Results on Alternating-Time Temporal Logics with Linear Past

Authors Laura Bozzelli, Aniello Murano, Loredana Sorrentino

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Laura Bozzelli
  • University of Napoli "Federico II", Italy
Aniello Murano
  • University of Napoli "Federico II", Italy
Loredana Sorrentino
  • University of Napoli "Federico II", Italy

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Laura Bozzelli, Aniello Murano, and Loredana Sorrentino. Results on Alternating-Time Temporal Logics with Linear Past. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We investigate the succinctness gap between two known equally-expressive and different linear-past 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 ATL_{lp}, of the known "memoryful" linear-past extension of ATL^{*}. We show that ATL_{lp} 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 ATL_{lp} are Exptime-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Verification by model checking
  • Alternating-time temporal logics
  • Linear Past
  • Model Checking


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