9786131260063 - Resource Bounded Measure: Lebesgue Measure, Complexity Class, Jack Lutz (4 Ergebnisse)

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Lutz''s resource bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of the Euclidean space R^n, resource bounded measure gives a method to classify the size of subsets of complexity classes. For instance, computer scientists generally believe that the complexity class P (the set of all decision problems solvable in polynomial time) is not equal to the complexity class NP (the set of all decision problems checkable, but not necessarily solvable, in polynomial time). Since P is a subset of NP, this would mean that NP contains more problems than P. A stronger hypothesis than 'P is not NP' is the statement, 'NP does not have p-measure 0'. Here, p-measure is a generalization of Lebesgue measure to subsets of the complexity class E, in which P is contained. P is known to have p-measure 0, and so the hypothesis 'NP does not have p-measure 0' would imply not only that NP and P are unequal, but that NP is, in a measure-theoretic sense, 'much bigger than P'. 84 pp. Englisch.

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Lutz''s resource bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of the Euclidean space R^n, resource bounded measure gives a method to classify the size of subsets of complexity classes. For instance, computer scientists generally believe that the complexity class P (the set of all decision problems solvable in polynomial time) is not equal to the complexity class NP (the set of all decision problems checkable, but not necessarily solvable, in polynomial time). Since P is a subset of NP, this would mean that NP contains more problems than P. A stronger hypothesis than 'P is not NP' is the statement, 'NP does not have p-measure 0'. Here, p-measure is a generalization of Lebesgue measure to subsets of the complexity class E, in which P is contained. P is known to have p-measure 0, and so the hypothesis 'NP does not have p-measure 0' would imply not only that NP and P are unequal, but that NP is, in a measure-theoretic sense, 'much bigger than P'.

Taschenbuch. Zustand: Neu. Resource Bounded Measure | Lebesgue Measure, Complexity Class, Jack Lutz | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131260063 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. Lutz's resourcebounded measure is a generalisation of Lebesgue measure to complexityclasses. It was originally developed by Jack Lutz. Just as Lebesguemeasure gives a method to quantify the size of subsets of the Euclideanspace R^n, resource bounded measure gives a method to classify the sizeof subsets of complexity classes. For instance, computer scientistsgenerally believe that the complexity class P (the set of all decisionproblems solvable in polynomial time) is not equal to the complexityclass NP (the set of all decision problems checkable, but notnecessarily solvable, in polynomial time). Since P is a subset of NPthis would mean that NP contains more problems than P. A strongerhypothesis than 'P is not NP' is the statement, 'NP does not havep-measure 0'. Here, p-measure is a generalization of Lebesgue measure tosubsets of the complexity class E, in which P is contained. P is knownto have p-measure 0, and so the hypothesis 'NP does not have p-measure0' would imply not only that NP and P are unequal, but that NP is, in ameasure-theoretic sense, 'much bigger than P'.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 84 pp. Englisch.