Call a log-space reduction a reduction that uses only O(logn) space in addition to the input itself, and...

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Electrical Engineering

Call a log-space reduction areduction that uses onlyO(logn) spacein addition to the input itself, and not countingthe produced result. In other words, there are three tapes: tape 1is read-only (the input), tape 2 is read-write (thework tape), and tape 3 is write-only (theoutput tape). Then we insist that tape 2use O(logn)space (tape 3 is unrestricted, but remember it is write-only). Sucha reduction is denoted â‰¤L. Show that3SAT â‰¤LCLIQUE.

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Answer Everyboolean formula can be written asvv vvv this is calledconjuctive nomal form CNF where v is nothing but varableseach set of variables denotesclauses so clause 1 clause 2 respectively from aboveso the both clauses to be satisfiedie they should be evaluated since it is connected by and failing which the whole formula willnot be satisfiedSo if one of the clauses is notsatisfied the whole formula wont be satisfiedLet G be an undirected graph Aclique in G is a set A of vertices such that all possible edgesbetween elements of A exist in GAny vertex forms a clique of size 1the endpoints of any edge form a clique of size 2 and any triangleis a clique of size 3 The CLIQUE language is a set of pairs G See Answer

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