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Q1) Create a standard 1-tape Turing machine M to compute the function sub3, which is defined as follows:
sub3(n) = n-3 if n > 2 0 if n ≤ 2.
Specifically, calculate sub3 of a natural number represented in binary. For example, on input 10111, M should output 10100. On input 11101, M should output 11010. (Hint: you may want to define a subroutine.)
Write down a structural induction principle for the PlayTree free type
Write a grammar for the language consisting of strings that have n copies of the letter a followed by same number of copies of the letter b, where n>0
Express the following set as a regular expression: The set of all strings of length at least three over {0,1} such that every three consecutive.
Redundant sequence identi cation
Show that the following identities hold for regular expressions over any alphabet: epsilon + R*R = R*. These should be done by interpreting the regular expressions as languages.
We showed to prove that if L can be identified by DFA then the language left half(L) = {x ∈ ∑*|∃y xy ∈ L and |x| = |y|} is also regular; here |x| means length of x.
Give a construction that assumes you are given a DFA for L and show how to construct an NFA (with or without ε-moves) to recognize sort(L).
Dynamic programming algorithm to compute a shortest superstring.
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
Design a syntactic analyzer for the language specified by the grammar
Consider a logic function with three outputs, A , B , and C , and three inputs, D , E , and F . The function is defined as follows: A is true if at least one input is true, B is true
How the problem would be encountered in attempting to represent the following statements in Predicate logic. it should be possible to: John only likes to see French movies.
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