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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.)
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.
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
Dynamic programming algorithm to compute a shortest superstring.
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
Design a syntactic analyzer for the language specified by the grammar
Create a finite-state machine design to turn your FPGA development board into a simple programmable music box.
Redundant sequence identi cation
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).
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
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
Considering a single programmed operating system, what is the minimal total time required to complete executions of the two processes? You should explain your answer with a diagram.
Discuss the impact of Moore's law on data center costs on such things as servers and communications equipment. List at least 3 steps or recommendations your data center can take to offset some or all of the effect of Moore's law.
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