Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
184 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Higher-Dimensional Timed Automata for Real-Time Concurrency (2401.17444v4)

Published 30 Jan 2024 in cs.FL and cs.LO

Abstract: We present a new language semantics for real-time concurrency. Its operational models are higher-dimensional timed automata (HDTAs), a generalization of both higher-dimensional automata and timed automata. In real-time concurrent systems, both concurrency of events and timing and duration of events are of interest. Thus, HDTAs combine the non-interleaving concurrency model of higher-dimensional automata with the real-time modeling, using clocks, of timed automata. We define languages of HDTAs as sets of interval-timed pomsets with interfaces. We show that language inclusion of HDTAs is undecidable. On the other hand, using a region construction we can show that untimings of HDTA languages have enough regularity so that untimed language inclusion is decidable. On a more practical note, we give new insights on when practical applications, like checking reachability, might benefit from using HDTAs instead of classical timed automata.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (52)
  1. Reactive Systems. Cambridge University Press, 2007.
  2. Automata for modeling real-time systems. In Mike Paterson, editor, ICALP, volume 443 of Lecture Notes in Computer Science, pages 322–335. Springer, 1990.
  3. A theory of timed automata. Theoretical Computer Science, 126(2):183–235, 1994.
  4. Languages of higher-dimensional timed automata. CoRR, abs/2401.17444, 2024.
  5. Closure and decision properties for higher-dimensional automata. In Erika Ábrahám, Clemens Dubslaff, and Silvia Lizeth Tapia Tarifa, editors, ICTAC, volume 14446 of Lecture Notes in Computer Science, pages 295–312. Springer, 2023.
  6. Étienne André. IMITATOR: A tool for synthesizing constraints on timing bounds of timed automata. In Martin Leucker and Carroll Morgan, editors, ICTAC, volume 5684 of Lecture Notes in Computer Science, pages 336–342. Springer, August 2009.
  7. Étienne André. IMITATOR 3: Synthesis of timing parameters beyond decidability. In Alexandra Silva and K. Rustan M. Leino, editors, CAV, volume 12759 of Lecture Notes in Computer Science, pages 552–565. Springer, July 2021.
  8. Eugene Asarin. Challenges in timed languages: From applied theory to basic theory. Bulletin of the EATCS, 83:106–120, 2004.
  9. Entropy of regular timed languages. Information and Computation, 241:142–176, 2015.
  10. Distance on timed words and applications. In David N. Jansen and Pavithra Prabhakar, editors, FORMATS, volume 11022 of Lecture Notes in Computer Science, pages 199–214. Springer, 2018.
  11. A causal semantics for time Petri nets. Theoretical Computer Science, 243(1-2):409–447, 2000.
  12. A concurrency-preserving translation from time Petri nets to networks of timed automata. Formal Methods in System Design, 40(3):330–355, 2012.
  13. A tutorial on Uppaal. In Marco Bernardo and Flavio Corradini, editors, SFM-RT, volume 3185 of Lecture Notes in Computer Science, pages 200–236. Springer, 2004.
  14. Uppaal 4.0. In QEST, pages 125–126. IEEE Computer Society, September 2006.
  15. Start pruning when time gets urgent: Partial order reduction for timed systems. In Hana Chockler and Georg Weissenbacher, editors, CAV, volume 10981 of Lecture Notes in Computer Science, pages 527–546. Springer, 2018.
  16. Model checking real-time systems. In Edmund M. Clarke, Thomas A. Henzinger, Helmut Veith, and Roderick Bloem, editors, Handbook of Model Checking, pages 1001–1046. Springer, 2018.
  17. Permissive strategies in timed automata and games. Electronic Communications of the EASST, 72, 2015.
  18. Thomas Chatain. Concurrency in Real-Time Distributed Systems, from Unfoldings to Implementability. PhD thesis, École normale supérieure de Cachan, 2013.
  19. Complete finite prefixes of symbolic unfoldings of safe time Petri nets. In Susanna Donatelli and P. S. Thiagarajan, editors, PETRI NETS, volume 4024 of Lecture Notes in Computer Science, pages 125–145. Springer, 2006.
  20. Back in time Petri nets. In Víctor A. Braberman and Laurent Fribourg, editors, FORMATS, volume 8053 of Lecture Notes in Computer Science, pages 91–105. Springer, 2013.
  21. Emily Clement. Robustness of Timed Automata: Computing the Maximally-Permissive Strategies. PhD thesis, University of Rennes 1, France, 2022.
  22. Computing maximally-permissive strategies in acyclic timed automata. In Nathalie Bertrand and Nils Jansen, editors, FORMATS, volume 12288 of Lecture Notes in Computer Science, pages 111–126. Springer, September 2020.
  23. Jérémy Dubut. Trees in partial higher dimensional automata. In Mikołaj Bojańczyk and Alex Simpson, editors, FOSSACS, volume 11425 of Lecture Notes in Computer Science, pages 224–241. Springer, 2019.
  24. Uli Fahrenberg. A Generic Approach to Quantitative Verification. Habilitation thesis, Paris-Saclay University, 2022.
  25. Uli Fahrenberg. Higher-dimensional timed and hybrid automata. Leibniz Transactions on Embedded Systems, 8(2):03:1–03:16, 2022.
  26. Languages of higher-dimensional automata. Mathematical Structures in Computer Science, page 1–39, 2021.
  27. A Kleene theorem for higher-dimensional automata. In Bartek Klin, Sławomir Lasota, and Anca Muscholl, editors, CONCUR, volume 243 of LIPIcs, pages 29:1–29:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.
  28. Posets with interfaces as a model for concurrency. Information and Computation, 285(B):104914, 2022.
  29. Catoids and modal convolution algebras. Algebra Universalis, 84(10), 2023.
  30. The quantitative linear-time–branching-time spectrum. Theoretical Computer Science, 538:54–69, 2014.
  31. Partial higher-dimensional automata. In Lawrence S. Moss and Pawel Sobocinski, editors, CALCO, volume 35 of LIPIcs, pages 101–115, 2015.
  32. A Myhill-Nerode theorem for higher-dimensional automata. In Luís Gomes and Robert Lorenz, editors, PETRI NETS, volume 13929 of Lecture Notes in Computer Science, pages 167–188. Springer, 2023.
  33. Peter C. Fishburn. Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. Wiley, 1985.
  34. Computing a finite prefix of a time Petri net. In Javier Esparza and Charles Lakos, editors, PETRI NETS, volume 2360 of Lecture Notes in Computer Science, pages 163–181. Springer, 2002.
  35. Romeo: A tool for analyzing time Petri nets. In Kousha Etessami and Sriram K. Rajamani, editors, CAV, volume 3576 of Lecture Notes in Computer Science, pages 418–423. Springer, July 2005.
  36. Abstractions for the local-time semantics of timed automata: A foundation for partial-order methods. In Christel Baier and Dana Fisman, editors, LICS, pages 24:1–24:14. ACM, 2022.
  37. Jan Grabowski. On partial languages. Fundamenta Informaticae, 4(2):427, 1981.
  38. Robust timed automata. In Oded Maler, editor, HART, volume 1201 of Lecture Notes in Computer Science, pages 331–345. Springer, 1997.
  39. Operational semantics, interval orders and sequences of antichains. Fundamenta Informaticae, 169(1-2):31–55, 2019.
  40. From timed automata to stochastic hybrid games. In Dependable Software Systems Engineering, pages 60–103. IOS Press, 2017.
  41. Uppaal in a nutshell. Int. J. Software Tools for Technology Transfer, 1(1-2):134–152, 1997.
  42. Romeo: A parametric model-checker for Petri nets with stopwatches. In Stefan Kowalewski and Anna Philippou, editors, TACAS, volume 5505 of Lecture Notes in Computer Science, pages 54–57. Springer, March 2009.
  43. Recoverability of communication protocols – implications of a theoretical study. IEEE Transactions on Communications, 24(9):1036–1043, 1976.
  44. Robin Milner. Communication and Concurrency. Prentice Hall, 1989.
  45. Petri nets, event structures and domains, part I. Theoretical Computer Science, 13:85–108, 1981.
  46. Carl A. Petri. Kommunikation mit Automaten. Bonn: Institut für Instrumentelle Mathematik, Schriften des IIM Nr. 2, 1962.
  47. Vaughan R. Pratt. Modeling concurrency with geometry. In David S. Wise, editor, POPL, pages 311–322. ACM Press, 1991.
  48. Rob J. van Glabbeek. Bisimulations for higher dimensional automata. Email message, June 1991. http://theory.stanford.edu/~rvg/hda.
  49. Rob J. van Glabbeek. On the expressiveness of higher dimensional automata. Theoretical Computer Science, 356(3):265–290, 2006. See also [50].
  50. Rob J. van Glabbeek. Erratum to “On the expressiveness of higher dimensional automata”. Theoretical Computer Science, 368(1-2):168–194, 2006.
  51. Rob J. van Glabbeek and Gordon D. Plotkin. Configuration structures. In LICS, pages 199–209. IEEE Computer Society, 1995.
  52. Rob J. van Glabbeek and Gordon D. Plotkin. Configuration structures, event structures and Petri nets. Theoretical Computer Science, 410(41):4111–4159, 2009.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now