Making Metric Temporal Logic Rational

We study an extension of MTL in pointwise time with rational expression guarded modality RatI(re) where re is a rational expression over subformulae. We study the decidability and expressiveness of this extension (MTL+φURatI,reφ+RatI,reφ), called RatMTL, as well as its fragment SfrMTL where only star-free rational expressions are allowed. Using the technique of temporal projections, we show that RatMTL has decidable satisfiability by giving an equisatisfiable reduction to MTL. We also identify a subclass MITL + URat of RatMTL for which our equi-satisfiable reduction gives rise to formulae of MITL, yielding elementary decidability. As our second main result, we show a tight automaton-logic connection between SfrMTL and partially ordered (or very weak) 1-clock alternating timed automata. Digital Object Identifier 10.4230/LIPIcs...