Comparing Expressive Power of Timed Logics BTP report

Timed temporal logics encompass a huge diversity of operators, as a result of which, the decidability and expressiveness properties vary considerably. Both pointwise and continuous interpretations of temporal logics can be defined (over finite words), and properties vary based on the interpretation too. The EhrenfeuchtFräıssé games (EF games) for Linear Temporal Logic, as defined by Etessami-Wilke [3] are extended to EF games for Metric Temporal Logic (MTL) [6], for both the pointwise and continuous interpretations. Using the corresponding EF Theorem, we show various results comparing the expressive power of various fragments of the full MTL. In particular, we also establish a hierarchy for MTL, based on the largest constant that can appear in the interval constraints. We show using EF games that this hierarchy holds for pointwise timed MTL, but collapses in the continuous case. For the continuous case, the major goal was to attack the open problems of comparing MTL with timed past and untimed past. The question is whether MTL[UI ,SI ] is strictly stronger than MTL[UI ,S]. We have been able to solve this for unary modalities.