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Computational complexity theory - Test
Contributed by: MacKenzie
  • 1. Computational complexity theory is a branch of theoretical computer science that focuses on classifying computational problems based on their inherent difficulty and the amount of resources required, such as time and space. It deals with understanding the efficiency of algorithms, analyzing the feasibility of solving problems on different types of machines, and determining the limitations of computing power. By studying computational complexity theory, researchers seek to investigate the boundaries of computation and identify the capabilities and limitations of computers in solving various types of problems.

    What is computational complexity theory focused on?
A) Developing new programming languages
B) Analyzing the resources required to solve computational problems
C) Hardware design for computers
D) Psychological aspects of human-computer interaction
  • 2. Which notation is commonly used to denote the complexity of algorithms?
A) Big O notation
B) Binary code
C) Roman numerals
D) Greek letters
  • 3. Which complexity class contains decision problems that are efficiently verifiable?
A) BPP
B) NP
C) EXP
D) PSPACE
  • 4. What is the main objective of computational complexity theory?
A) To create faster computers
B) To classify computational problems based on their inherent difficulty
C) To build supercomputers
D) To generate random numbers
  • 5. What is the complexity class that represents the hardest problems in NP?
A) NP-complete
B) BPP
C) P
D) EXPTIME
  • 6. What does 'EXP' stand for in computational complexity theory?
A) Expert
B) Exploratory
C) Exponential time
D) Expanded
  • 7. What is the Cook-Levin theorem related to in computational complexity theory?
A) Quantum algorithms
B) Parallel computing
C) P vs NP problem
D) NP-completeness
  • 8. What complexity class is used to classify problems that can be solved by a quantum computer in polynomial time?
A) EXPSPACE
B) BQP
C) PSPACE
D) NP-complete
  • 9. What is a computational problem?
A) A task solved by a computer using an algorithm
B) A mathematical equation that cannot be solved
C) An unsolvable theoretical question
D) A hardware issue in computers
  • 10. What is the usual choice for the alphabet when representing problem instances?
A) The hexadecimal alphabet
B) The binary alphabet {0,1}
C) The set of all lowercase letters
D) The set of ASCII characters
  • 11. What is a common assumption in proofs of complexity-theoretic theorems?
A) Use of decimal notation only
B) Some concrete choice of input encoding
C) Encoding using natural language
D) No need for any encoding
  • 12. Give an example of a decision problem involving graphs.
A) Calculating the maximum flow in a network.
B) Finding the shortest path in a graph.
C) Deciding whether a given graph is connected or not.
D) Determining the number of nodes in a graph.
  • 13. What is an example of a function problem?
A) Determining if two graphs are isomorphic.
B) The traveling salesman problem.
C) Deciding if a number is prime.
D) Checking if a graph is bipartite.
  • 14. What is typically used to measure the input size in computational complexity theory?
A) Bits
B) Characters
C) Words
D) Bytes
  • 15. What is the primary purpose of a Turing machine?
A) A theoretical model for general computation.
B) A practical computing technology.
C) An early form of computer hardware.
D) A device to manipulate physical objects.
  • 16. Which thesis is associated with the statement that any problem solvable by an algorithm can be solved by a Turing machine?
A) Gödel's incompleteness theorems.
B) The Church–Turing thesis.
C) Cook-Levin theorem.
D) P vs NP theorem.
  • 17. Which type of Turing machine uses random bits to make decisions?
A) Probabilistic Turing machine.
B) Non-deterministic Turing machine.
C) Deterministic Turing machine.
D) Quantum Turing machine.
  • 18. What is a common feature of all machine models discussed in complexity theory?
A) They operate deterministically.
B) They are limited to polynomial time.
C) They use random bits for computation.
D) They require physical realizability.
  • 19. Which axiom set is used to define complexity measures very generally?
A) P vs NP axioms
B) Cook-Levin theorem
C) Blum complexity axioms
D) Turing completeness axioms
  • 20. Which of the following is NOT a commonly used complexity measure in complexity theory?
A) Quantum entanglement complexity
B) Decision tree complexity
C) Communication complexity
D) Circuit complexity
  • 21. Which complexity measure involves the amount of information exchanged between parties?
A) Time complexity
B) Space complexity
C) Circuit complexity
D) Communication complexity
  • 22. What did Raymond Smullyan study in 1961?
A) Complexity measures
B) Rudimentary sets
C) Real-time computations
D) Linear bounded automata
  • 23. Which theorem states that PSPACE = NPSPACE?
A) P vs NP problem
B) Cook-Levin theorem
C) Time hierarchy theorem
D) Savitch's theorem
  • 24. Which complexity class is defined using probabilistic Turing machines?
A) NC
B) QMA
C) BPP
D) AC
  • 25. Which theorem implies that L is strictly contained in PSPACE?
A) Space hierarchy theorem
B) Time hierarchy theorem
C) Savitch's theorem
D) Cook-Levin theorem
  • 26. In which year did Boris Trakhtenbrot begin his study of computational complexity?
A) 1955
B) 1960
C) 1971
D) 1956
  • 27. Which complexity class is known to be contained within PSPACE?
A) BQP
B) MA
C) PH
D) PP
  • 28. Who authored 'Computational Complexity: A Conceptual Perspective'?
A) Oded Goldreich
B) Michael R. Garey; David S. Johnson
C) Sanjeev Arora; Boaz Barak
D) Christos Papadimitriou
  • 29. In what year did Richard Karp publish his paper on NP-complete problems?
A) 1965
B) 1971
C) 1972
D) 1967
  • 30. What term did Boris Trakhtenbrot coin in 1955 that is now known as 'complexity measure'?
A) "Turing machine"
B) "Computational complexity"
C) "Signalizing function"
D) "Polynomial time"
  • 31. Which type of reduction is most commonly used in complexity theory?
A) Exponential-time reduction.
B) Linear-time reduction.
C) Logarithmic-time reduction.
D) Polynomial-time reduction.
  • 32. In what year did Alan Turing define Turing machines?
A) 1965
B) 1950
C) 1936
D) 1945
  • 33. Who edited the book 'Unravelling Complexity: The Life and Work of Gregory Chaitin'?
A) Arora, Sanjeev; Barak, Boaz
B) Downey, Rod; Fellows, Michael
C) Wuppuluri, Shyam; Doria, Francisco A.
D) Garey, Michael R.; Johnson, David S.
  • 34. If P equals NP, what can be inferred about co-P and co-NP?
A) co-P would equal co-NP
B) P would not equal NP
C) co-P would not equal co-NP
D) NP would not equal co-NP
  • 35. Which complexity class is defined using Boolean circuits?
A) BPP
B) AC
C) QMA
D) RP
  • 36. Who conducted the running time analysis of the Euclidean algorithm in 1844?
A) Juris Hartmanis
B) Gabriel Lamé
C) Alan Turing
D) Richard E. Stearns
  • 37. Who studied real-time computations in 1962?
A) Hisao Yamada
B) Raymond Smullyan
C) Boris Trakhtenbrot
D) John Myhill
  • 38. Which complexity class contains problems solvable in logarithmic space?
A) NL
B) L
C) NC
D) PP
  • 39. What is the corresponding set of function problems for P?
A) PSPACE
B) EXPTIME
C) NP
D) FP
  • 40. Who defined linear bounded automata in 1960?
A) Boris Trakhtenbrot
B) John Myhill
C) Raymond Smullyan
D) Hisao Yamada
  • 41. In the context of continuous complexity theory, what is approximated by discretizations?
A) Quantum states.
B) Continuous functions.
C) Boolean expressions.
D) Discrete graphs.
  • 42. Which complexity class includes all decision problems?
A) P
B) NP
C) EXPTIME
D) ALL
  • 43. Who are the authors of 'Parameterized complexity'?
A) Cook, Stephen; Fortnow, Lance
B) Papadimitriou, Christos; Sipser, Michael
C) Wuppuluri, Shyam; Doria, Francisco A.
D) Downey, Rod; Fellows, Michael
  • 44. How many combinatorial and graph theoretical problems did Richard Karp show to be NP-complete?
A) 21
B) 15
C) 10
D) 30
  • 45. Which analysis considers both costly and less costly operations together over the whole series of operations?
A) Worst-case complexity
B) Average-case complexity
C) Amortized analysis
D) Best-case complexity
  • 46. Which complexity class is believed to contain the complement problems of NP?
A) co-NP
B) NP
C) BQP
D) PP
  • 47. What does analog computation involve according to continuous complexity theory?
A) Finite state machines.
B) Probabilistic algorithms.
C) Digital signal processing.
D) Continuous dynamical systems and differential equations.
  • 48. Who wrote 'A Short History of Computational Complexity'?
A) Cook, Stephen
B) Khalil, Hatem; Ulery, Dana
C) Mertens, Stephan
D) Fortnow, Lance; Homer, Steven
  • 49. Which complexity class is defined using interactive proof systems?
A) NC
B) IP
C) QMA
D) BPP
  • 50. Who are the authors of 'Computational Complexity' published in 1994?
A) Michael R. Garey; David S. Johnson
B) Sanjeev Arora; Boaz Barak
C) Oded Goldreich
D) Christos Papadimitriou
  • 51. Who suggested that a 'good' algorithm should have running time bounded by a polynomial of the input size?
A) Gabriel Lamé
B) Juris Hartmanis
C) Leonid Levin
D) Edmonds
  • 52. Who authored 'Introduction to the Theory of Computation'?
A) Christos Papadimitriou
B) Michael Sipser
C) Boaz Barak
D) Sanjeev Arora
  • 53. Which complexity class includes counting problems?
A) NC
B) BPP
C) #P
D) RP
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