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assignment3 - mentation 3 Let A ={h R,S i| R and S are...

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CSC544 Assignment #3 due Thursday 3/10 in class version 1.0 Problems 1. A Turing machine with a doubly infinite tape is similar to an ordinary Turing machines, but its tape is infinite to the left as well as to the right. The tape is initially filled with blanks except for the portion that con- tains the input. Computation is defined as usual except that the head never encounters an end to the tape as it moves leftward. Show that this type of Turing machine recognizes exactly the class of Turing-recognizable languages. 2. Show that the collection of decidable languages is closed under comple-
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Unformatted text preview: mentation. 3. Let A = {h R,S i| R and S are regular expressions and L ( R ) ⊆ L ( S ) } . Show that A is decidable. (Hint: regular languages are closed under complemen-tation, intersection, and union). 4. Prove that EQ DFA is decidable by testing the two D±As on all strings up to a certain size. Calculate a size that works. 5. A language is prefx-Free iF no member is a proper prefx oF another mem-ber. Let PF REX = {h R i| R is a regular expression where L ( R ) is prefx-Free } . Show hat PF REX is decidable. 1...
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