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Q1) In this problem, we consider a very restricted subset of Boolean expressions. Define an operator to be one of the four symbols: ¬, ∧, ∨, and →. Define a variable to be one of the five symbols: P, Q, R, S and T. Let L = {w : w is a syntactically legal Boolean expression without parentheses and the number of operators in w is exactly equal to the number of variables in w}. Examples:
¬P → Q is in L. P ∧ R ∧ ¬S → R is in L. P → Q is not in L. ¬ ¬P is not in L. Is L regular? Prove your answer.
Redundant sequence identi cation
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Show that the language F = {a^i b^j c^k | i, j, k greater than or equal to 0 and if i = 1 then j = k} is not regular. Show, however, that it satisfies the statement of the pumping lemma
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
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