Lecture 24 Scribble Topics Sample Reduction

Chat Moderators Junyeob complexity classes

Emerson NP NP hard

Certifiers Verifiers

Example ReductionSAT Given CNF formula 0 NphardQ I Cf satisfiable

MAXINOSET Given GCU EAssume NP hardQ Is there an independentset K

R Ay MAXINOSETYes

NoIx CNF Iy GCU

Ax SAT Algorithm

satisfiedIx Example au b A EV b A AVI a b I

60 ft 9 GLUECreateagraph G fromSA

edge between wars ina

Jsame clause

edge between vars6 and their complements

If is sat thenI.S G K C of cleans

au b A EV b A Cav E A a VIS

Q

I

o

Re review Complexity classesyTNP hard P solvablebydet

NPhard if It is NPhard EXPSPACE halting Tmisupolytimeand LE NP then there problemexists a polynomial time EXTTIMEL IP If answer isYereduction from L to H thenproof can

be checked in

ion.co

iproblems can be checked

i p Ji iexponential PSPACE everyassignmenttime expr is true

factorization does u have a factor smallerthan K x Y or X Y

in NP yes can be elected by showing u d wheredLK

in co DP no can be cheeked n X y z

where all are RTimes

P e NP

NP a set of decision problems that have a polynomialsnon deterministic algorithm

Deterministic Non Deterministic

q In Inu to Analogous OFA

NFAt o.AT

of t.EE E tq.Iyea

I ha 24is

YooOut Out

CertifiersCertifiers are algorithms that verify a solution to a problem

A problem is in NP if it has a poly time certifier

Problem X s EX t

GSAT O Assignment I o I BXo x Xz

Bet output yesAn efficient certifier ruins in polynomial time

0Example Vertex CoverProblem Does G have a vertex cover of size Ek y.jpCertificate Ssw

Certifier sik For every e C F check to see one vertexisin S

aus

Example STAT

Problem Does 6 has a sat assignmentCertificate Assignment

Certifier Checkeach clause and mark if clause is truereturn yes if all clauses true