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1) "Explain primal dual construction found at:https://en.wikipedia.org/wiki/Max-flow_min-cut_theorem. Is the dual correct?
2) Argue that the following prob is NP Complete. Given a list of positive integers, u1,u2,...un (in binary representation) and asked if there is a partition of this set into 3 subsets, each of which has the same sum.
3) Argue that the problem above is NP Complete if k>3 subsets are required in the partition.
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
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.
Prove that L is not regular. (Be particularly careful if you use the Pumping Theorem. You must choose a w that is actually in L.)
Design in JFLAP a Truing machine that takes as input a tape containing a series of n 1s, Where n >= 0, terminated by an = sign.
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
Write down a structural induction principle for the PlayTree free type
Design a syntactic analyzer for the language specified by the grammar
Consider the language L = L1 ∩ L2, where L1 = {ww^R : w ∈ {a, b}* and L2 = {a^n b*a^n: n ≥ 0}. Write the first four strings in the lexicographic enumeration of L?
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.
Rewrite the productions for each of the following nonterminals as right regular grammars: Identifier, Float. Show the moves made using the DFSA for identifiers in accepting.
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
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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