Intractable Problems

May 5th, 2015
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Intractable Problems The Classes P and NP Mohamed M. El Wakil Mohamed M. El Wakil

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IntractableProblems IntractableProblems Intractable Problems TheClassesPandNP MohamedM.ElWakil Mohamed M. El Wakil mohamed@elwakil.net1Agenda1. 2. 3. 4. 5. 5 Whatisaproblem? Decidableornot? Decidable or not? ThePclass TheNPClass TheNP Completeclass The NPComplete class2Whatisaproblem? What is a problem? Aproblem isaquestiontobeanswered. WhatisthevalueofX/Y? Aproblemusuallyhasparameters. p y p X,andY A decision problem is a version of the Adecisionproblem,isaversion ofthe problemwithonlytwopossibleanswers:Yes orNo! or No! GiventwonumbersX,andY,doesYevenlydivide X? Aninstance:aspecificprobleminstance Does3evenlydivide6?3Decidableornot? Decidable or not? Adecidableproblem,isaproblemthatcould besolvedusingacomputer. A Anundecidableproblem,isaproblemthat d id bl bl i bl th t cannever besolvedusingacomputer,neither noworinthefuture. Onlydecidableproblems! 4Classification Weneedtoclassifyproblemsintermsoftheir p y computability. Th Threeclasses: l Pclass NPClass NPComplete class NPCompleteclass5Pclass,wrt P class wrt Computers Problemswithatleastonealgorithmthat solvestheprobleminpolynomialtimewrt to l h bl

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