▁mart ing ales ▁( S chn orr ▁ 1 9 7 1 ): ▁A ▁mart ing ale ▁is ▁a ▁function ▁ ▁such ▁that , ▁for ▁all ▁finite ▁strings ▁w , ▁, ▁where ▁ ▁is ▁the ▁concaten ation ▁of ▁the ▁strings ▁a ▁and ▁b . ▁This ▁is ▁called ▁the ▁" f air ness ▁condition ": ▁if ▁a ▁mart ing ale ▁is ▁viewed ▁as ▁a ▁bet ting ▁strategy , ▁then ▁the ▁above ▁condition ▁requires ▁that ▁the ▁bet tor ▁plays ▁against ▁fair ▁odd s . ▁A ▁mart ing ale ▁d ▁is ▁said ▁to ▁succeed ▁on ▁a ▁sequence ▁S ▁if ▁ ▁where ▁ ▁is ▁the ▁first ▁n ▁bits ▁of ▁S . ▁A ▁mart ing ale ▁d ▁is ▁construct ive ▁( also ▁known ▁as ▁weak ly ▁comput able , ▁lower ▁semi - comput able ) ▁if ▁there ▁exists ▁a ▁comput able ▁function ▁ ▁such ▁that , ▁for ▁all ▁finite ▁binary ▁strings ▁w ▁▁ ▁for ▁all ▁positive ▁integers ▁t , ▁▁▁ ▁A ▁sequence ▁is ▁Martin - L ö f ▁random ▁if ▁and ▁only ▁if ▁no ▁construct ive ▁mart ing ale ▁succeed s ▁on ▁it . ▁▁ ▁Inter pret ations ▁of ▁the ▁definitions ▁▁ ▁The ▁Kol m og or ov ▁complexity ▁character ization ▁con ve ys ▁the ▁intu ition ▁that ▁a ▁random ▁sequence ▁is ▁in com press ible : ▁no ▁prefix ▁can ▁be ▁produced ▁by ▁a ▁program ▁much ▁shorter ▁than ▁the ▁prefix . ▁ ▁The ▁null ▁cover ▁character ization ▁con ve ys ▁the ▁intu ition ▁that ▁a ▁random ▁real ▁number ▁should ▁not ▁have ▁any ▁property ▁that ▁is ▁“ un common