계산 복잡도 이론

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  1. Complexity theory helps computer scientists relate and group problems together into complexity classes.[1]
  2. Complexity theory has real world implications too, particularly with algorithm design and analysis.[1]
  3. Computational complexity theory is a field that challenges computer problems.[2]
  4. In complexity theory, it is asked that how much time we need to solve a computer problem.[2]
  5. One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.[3]
  6. More precisely, computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources.[3]
  7. In computational complexity theory, a problem refers to the abstract question to be solved.[3]
  8. For this reason, complexity theory addresses computational problems and not particular problem instances.[3]
  9. In Computational Complexity theory the most commonly used problems are decision problems, in fact most of the optimisation problems can be converted into decision problems.[4]
  10. These problems are typical of those studied in complexity theory in two fundamental respects.[5]
  11. This qualifies \(\sc{PRIMES}\) as feasibly decidable relative to the standards which are now widely accepted in complexity theory and algorithmic analysis (see Section 2.2).[5]
  12. In computational complexity theory, it is problems – i.e. infinite sets of finite combinatorial objects like natural numbers, formulas, graphs – which are assigned ‘complexities’.[5]
  13. A distinct notion of complexity is studied in Kolmogorov complexity theory (e.g., Li and Vitányi 1997).[5]
  14. The other goal is to use complexity theory as an "excuse" to learn about several tools of broad applicability in computer science.[6]
  15. Complexity theory aims to answer this question by describing how many resources we need to compute the solution as a function of the problem size.[7]
  16. In fact, much of contemporary complexity theory studies the relative power of those various models.[7]
  17. The intriguing results on IPSs and PCPs of the early nineties got me interested in computational complexity theory.[7]
  18. The most important open question of complexity theory is whether the complexity class P is the same as the complexity class NP, or is merely a subset as is generally believed.[8]
  19. If the NP class is larger than P, then no easily scalable solution exists for these problems; whether this is the case remains the most important open question in computational complexity theory.[8]
  20. Complexity theory distinguishes between problems verifying yes and problems verifying no answers.[8]
  21. An important result in complexity theory is the fact that no matter how hard a problem can get (i.e. how much time and space resources it requires), there will always be even harder problems.[8]
  22. Computational complexity theory studies the impact of limited resources on computation, and gives many new refined answers to the general problem of "what is tractable.[9]
  23. Along the way, we will learn whatever necessary math is needed to get the job done -- complexity theory often uses interesting math in unexpected ways.[9]
  24. In this course, mathematical aspects of computational complexity theory will be broadly covered.[10]
  25. Computational complexity theory focuses on classifying computational problems according to their inherent difficulty, and relating these classes to each other.[11]
  26. infinite functions and the ultimate behavior of run times on large arguments yield useful insights into computational complexity theory .[12]
  27. By the end of the course, you should have a broad understanding of the various notions used in computational complexity theory to classify computational problems as hard or easy to solve.[13]
  28. The course will also briefly introduce you to applications of complexity theory to cryptography.[13]
  29. Inherent limitations of the currently known techniques is also something that is currently explored on the research frontier of complexity theory.[14]
  30. The course will give a quick introduction to the classical results and techniques in complexity theory and thereafter cover (selected) newer results and areas.[14]
  31. The choice of topics is based on the view that the course should provide a platform for the current topics of research in the area of complexity theory.[14]
  32. We might possibly be skipping some of the basic material in a standard complexity theory course.[14]
  33. Here, we use concepts from computational complexity theory to expose two major weaknesses of the framework.[15]
  34. Then, in §4, we introduce some concepts from computational complexity theory, which we use to assess the computational tractability of the Savage framework.[15]
  35. In §4, we will use computational complexity theory to quantify the computational resource requirements that implementation of the completeness axiom would require.[15]
  36. To demonstrate that this is indeed the case, we now introduce some key concepts from computational complexity theory.[15]
  37. If you know a bit of complexity theory, this should set off alarm bells, because any problem of the form “Program \(P\) has behavior \(B\)” tends to be a big ball of undecidable pain.[16]
  38. How did complexity theory enter the picture?[16]
  39. It’s time to jump into complexity theory.[16]
  40. Many central questions in computational complexity theory remain open today.[17]
  41. That branch of computational complexity theory is called descriptive complexity, and is usually taught second.[17]
  42. Of course, he acknowledges the limitations of computational complexity theory.[18]
  43. But he says these criticisms do not allow philosophers (or anybody else) to arbitrarily dismiss the arguments of complexity theory.[18]
  44. Computational complexity theory is a relatively new discipline which builds on advances made in the 70s, 80s and 90s.[18]

소스

  1. ↑ 1.0 1.1 Brilliant Math & Science Wiki
  2. ↑ 2.0 2.1 Computational Complexity Theory
  3. ↑ 3.0 3.1 3.2 3.3 Computational complexity theory
  4. ↑ What is computational complexity?
  5. ↑ 5.0 5.1 5.2 5.3 Computational Complexity Theory (Stanford Encyclopedia of Philosophy)
  6. ↑ Computational Complexity
  7. ↑ 7.0 7.1 7.2 Research on Computational Complexity Theory
  8. ↑ 8.0 8.1 8.2 8.3 Computational complexity theory
  9. ↑ 9.0 9.1 CS254 -- Computational Complexity Theory -- Fall 2016
  10. ↑ Math 278 Topics: Geometry and algebra of computational complexity
  11. ↑ About: Computational complexity theory
  12. ↑ Computational complexity theory
  13. ↑ 13.0 13.1 Computational Complexity
  14. ↑ 14.0 14.1 14.2 14.3 Computational Complexity Theory
  15. ↑ 15.0 15.1 15.2 15.3 Uncertainty and computational complexity
  16. ↑ 16.0 16.1 16.2 How Computational Complexity Theory Crept Into A Cognitive Science Study
  17. ↑ 17.0 17.1 Computational complexity theory
  18. ↑ 18.0 18.1 18.2 How Computational Complexity Will Revolutionize Philosophy

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  • [{'LOWER': 'computational'}, {'LOWER': 'complexity'}, {'LEMMA': 'theory'}]
  • [{'LOWER': 'complexity'}, {'LEMMA': 'theory'}]
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