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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.
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
We know by rice's theorem that none of the following problems are decidable. However,are they recursively enumerable,or non-RE? IS L(M) infinite?
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
Suppose f is a function that returns the result of reversing the string of symbols given as its input, and g. What ambiguity exists in the statement x?
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.
Dynamic programming algorithm to compute a shortest superstring.
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
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?
Describe the difference between a Deterministic Finite Automata and Non-Deterministic Finite Automata. In general, which one is expected to have less number of states ?
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.
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.)
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