We investigate NLTL, a linear-time temporal logic with forgettable past. NLTL can be exponentially more succinct than LTL +Past (which in turn can be more succinct than LTL). We study satisfiability and model checking for NLTL and provide optimal automata-theoretic algorithms for these EXPSPACE-complete problems.
Citation:
François Laroussinie, Nicolas Markey, Philippe Schnoebelen, "Temporal Logic with Forgettable Past," lics, pp.383, 17th Annual IEEE Symposium on Logic in Computer Science (LICS'02), 2002