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2001Lec8 - CSE 2001 Introduction to Theory of Computation...

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3/14/2006 CSE 2001, Winter 2006 1 CSE 2001: Introduction to Theory of Computation Winter 2006 Suprakash Datta [email protected] Office: CSEB 3043 Phone: 416-736-2100 ext 77875 Course page: http://www.cs.yorku.ca/course/2001 Some of these slides are adapted from Wim van Dam’s slides ( www.cs.berkeley.edu/~vandam/CS172/ ) 3/14/2006 CSE 2001, Winter 2006 2 Next Computability Turing machines TM-computable/recognizable languages Variants of TMs 3/14/2006 CSE 2001, Winter 2006 3 Turing Machines After Alan M. Turing (1912–1954) In 1936, Turing introduced his abstract model for computation in his article “ On Computable Numbers, with an application to the Entscheidungsproblem ”. At the same time, Alonzo Church published similar ideas and results. However, the Turing model has become the standard model in theoretical computer science. 3/14/2006 CSE 2001, Winter 2006 4 Informal Description TM Depending on its state and the letter x i , the TM - writes down a letter, - moves its read/write head left or right, and - jumps to a new state. internal state set Q R L L _ _ 1 # 0 _ 1 1 0 1 At every step, the head of the TM M reads a letter x i from the one-way infinite tape. 3/14/2006 CSE 2001, Winter 2006 5 Input Convention state q 0 L L _ _ _ w w w n 2 1 Initially, the tape contains the input w ∈Σ *, padded with blanks “_”, and the TM is in start state q 0 .
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