▁of ▁whether ▁there ▁exists ▁a ▁path ▁between ▁two ▁vertices ▁in ▁a ▁given ▁und irect ed ▁graph , ▁is ▁in ▁L , ▁showing ▁that ▁L ▁= ▁SL , ▁since ▁U ST CON ▁is ▁SL - complete . ▁ ▁One ▁consequence ▁of ▁this ▁is ▁a ▁simple ▁logical ▁character ization ▁of ▁L : ▁it ▁contains ▁precisely ▁those ▁languages ▁express ible ▁in ▁first - order ▁logic ▁with ▁an ▁added ▁commut ative ▁trans itive ▁closure ▁operator ▁( in ▁graph ▁theoretical ▁terms , ▁this ▁turns ▁every ▁connected ▁component ▁into ▁a ▁cli que ). ▁This ▁result ▁has ▁application ▁to ▁database ▁query ▁languages : ▁data ▁complexity ▁of ▁a ▁query ▁is ▁defined ▁as ▁the ▁complexity ▁of ▁answering ▁a ▁fixed ▁query ▁considering ▁the ▁data ▁size ▁as ▁the ▁variable ▁input . ▁For ▁this ▁measure , ▁queries ▁against ▁rel ational ▁databases ▁with ▁complete ▁information ▁( h aving ▁no ▁notion ▁of ▁null s ) ▁as ▁expressed ▁for ▁instance ▁in ▁rel ational ▁algebra ▁are ▁in ▁L . ▁ ▁Rel ated ▁complexity ▁classes ▁ ▁L ▁is ▁a ▁subclass ▁of ▁N L , ▁which ▁is ▁the ▁class ▁of ▁languages ▁decid able ▁in ▁log arith mic ▁space ▁on ▁a ▁n ond et erm in istic ▁T uring ▁machine . ▁A ▁problem ▁in ▁N L ▁may ▁be ▁transformed ▁into ▁a ▁problem ▁of ▁reach ability ▁in ▁a ▁directed ▁graph ▁representing ▁states ▁and ▁state ▁trans itions ▁of ▁the ▁n ond et erm in istic ▁machine , ▁and ▁the ▁log arith mic ▁space ▁bound ▁implies ▁that ▁this ▁graph ▁has ▁a ▁polynomial ▁number ▁of ▁vertices ▁and ▁edges , ▁from ▁which ▁it ▁follows ▁that ▁N L