7 3 ): ▁Algorithm ic ▁complexity ▁( aka ▁Kol m og or ov ▁complexity ▁or ▁program - size ▁complexity ) ▁can ▁be ▁thought ▁of ▁as ▁a ▁lower ▁bound ▁on ▁the ▁algorithm ic ▁compress ibility ▁of ▁a ▁finite ▁sequence ▁( of ▁characters ▁or ▁binary ▁digits ). ▁It ▁assign s ▁to ▁each ▁such ▁sequence ▁w ▁a ▁natural ▁number ▁K ( w ) ▁that , ▁intuit ively , ▁measures ▁the ▁minimum ▁length ▁of ▁a ▁computer ▁program ▁( written ▁in ▁some ▁fixed ▁programming ▁language ) ▁that ▁takes ▁no ▁input ▁and ▁will ▁output ▁w ▁when ▁run . ▁The ▁complexity ▁is ▁required ▁to ▁be ▁prefix - free : ▁ ▁The ▁program ▁( a ▁sequence ▁of ▁ 0 ▁and ▁ 1 ) ▁is ▁followed ▁by ▁an ▁infinite ▁string ▁of ▁ 0 s , ▁and ▁the ▁length ▁of ▁the ▁program ▁( ass uming ▁it ▁hal ts ) ▁includes ▁the ▁number ▁of ▁zero es ▁to ▁the ▁right ▁of ▁the ▁program ▁that ▁the ▁universal ▁T uring ▁machine ▁reads . ▁ ▁The ▁additional ▁requirement ▁is ▁needed ▁because ▁we ▁can ▁choose ▁a ▁length ▁such ▁that ▁the ▁length ▁codes ▁information ▁about ▁the ▁substring . ▁ ▁Given ▁a ▁natural ▁number ▁c ▁and ▁a ▁sequence ▁w , ▁we ▁say ▁that ▁w ▁is ▁c - in com press ible ▁if ▁. ▁An ▁infinite ▁sequence ▁S ▁is ▁Martin - L ö f ▁random ▁if ▁and ▁only ▁if ▁there ▁is ▁a ▁constant ▁c ▁such ▁that ▁all ▁of ▁S s ▁finite ▁prefix es ▁are ▁c - in com press ible . ▁▁ ▁Con struct ive ▁null ▁covers ▁( Martin - L ö