MCQs on Reduction Techniques
What is the main purpose of reduction techniques in computational complexity theory?
A) To increase the efficiency of algorithms
B) To decrease the time complexity of problems
C) To simplify the analysis of problem difficulty
D) To eliminate undecidable problems
Answer: C) To simplify the analysis of problem difficulty
Which statement best describes a polynomial-time reduction between two computational problems?
A) It converts one problem into another with polynomially related input sizes.
B) It converts one problem into another with polynomial time complexity.
C) It converts one problem into another with linear time complexity.
D) It converts one problem into another with exponential time complexity.
Answer: A) It converts one problem into another with polynomially related input sizes.
True or False: Reduction techniques are used to find exact solutions to computational problems.
A) True
B) False
Answer: B) False
Which complexity class is typically targeted to demonstrate hardness through reduction?
A) P
B) NP
C) PSPACE
D) EXP
Answer: B) NP
In the context of NP-completeness, what does it mean for a problem to be NP-hard?
A) The problem is solvable in polynomial time.
B) The problem is harder than any problem in NP.
C) The problem is reducible to any problem in NP.
D) The problem is unsolvable.
Answer: B) The problem is harder than any problem in NP.
Which of the following is an example of a problem commonly used in reduction proofs for NP-completeness?
A) Calculating the Fibonacci sequence
B) Determining if a number is prime
C) Sorting a list of integers
D) Finding the minimum spanning tree in a graph
Answer: D) Finding the minimum spanning tree in a graph
Which technique is commonly used to establish the NP-completeness of a problem?
A) NP reduction
B) Polynomial-time reduction
C) Linear-time reduction
D) Exponential-time reduction
Answer: A) NP reduction
What does a reduction from problem A to problem B indicate in computational complexity theory?
A) Problem A is solvable if and only if problem B is solvable.
B) Problem B is harder than problem A.
C) Problem A is unsolvable.
D) Problem B can be solved in constant time.
Answer: A) Problem A is solvable if and only if problem B is solvable.
Which statement best describes the computational relationship established by a reduction?
A) It shows that two problems have the same time complexity.
B) It demonstrates that one problem can solve another problem.
C) It proves that a problem is in P.
D) It reduces the space complexity of algorithms.
Answer: B) It demonstrates that one problem can solve another problem.
Which area of computer science heavily relies on reduction techniques to classify problems?
A) Software development
B) Machine learning
C) Cryptography
D) Operating systems
Answer: C) Cryptography
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