory: Turing Machines Consider a system consisting of Finite State Machine M which is coupled through a read/write head to an arbitrarily long storage register called the tape . The tape is divided into squares, with each square storing a single symbol. Blank == 0. The head can do three things: read current symbol write a new (not necessarily distinct) symbol move the tape one position left or right 1 1 1 1 Tape Finite State Control Unit Head
3 Turing Machine operation In one computation cycle: – Starting from state S i , machine reads current symbol writes a new symbol (could be the same) moves one position left or right – enters state S j . 1 1 1 1 Tape Finite State Control Unit Head

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4 Turing machine example Design Turing FSM that, given two finite blocks of 1’s separated by a finite block of 0’s (blanks) on the tape, will shift the left- hand block of 1’s to the right until it touches the right-hand group and then halt (i.e. unary addition!). Initial conditions: machine is in state A positioned over leftmost square containing a 1. 1 1 1 1 A 1 1 1 1 HLT
5 Algorithm At each step, erase left-most one and write a new one in first open blank square (blank=0) 1 1 1 1 A 1 1 1 1 C 1 1 1 1 A 1 1 1 1 C 1 1 1 1 C->HLT Present State Next State, write, shift 0 1 A - B,0R B C,1R B,1R C D,0L Halt D A,0R D,1L Halt Halt Halt

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6 So why do we care? Provides theoretical framework (CPS140) for thinking about problems that are computable but not with a FSM alone not computable even with infinite tape (memory) Any “Turing-complete” computer can in principle run any computable problem
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Lecture 35 - ECE52 Spring 11 Lecture 35 Interim project...

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