It follows from the definition of the operators of concatenation, and that the set of regular languages is closed under concatenation, union and Kleene closure. The set of regular languages is closed under concatenation, union and Kleene closure. Q6) For any solvable decision problem, there is a way to encode instances of a problem so that the corresponding language can be recognized by a TM with. 3.2.1 Concatenation, Kleene Closure and Union. Q5) Which of the following is not primitive recursive but partially recursive? Let L1,L2 be two NP languages, and M1,M2 be their polynomial time. Q4) Which of the following problems is solvable?Ī) Determining of an arbitrary turing M/c is a universal turing m/cĬ) Determining of universal Turing m/c can be written in fewer than k instructions for some k.ĭ) Determining of universal turing machine and some input will halt. Show that NP is closed under union and concatenation. Q3) The number of symbols necessary to simulate a Turing M/C with m symbols and n states is Q2) Both P and Np are closed under operation Apply this technique to the formula in the previous problem.Q1) The language L = is a.For a formula with $m$ clauses, how long does the purge of a single variable take?. #SHOW THAT NP IS CLOSED UNDER UNION AND CONCATENATION. SERIES#A series of successful purges that results in no remaining clauses constructs a satisfying truth assignment in the process. If neither purge succeeds, the formula is not satisfiable. If it succeeds, continue with the remaining clauses. Choose an arbitrary element $x_i$ in the remaining clauses and set its value to True, and execute the purge algorithm. If the purge does not fail, any resulting clauses have exactly two literals. If during the purge process all variables from a clause are excluded via simplification, the purge fails. Call this process of eliminating one-literal clauses a purge. In computational complexity theory, a problem is NP-complete when: it is a problem for which the correctness of each solution can be verified quickly.
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