304_HW6_F11

304_HW6_F11 - M . d. List the sequence of configurations...

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Homework Set #6 Assigned: Wednesday, 11/2 Due: Wednesday, 11/9 (start of lecture) This assignment covers textbook material in Chapter 3, Section 3.1. Note: Refer to course web site for homework policies. Remember to attach signed honor statement. Note : Different printings or editions of the textbook may have different exercise numbering. Please note the textual problem descriptions below to resolve ambiguity. 1. (24 points) Turing Machine Design: Design a Turing machine M that operates on inputs that are strings in {0,1}*. Design M so that it halts on all inputs that are strings in {0,1}*. When M halts it should be in an accepting state if and only if it has found two consecutive 1's in the input string. It can halt as soon as it finds 11. Try to design M so that it efficiently processes the input; that is, do not waste steps. a. Provide an implementation-level description of M . b. List the parts of the formal 7-tuple for M . c. Draw a detailed pictorial state diagram for
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Unformatted text preview: M . d. List the sequence of configurations (instantaneous descriptions) that M enters for each of these two inputs: i. 010110 (which M should accept); ii. 101001 (which M should reject). 2. (26 points) Turing Machine Design: Textbook Exercise 3.8(c) on p. 160. 3. (26 points) Turing Machine Design: Provide an implementation-level description of a Turing Machine M ' that is given, as input, a string over the alphabet {0,1} which originally appears on the tape preceded by the character s . Assume that the string is known to be of even length. Thus, the input on the tape is of the form: n w w sw 2 2 1 L followed by blanks, where ≥ n and w i is in {0,1} . M ' s hould find the middle of the string, insert the character c there, and then halt. Upon halting, the tape should therefore contain: n n n w cw w w sw 2 1 2 1 L L + followed by blanks . 4. (24 points) Closure : Textbook Exercise 3.16(d) on p. 161 ( Σ 1 closure under intersection) ....
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This note was uploaded on 02/13/2012 for the course CS 91.304 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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