We investigate the decidability of the {0,∞} fragment of Timed Propositional Temporal Logic (TPTL). We show that the satisfiability checking of TPTL^{0,∞} is PSPACE-complete. Moreover, even its 1-variable fragment (1-TPTL^{0,∞}) is strictly more expressive than Metric Interval Temporal Logic (MITL) for which satisfiability checking is EXPSPACE complete. Hence, we have a strictly more expressive logic with computationally easier satisfiability checking. To the best of our knowledge, TPTL^{0,∞} is the first multi-variable fragment of TPTL for which satisfiability checking is decidable without imposing any bounds/restrictions on the timed words (e.g. bounded variability, bounded time, etc.). The membership in PSPACE is obtained by a reduction to the emptiness checking problem for a new "non-punctual’’ subclass of Alternating Timed Automata with multiple clocks called Unilateral Very Weak Alternating Timed Automata (VWATA^{0,∞}) which we prove to be in PSPACE. We show this by constructing a simulation equivalent non-deterministic timed automata whose number of clocks is polynomial in the size of the given VWATA^{0,∞}.
@InProceedings{krishna_et_al:LIPIcs.CONCUR.2023.23, author = {Krishna, Shankara Narayanan and Madnani, Khushraj Nanik and Majumdar, Rupak and Pandya, Paritosh}, title = {{Satisfiability Checking of Multi-Variable TPTL with Unilateral Intervals Is PSPACE-Complete}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {23:1--23:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-299-0}, ISSN = {1868-8969}, year = {2023}, volume = {279}, editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.23}, URN = {urn:nbn:de:0030-drops-190171}, doi = {10.4230/LIPIcs.CONCUR.2023.23}, annote = {Keywords: TPTL, Satisfiability, Non-Punctuality, Decidability, Expressiveness, ATA} }
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