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