Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 34.2, Problem 4E
Program Plan Intro
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.
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Present a language B such that B is complete for the class of Turing-decidable languges under ≤m reductions.
Prove that the language L1 = {b^k c^2k | k >= 0 } is not regular language with the pumping lemma.
It is well-known that regular languages are closed under the following operations: union, complement, and intersection. It is also well-known that all finite languages are regular. For each of the operations, union, intersection and complement, are finite languages closed under them? If yes, prove it. Else provide couter examples.
Chapter 34 Solutions
Introduction to Algorithms
Ch. 34.1 - Prob. 1ECh. 34.1 - Prob. 2ECh. 34.1 - Prob. 3ECh. 34.1 - Prob. 4ECh. 34.1 - Prob. 5ECh. 34.1 - Prob. 6ECh. 34.2 - Prob. 1ECh. 34.2 - Prob. 2ECh. 34.2 - Prob. 3ECh. 34.2 - Prob. 4E
Ch. 34.2 - Prob. 5ECh. 34.2 - Prob. 6ECh. 34.2 - Prob. 7ECh. 34.2 - Prob. 8ECh. 34.2 - Prob. 9ECh. 34.2 - Prob. 10ECh. 34.2 - Prob. 11ECh. 34.3 - Prob. 1ECh. 34.3 - Prob. 2ECh. 34.3 - Prob. 3ECh. 34.3 - Prob. 4ECh. 34.3 - Prob. 5ECh. 34.3 - Prob. 6ECh. 34.3 - Prob. 7ECh. 34.3 - Prob. 8ECh. 34.4 - Prob. 1ECh. 34.4 - Prob. 2ECh. 34.4 - Prob. 3ECh. 34.4 - Prob. 4ECh. 34.4 - Prob. 5ECh. 34.4 - Prob. 6ECh. 34.4 - Prob. 7ECh. 34.5 - Prob. 1ECh. 34.5 - Prob. 2ECh. 34.5 - Prob. 3ECh. 34.5 - Prob. 4ECh. 34.5 - Prob. 5ECh. 34.5 - Prob. 6ECh. 34.5 - Prob. 7ECh. 34.5 - Prob. 8ECh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4P
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- Prove that the language L1={} is not regular language with the pumping lemma.arrow_forward. Prove that xn A yn is a non-regular language.Hint: as you know that according to pumping lemma version-I an bn is a non-regular.arrow_forwardShow that the class of context free languages is closed under Kleene stararrow_forward
- Show that if M is a DFA that recognizes language A, swapping the accept and nonaccept states in Myields a DFA that recognizes the complement of A. Show that the class of regular languages is closedunder complement.arrow_forwardThe complement of a language is the set of all strings that are not in the language.Let L be a language over Σ Prove that if L is regular then so is its complementarrow_forwardShow using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.arrow_forward
- Prove that the class of context free languages is not closed under complement.arrow_forwardShow that language is not regular using pumping lemma. Proofarrow_forwardWe know that for Σ = {0, 1}, there are uncountably many languages over Σ. Is this also true for the languages over the unary alphabet {1}? Give proof from scratch (not using known theorems).arrow_forward
- Find the language L recognized by the non-deterministic finite-state automaton:arrow_forwardProve that every regular language is accepted by a planar NFA, possibly with ǫ-moves. A finite state machine (or a graph) is planar if its transition diagram can be drawn in the plane without having edges crossing with each other.arrow_forwardProve that the language containing strings of the form 0k where k is multiple of n is a regular language for all narrow_forward
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