▁This ▁can ▁be ▁proven ▁by ▁applying ▁the ▁following ▁re writing ▁rules ▁to ▁a ▁M IT L ▁formula . ▁▁▁ ▁is ▁equivalent ▁to ▁ ▁( the ▁construction ▁for ▁half - closed ▁and ▁closed ▁intervals ▁is ▁similar ). ▁▁ ▁is ▁equivalent ▁to ▁ ▁if ▁. ▁▁ ▁is ▁equivalent ▁to ▁ ▁if ▁. ▁▁ ▁is ▁equivalent ▁to ▁. ▁ ▁App lying ▁those ▁re writing ▁rules ▁expon entially ▁increases ▁the ▁size ▁of ▁the ▁formula . ▁Indeed , ▁the ▁numbers ▁ ▁and ▁ ▁are ▁tradition ally ▁written ▁in ▁binary , ▁and ▁those ▁rules ▁should ▁be ▁applied ▁ ▁times . ▁ ▁Express iveness ▁over ▁tim ed ▁words ▁ ▁Con tr ary ▁to ▁the ▁case ▁of ▁signals , ▁M IT L ▁is ▁strictly ▁more ▁express ive ▁than ▁M IT L 0 , ∞ . ▁The ▁ ▁re writing ▁rules ▁given ▁above ▁do ▁not ▁apply ▁in ▁the ▁case ▁of ▁tim ed ▁words ▁because , ▁in ▁order ▁to ▁rewrite ▁ ▁the ▁assumption ▁must ▁be ▁that ▁some ▁event ▁occurs ▁between ▁times ▁ 0 ▁and ▁, ▁which ▁is ▁not ▁necessarily ▁the ▁case . ▁ ▁Ad vis ability ▁problem ▁ ▁The ▁problem ▁of ▁dec iding ▁whether ▁a ▁M IT L ▁formula ▁is ▁satisf i able ▁over ▁a ▁signal ▁is ▁in ▁P SP ACE - complete . ▁ ▁References ▁ ▁Category : Tem por al ▁logic ▁Category : Model ▁checking <0x0A> </s> ▁Vir icon ium ▁is ▁an ▁om n ibus ▁collection ▁of ▁two ▁books ▁of ▁the ▁Vir icon ium ▁series ▁by ▁M . ▁John ▁Harrison . ▁ ▁It ▁was ▁published ▁in ▁ 1 9 8 8