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# hw5cs - beyond the left margin a new blank cell is created...

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CSE 105: Introduction to the Theory of Comptuation Fall 2010 Problem Set 5 Instructor: Daniele Micciancio Due on: Wed. Nov 10, 2010 Problem 1 Let BIGGER be the set of all strings over the alphabet { 0 , 1 ,> } of the form x > y , where x and y are binary numbers such that x is bigger than y . For example, 100#0011 and 11#00 are in BIGGER, but 1010#1111 and 11#11 are not. Give a deterministic Turing machine that decides the language BIGGER. Design your TM using jﬂap, and submit your jﬂap ﬁle (1.jﬀ) together with a brief English description of your solution. Problem 2 The textbook deﬁnes Turing machines as ﬁnite state automata with a read/write tape that extends indef- initely to the right. If the Turing machine attempts to move beyond the left hand boundary of the tape, the tape head simply stays in its current position. JFLAP allows a seemingly more powerful type of Turing machine, whose tape in unbounded both to the left and to the right, and if the machine attepts to move
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Unformatted text preview: beyond the left margin, a new blank cell is created to allow moving left. In this problem you are asked to give a formal deﬁnition of this extended Turing machine, including 1. the deﬁnition of a machine as a tuple of sets and functions 2. an appropriate set of conﬁgurations 3. an appropriate transition relation between conﬁgurations 4. the set of strings accepted by the machine Problem 3 Prove that the model of computation deﬁned in problem 2 is not more powerful than the Turing machine as deﬁned in the textbook, giving a method to transform any extended Turing machine (with doubly inﬁnite tape) into an equivalent regular Turing machine. Describe your transformation in detail, either by giving a formal description of the resulting Turing machine, or by providing an accurate low level description of all the steps it performs....
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