Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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2. Consider the following multi-step implementation level description of a Turing machine with input alphabet
Σ = {a,b,#}.
Alice On input string w:
1. Check the form of w is {a,b} #{a,b}+. Return the read head to the start (left end) of the string.
2. Scroll right to the left-most unmarked symbol before the # sign.
A. If there are no more unmarked symbols before the # sign, goto step 5
B. Mark the left-most unmarked symbol remembering if it's an a or b.
Dickinson
3. Scroll right to the first unmarked symbol after the # sign.
A. If there is no unmarked symbol after the # sign then Alice rejects w.
B. If this symbol does not match the remembered symbol from step 2B then Alice rejects w.
C. Mark the this symbol
2
4. Scroll to the left most end of the tape and goto step 2.
5. Check that all symbols after the # sign are marked. If any unmarked symbols are found, Alice rejects w,
otherwise Alice accepts w.
(a) What language does Alice recognize/decide?
(b) Is Alice a decider or a recognizer? Explain (with more then Alice loops or doesn't loop).
(c) Write a few sentences analyzing the time complexity of Alice. Is the language Alice decides/recognizes a
member of P? Why or why not?
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Transcribed Image Text:2. Consider the following multi-step implementation level description of a Turing machine with input alphabet Σ = {a,b,#}. Alice On input string w: 1. Check the form of w is {a,b} #{a,b}+. Return the read head to the start (left end) of the string. 2. Scroll right to the left-most unmarked symbol before the # sign. A. If there are no more unmarked symbols before the # sign, goto step 5 B. Mark the left-most unmarked symbol remembering if it's an a or b. Dickinson 3. Scroll right to the first unmarked symbol after the # sign. A. If there is no unmarked symbol after the # sign then Alice rejects w. B. If this symbol does not match the remembered symbol from step 2B then Alice rejects w. C. Mark the this symbol 2 4. Scroll to the left most end of the tape and goto step 2. 5. Check that all symbols after the # sign are marked. If any unmarked symbols are found, Alice rejects w, otherwise Alice accepts w. (a) What language does Alice recognize/decide? (b) Is Alice a decider or a recognizer? Explain (with more then Alice loops or doesn't loop). (c) Write a few sentences analyzing the time complexity of Alice. Is the language Alice decides/recognizes a member of P? Why or why not?
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