Test membership with dynamic programming table - O(n^3)Ģ.11.7. Substitution - replace each letter of alphabet with a languageĬonverstion to CNF: O(n^2) with size O(n^2) Not closed under intersection, complement Step-by-step solution 94 (17 ratings) for this solution Step 1 of 5 The class NP is closed under union and concatenation NP class: NP is a class of languages that are decidable in nondeterministic polynomial time on a non deterministic Turing machine. Intersection with a regular language (basically run in parallel) \(\vert vwx\vert \leq n\), middle portion not too longĬlosed under union, concatenation, closure, and positive closure, homomorphism, reversal, inverse homomorphism, substitutions If L CFL, then \(\vert z\vert \geq n\), we can break z into 5 strings z=uvwxy, such that: Therefore we showed the non-deterministic Turing machine U precisely accept X union Y. \(L_0=L_^*\) aXb for some a,bĬFL pumping lemma - pick two small strings to pump 7.9 A triangle in an undirected graph is a 3-clique. Show that NP is closed under union and concatenation. introduction #Ĭhomsky hierarchy of languages: \(L_3 \subset L_2 \subset L_1 \subset L_R \subset L_0 \subset Σ*\) Analyze the algorithm given on page 157 to show that this language is in P. 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.Some notes on theoretical computer science, based on UVA’s course. Q5) Which of the following is not primitive recursive but partially recursive? To prove that the class NPof languages is closed under union, intersection, concatenation and Kleene star and also discuss the. 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. To prove that the class NPof languages is closed under union, intersection, concatenation and Kleene star and also discuss the closure of NP under complement. The class of regular languages is closed under union, concatenation and Kleene star. 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
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