Results on Alternating-Time Temporal Logics with Linear Past

We investigate the succinctness gap between two known equally-expressive and different linearpast extensions of standard CTL∗ (resp., ATL∗). We establish by formal non-trivial arguments that the ‘memoryful’ linear-past extension (the history leading to the current state is taken into account) can be exponentially more succinct than the standard ‘local’ linear-past extension (the history leading to the current state is forgotten). As a second contribution, we consider the ATL-like fragment, denoted ATLlp, of the known ‘memoryful’ linear-past extension of ATL∗. We show that ATLlp is strictly more expressive than ATL, and interestingly, it can be exponentially more succinct than the more expressive logic ATL∗. Moreover, we prove that both satisfiability and model-checking for the logic ATLlp are Exptime-complete. Digital Object Identifier 10.4230/LIPIcs...