Lecture 24 Scribble Topics Sample Reduction Chat Moderators Junyeob complexity classes Emerson NP NP hard Certifiers Verifiers Example Reduction SAT Given CNF formula 0 Np hard Q I Cf satisfiable MAXINOSET Given GCU E Assume NP hard Q Is there an independent set K R Ay MAXINOSET Yes No Ix CNF Iy GCU Ax SAT Algorithm satisfied Ix Example au b A EV b A AVI a b I 60 ft 9 GLUE Create agraph G from SA edge between wars in a J same clause edge between vars 6 and their complements If is sat then I.S G K C of cleans
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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