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Explain why every nonempty propositional clause, by itself, is satisfiable. Prove rigorously that every set of five 3-SAT clause is satisfiable, provided that each clause mentions exactly three distinct variables. What is the smallest set of such clauses that is unsatisfiable? Construct such a set.
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.
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.
Argue that the following prob is NP Complete. Given list of positive integers, u1,u2,...un (in binary representation) and asked if there is partition of this set into 3 subsets, each of which has same sum.
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.
Design a syntactic analyzer for the language specified by the grammar
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
Create a Mealy Machine which produces the output of 1 whenever discrepancy in above pattern is detected, and produces the output of 0 otherwise. Write states meaningful names.
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.
Write some examples of declarative knowledge. Write some examples of procedural knowledge. Then, compare examples, highlighting the similarities & differences.
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
Dynamic programming algorithm to compute a shortest superstring.
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