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Q1) Show that the following identities hold for regular expressions over any alphabet:
1. epsilon + R*R = R* 2. (R*S*) = (R + S)*
These should be done by interpreting the regular expressions as languages (i.e. sets of words) and arguing that the sets are equal. The proofs do not have to be formal proofs by induction; a compelling argument will suffice.
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
Design a syntactic analyzer for the language specified by the grammar
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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).
Write a program would read two numbers and then print all numbers between the first and the second, inclusive. Design unambiguous grammar to parse expressions
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.
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
Redundant sequence identi cation
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.
Dynamic programming algorithm to compute a shortest superstring.
Write down a structural induction principle for the PlayTree free type
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