Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-22T02:55:56.493Z Has data issue: false hasContentIssue false
  • English
  • Français

Submit content

Help address this Question with your content Submit Content

Time-Sensitive Software

Published online by Cambridge University Press:  13 February 2023

Edward A. Lee Open the ORCID record for Edward A. Lee [Opens in a new window]  and
Jim Woodcock
Edward A. Lee*
Affiliation:
UC Berkeley, Berkeley, USA
Jim Woodcock
Affiliation:
University of York, York, UK
*
Author for correspondence: Edward A. Lee, Email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Type
Question
Information
Research Directions: Cyber-Physical Systems , Volume 1 , 2023 , e1
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Context

Timing of software execution is usually considered a performance property rather than a correctness property. But in software for cyber-physical systems, timing is often a critical feature of the execution of the software. Today, no widely used programming language specifies timing. Instead, timing is an emergent consequence of a particular implementation and is sensitive to every detail of the hardware on which the software runs and to what other software may be sharing the same hardware. Even a small change in the hardware or software context can lead to drastically different timing behaviour, making maintenance and upgrades difficult.

This question seeks contributions that turn this picture around. Just as a programmer delegates to the compiler and the microprocessor corrects execution of the program logic, we seek ways to similarly delegate the delivery of timing requirements. The contributions can include programming language enhancements, compilation techniques, innovative computer architectures, modelling methods and formal analysis techniques.

Some problems to consider include:

  • How to model time (e.g., discrete, dense, super-dense; totally or partially ordered; linear vs. branching time; logical vs. physical time; hard vs. soft real time).

  • How to analyse temporal properties (e.g., temporal logics, explicit-time logics, fundamental limits; temporal calculi).

  • Programming language constructs (e.g., mechanisms for concurrency and composition; synchronous vs. asynchronous; comparisons of timing constructs in legacy programming languages; priorities vs. explicit timing requirements).

  • Static analysis techniques (e.g., execution time analysis; feasibility analysis).

  • Operating-system capabilities (e.g., real-time operating systems; clock synchronisation; distributed systems coordination; scheduling).

  • Measurement and evaluation (e.g., testing frameworks; benchmarking; repeatability).

How to contribute to this Question

If you believe you can contribute to answering this Question with your research outputs, find out how to submit them in the Instructions for authors (https://www.cambridge.org/core/journals/research-directions-cyber-physical-systems/information/author-instructions/preparing-your-materials). This journal publishes Results, Analyses, Impact papers and additional content such as preprints and “grey literature”. Questions will be closed when the editors agree that enough has been published to answer the Question so before submitting, check if this is still an active Question. If it is closed, another relevant Question may be currently open, so do review all the open Questions in your field. For any further queries, check the information pages (https://www.cambridge.org/core/journals/research-directions-cyber-physical-systems/information/about-this-journal) or contact this email ().

Competing interests

The authors declare none.

References

References

Lee, I and Davidson, S (1987) Adding time to synchronous process communications. IEEE Transactions on Computers.CrossRefGoogle Scholar
Stankovic, JA (1988) Misconceptions about real-time computing: a serious problem for next-generation systems. Computer, 21, 10–19.CrossRefGoogle Scholar
Alur, R and Henzinger, T (1991) Logics and models of real time: A survey. In REX Workshop, Mook, The Netherlands, De Bakker, J. W., Huizing, C., De Roever, W. P. and Rozenberg, G. (Eds.), June 3–7 , vol. LNCS 600, Berlin/Heidelberg: Springer, pp. 74–106.Google Scholar
Abadi, M and Lamport, L (1994) An old-fashioned recipe for real time. ACM Transactions on Programming Languages and Systems (TOPLAS), 16, 1543–1571.CrossRefGoogle Scholar
Alur, R and Dill, DL (1994) A theory of timed automata. Theoretical Computer Science, 126, 183–235.CrossRefGoogle Scholar
Thiele, L, Chakraborty, S and Naedele, N (2000) Real-time calculus for scheduling hard real-time systems. In International Symposium on Circuits and Systems (ISCAS), vol. 4, pp. 101–104.CrossRefGoogle Scholar
Broy, M, Refinement of time. Theoretical Computer Science, 253, 3–26.CrossRefGoogle Scholar
Kaynar, DK, Lynch, N, Segala, R and Vaandrager, F (2006) The Theory of Timed I/O Automata (Synthesis Lectures on Computer Science). Morgan Claypool Publishers.Google Scholar
Lee, EA (2006) Concurrent semantics without the notions of state or state transitions. In International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS), Paris, France, Asarin, E. and Bouyer, P. (Eds.), September 25–27, LNCS, vol. 4202: Springer-Verlag. doi: 10.1007/11867340_2.CrossRefGoogle Scholar
Liu, X, Matsikoudis, E and Lee, EA (2006) Modeling timed concurrent systems. In CONCUR 2006 - Concurrency Theory, Bonn, Germany, August 27–30, LNCS, vol. 4137. Springer, pp. 1–15. doi: 10.1007/11817949_1.CrossRefGoogle Scholar
Nain, S and Vardi, MY (2007) Branching vs. linear time: Semantical perspective. In ATVA.Google Scholar
André, C, Mallet, F and de Simone, R (2007) Modeling Time(s). In ACM/IEEE International Conference on Model Driven Engineering Languages and Systems (MoDELS/UML), Nashville, TN, United States, pp. 559–573. doi: 10.1007/978-3-540-75209-7_38.CrossRefGoogle Scholar
Liu, X and Lee, EA (2008). CPO semantics of timed interactive actor networks. Theoretical Computer Science, 409, 110–125. doi: 10.1016/j.tcs.2008.08.044.CrossRefGoogle Scholar
Lee, EA (2009) Computing needs time. Communications of the ACM, 52, 70–79. doi: 10.1145/1506409.1506426.CrossRefGoogle Scholar
Furia, CA, Mandrioli, D, Morzenti, A and Rossi, M (2010) Modeling time in computing: A taxonomy and a comparative survey. Computing Surveys, 42, 6:1–6:59.CrossRefGoogle Scholar
Benveniste, A, Caillaud, B and Pouzet, M (2010) The fundamentals of hybrid systems modelers. In IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, Dec. 15–17. doi: 10.1109/CDC.2010.5717614.CrossRefGoogle Scholar
Matsikoudis, E and Lee, EA (2013) On fixed points of strictly causal functions. In International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS), Buenos Aires, Argentina, LNCS, vol. 8053. Springer-Verlag, pp. 183–197. doi: 10.1007/978-3-642-40229-6_13.CrossRefGoogle Scholar
Boulanger, F, Jacquet, C, Hardebolle, C and Prodan, I (2014) TESL: A language for reconciling heterogeneous execution traces. In ACM/IEEE Conference on Formal Methods and Models for Codesign (MEMOCODE), Lausanne, Switzerland. doi: 10.1109/MEMCOD.2014.6961849.CrossRefGoogle Scholar
Cremona, F, Lohstroh, M, Broman, D, Lee, EA, Masin, M and Tripakis, S (2017) Hybrid co-simulation: It’s about time. Software and Systems Modeling, 18, 1655–1679. doi: 10.1007/s10270-017-0633-6.CrossRefGoogle Scholar
Lee, EA (2018) Models of timed systems. In FORMATS, Beijing, China, September 4-6, LNCS, vol. 11022. Springer, pp. 17–33.Google Scholar
Ernst, R, Kuntz, S, Quinton, S and Simons, M (2018) The logical execution time paradigm: New perspectives for multicore systems (Dagstuhl Seminar 18092). Dagstuhl Reports, 8, 122–149. doi: 10.4230/DagRep.8.2.122.Google Scholar
Gemlau, K, Köhler, L, Ernst, R and Quinton, S (2021) System-level Logical execution time: augmenting the logical execution time paradigm for distributed real-time automotive software. ACM Transactions on Cyber-Physical Systems, 5, 1–27. doi: 10.1145/3381847.CrossRefGoogle Scholar
Lee, EA (2021) Determinism. ACM Transactions on Embedded Computing Systems (TECS), 20, 1–34. doi: 10.1145/3453652.Google Scholar
Lee, EA, Bateni, S, Lin, S, Lohstroh, M and Menard, C (2021) Quantifying and Generalizing the CAP Theorem, arXiv:2109.07771 [cs.DC], September 16. [Online]. Available: https://arxiv.org/abs/2109.07771.Google Scholar
Lamport, L (1978) Time, clocks, and the ordering of events in a distributed system. Communications of the ACM, 21, 558–565. doi: 10.1145/359545.359563.CrossRefGoogle Scholar
Liskov, B (1993). Practical uses of synchronized clocks in distributed systems. Distributed Computing, 6, 211–219. doi: 10.1007/BF02242709.CrossRefGoogle Scholar
Jantsch, A (2003) Modeling Embedded Systems and SoCs - Concurrency and Time in Models of Computation. Morgan Kaufmann.Google Scholar
Zhao, Y, Lee, EA and Liu, J (2007) A programming model for time-synchronized distributed real-time systems. In Real-Time and Embedded Technology and Applications Symposium (RTAS), Bellevue, WA, USA, April 3–6. IEEE, pp. 259–268. doi: 10.1109/RTAS.2007.5 CrossRefGoogle Scholar
Meseguer, J and Ölveczky, PC (2010) Formalization and correctness of the PALS architectural pattern for distributed real-time systems. In Forrmal Methods and Software Engineering, LNCS, vol. 6447. Springer, pp. 303–320.CrossRefGoogle Scholar
Corbett, JC et al. (2012) Spanner: Google’s globally-distributed database. In OSDI. doi: 10.1145/2491245.Google Scholar
Brewer, E (2017) Spanner, TrueTime & the CAP Theorem, Google, February 14. [Online]. Available: https://storage.googleapis.com/pub-tools-public-publication-data/pdf/45855.pdf Google Scholar
Lee, EA and Lohstroh, M (2021) Time for all programs, not just real-time programs. In International Symposium on Leveraging Applications of Formal Methods (ISoLA). doi: 10.1007/978-3-030-89159-6_15.CrossRefGoogle Scholar
Martin, T, Real-Time Programing Language PEARL - Concept and Characteristics. In Computer Software and Applications Conference (COMPSAC), Chicago, 1978, pp. 301–306.Google Scholar
Mok, AK (1987) Annotating ADA for real-time program synthesis. In IEEE Conference on Computer Assurance (COMPASS), IEEE.Google Scholar
Henzinger, TA, Horowitz, B and Kirsch, CM (2003) Giotto: A time-triggered language for embedded programming. Proceedings of IEEE, 91, 84–99. doi: 10.1109/JPROC.2002.805825.CrossRefGoogle Scholar
Andalam, S, Roop, PS and Girault, A (2010) Predictable multithreading of embedded applications using PRET-C. In Formal Methods and Models for Codesign (MEMOCODE), Grenoble, France, June 4. IEEE/ACM, pp. 159–168. doi: 10.1109/MEMCOD.2010.5558636.Google Scholar
Elmqvist, H, Otter, M and Mattsson, SE (2012) Fundamentals of Synchronous Control in Modelica. In International Modelica Conference, Munich Germany, September 3–5. doi: 10.3384/ecp1207615.CrossRefGoogle Scholar
Natarajan, S and Broman, D (2018) Timed C: An extension to the C Programming language for real-time systems. In Real-Time and Embedded Technology and Applications Symposium (RTAS), Porto, Portugal, April 11–13, pp. 227–239. doi: 10.1109/RTAS.2018.00031.CrossRefGoogle Scholar
Lohstroh, M, Menard, C, Bateni, S and Lee, EA (2021) Toward a Lingua Franca for deterministic concurrent systems. ACM Transactions on Embedded Computing Systems (TECS), 20, Article 36. doi: 10.1145/3448128.CrossRefGoogle Scholar
Manna, Z and Pnueli, A (1993) Verifying hybrid systems. Hybrid Systems, LNCS, vol. 736, pp. 4–35.CrossRefGoogle Scholar
Clarke, EM and Emerson, EA (1981). Design and Synthesis of Synchronization Skeletons using Branching-Time Temporal Logic. In Workshop on Logic of Programs, LNCS, vol. 131. Springer-Verlag.Google Scholar
Matsikoudis, E, Stergiou, C and Lee, EA (2013) On the schedulability of real-time discrete-event systems. In International Conference on Embedded Software (EMSOFT), Montreal, Canada, September 29–October 4. ACM. doi: 10.1109/EMSOFT.2013.6658590.CrossRefGoogle Scholar
Sirjani, M, Lee, EA and Khamespanah, E (2020) Verification of cyberphysical systems. Mathematics, 8. doi: 10.3390/math8071068.CrossRefGoogle Scholar
Galison, P (2003) Einstein’s Clocks, Poincaré's Maps. New York: W. W. Norton & Company.Google Scholar
Muller, RA (2016) Now – The Physics of Time. W. W. Norton and Company.Google Scholar
Rovelli, C (2018) The Order of Time. New York: Riverhead Books.Google Scholar
Kopetz, H and Bauer, G (2003) The time-triggered architecture. Proceedings of the IEEE, 91, 112–126.CrossRefGoogle Scholar
Wilhelm, R (2003) Run-time guarantees for real-time systems. In Formal Modeling and Analysis of Timed Systems (FORMATS), LNCS, vol. 2791. Springer, pp. 166–167.CrossRefGoogle Scholar
Thiele, L and Wilhelm, R (2004) Design for timing predictability. Real-Time Systems, 28, 157–177. doi: 10.1023/B:TIME.0000045316.66276.6e.CrossRefGoogle Scholar
Edwards, SA and Lee, EA (2007) The Case for the Precision Timed (PRET) Machine. In Design Automation Conference (DAC), San Diego, CA, June 4–8.Google Scholar
Wilhelm, R et al. (2008) The worst-case execution-time problem - overview of methods and survey of tools, ACM Transactions on Embedded Computing Systems (TECS), 7, 1–53.CrossRefGoogle Scholar
Wilhelm, R, Grund, D, Reineke, J, Schlickling, M, Pister, M and Ferdinand, C (2009) Memory hierarchies, pipelines, and buses for future architectures in time-critical embedded systems. IEEE Transactions on Computer Aided Design, 28, 966–978. doi: 10.1109/TCAD.2009.2013287.CrossRefGoogle Scholar
Schoeberl, M (2009) Time-predictable computer architecture. EURASIP Journal on Embedded Systems, Article ID 758480, 17 pages. doi: 10.1155/2009/758480.Google Scholar
Lee, EA, Reineke, J and Zimmer, M (2017) Abstract PRET machines. In IEEE Real-Time Systems Symposium (RTSS), Paris, France.CrossRefGoogle Scholar
Lee, I and Davidson, S (1987) Adding time to synchronous process communications. IEEE Transactions on Computers.CrossRefGoogle Scholar
Stankovic, JA (1988) Misconceptions about real-time computing: a serious problem for next-generation systems. Computer, 21, 10–19.CrossRefGoogle Scholar
Alur, R and Henzinger, T (1991) Logics and models of real time: A survey. In REX Workshop, Mook, The Netherlands, De Bakker, J. W., Huizing, C., De Roever, W. P. and Rozenberg, G. (Eds.), June 3–7 , vol. LNCS 600, Berlin/Heidelberg: Springer, pp. 74–106.Google Scholar
Abadi, M and Lamport, L (1994) An old-fashioned recipe for real time. ACM Transactions on Programming Languages and Systems (TOPLAS), 16, 1543–1571.CrossRefGoogle Scholar
Alur, R and Dill, DL (1994) A theory of timed automata. Theoretical Computer Science, 126, 183–235.CrossRefGoogle Scholar
Thiele, L, Chakraborty, S and Naedele, N (2000) Real-time calculus for scheduling hard real-time systems. In International Symposium on Circuits and Systems (ISCAS), vol. 4, pp. 101–104.CrossRefGoogle Scholar
Broy, M, Refinement of time. Theoretical Computer Science, 253, 3–26.CrossRefGoogle Scholar
Kaynar, DK, Lynch, N, Segala, R and Vaandrager, F (2006) The Theory of Timed I/O Automata (Synthesis Lectures on Computer Science). Morgan Claypool Publishers.Google Scholar
Lee, EA (2006) Concurrent semantics without the notions of state or state transitions. In International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS), Paris, France, Asarin, E. and Bouyer, P. (Eds.), September 25–27, LNCS, vol. 4202: Springer-Verlag. doi: 10.1007/11867340_2.CrossRefGoogle Scholar
Liu, X, Matsikoudis, E and Lee, EA (2006) Modeling timed concurrent systems. In CONCUR 2006 - Concurrency Theory, Bonn, Germany, August 27–30, LNCS, vol. 4137. Springer, pp. 1–15. doi: 10.1007/11817949_1.CrossRefGoogle Scholar
Nain, S and Vardi, MY (2007) Branching vs. linear time: Semantical perspective. In ATVA.Google Scholar
André, C, Mallet, F and de Simone, R (2007) Modeling Time(s). In ACM/IEEE International Conference on Model Driven Engineering Languages and Systems (MoDELS/UML), Nashville, TN, United States, pp. 559–573. doi: 10.1007/978-3-540-75209-7_38.CrossRefGoogle Scholar
Liu, X and Lee, EA (2008). CPO semantics of timed interactive actor networks. Theoretical Computer Science, 409, 110–125. doi: 10.1016/j.tcs.2008.08.044.CrossRefGoogle Scholar
Lee, EA (2009) Computing needs time. Communications of the ACM, 52, 70–79. doi: 10.1145/1506409.1506426.CrossRefGoogle Scholar
Furia, CA, Mandrioli, D, Morzenti, A and Rossi, M (2010) Modeling time in computing: A taxonomy and a comparative survey. Computing Surveys, 42, 6:1–6:59.CrossRefGoogle Scholar
Benveniste, A, Caillaud, B and Pouzet, M (2010) The fundamentals of hybrid systems modelers. In IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, Dec. 15–17. doi: 10.1109/CDC.2010.5717614.CrossRefGoogle Scholar
Matsikoudis, E and Lee, EA (2013) On fixed points of strictly causal functions. In International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS), Buenos Aires, Argentina, LNCS, vol. 8053. Springer-Verlag, pp. 183–197. doi: 10.1007/978-3-642-40229-6_13.CrossRefGoogle Scholar
Boulanger, F, Jacquet, C, Hardebolle, C and Prodan, I (2014) TESL: A language for reconciling heterogeneous execution traces. In ACM/IEEE Conference on Formal Methods and Models for Codesign (MEMOCODE), Lausanne, Switzerland. doi: 10.1109/MEMCOD.2014.6961849.CrossRefGoogle Scholar
Cremona, F, Lohstroh, M, Broman, D, Lee, EA, Masin, M and Tripakis, S (2017) Hybrid co-simulation: It’s about time. Software and Systems Modeling, 18, 1655–1679. doi: 10.1007/s10270-017-0633-6.CrossRefGoogle Scholar
Lee, EA (2018) Models of timed systems. In FORMATS, Beijing, China, September 4-6, LNCS, vol. 11022. Springer, pp. 17–33.Google Scholar
Ernst, R, Kuntz, S, Quinton, S and Simons, M (2018) The logical execution time paradigm: New perspectives for multicore systems (Dagstuhl Seminar 18092). Dagstuhl Reports, 8, 122–149. doi: 10.4230/DagRep.8.2.122.Google Scholar
Gemlau, K, Köhler, L, Ernst, R and Quinton, S (2021) System-level Logical execution time: augmenting the logical execution time paradigm for distributed real-time automotive software. ACM Transactions on Cyber-Physical Systems, 5, 1–27. doi: 10.1145/3381847.CrossRefGoogle Scholar
Lee, EA (2021) Determinism. ACM Transactions on Embedded Computing Systems (TECS), 20, 1–34. doi: 10.1145/3453652.Google Scholar
Lee, EA, Bateni, S, Lin, S, Lohstroh, M and Menard, C (2021) Quantifying and Generalizing the CAP Theorem, arXiv:2109.07771 [cs.DC], September 16. [Online]. Available: https://arxiv.org/abs/2109.07771.Google Scholar
Lamport, L (1978) Time, clocks, and the ordering of events in a distributed system. Communications of the ACM, 21, 558–565. doi: 10.1145/359545.359563.CrossRefGoogle Scholar
Liskov, B (1993). Practical uses of synchronized clocks in distributed systems. Distributed Computing, 6, 211–219. doi: 10.1007/BF02242709.CrossRefGoogle Scholar
Jantsch, A (2003) Modeling Embedded Systems and SoCs - Concurrency and Time in Models of Computation. Morgan Kaufmann.Google Scholar
Zhao, Y, Lee, EA and Liu, J (2007) A programming model for time-synchronized distributed real-time systems. In Real-Time and Embedded Technology and Applications Symposium (RTAS), Bellevue, WA, USA, April 3–6. IEEE, pp. 259–268. doi: 10.1109/RTAS.2007.5 CrossRefGoogle Scholar
Meseguer, J and Ölveczky, PC (2010) Formalization and correctness of the PALS architectural pattern for distributed real-time systems. In Forrmal Methods and Software Engineering, LNCS, vol. 6447. Springer, pp. 303–320.CrossRefGoogle Scholar
Corbett, JC et al. (2012) Spanner: Google’s globally-distributed database. In OSDI. doi: 10.1145/2491245.Google Scholar
Brewer, E (2017) Spanner, TrueTime & the CAP Theorem, Google, February 14. [Online]. Available: https://storage.googleapis.com/pub-tools-public-publication-data/pdf/45855.pdf Google Scholar
Lee, EA and Lohstroh, M (2021) Time for all programs, not just real-time programs. In International Symposium on Leveraging Applications of Formal Methods (ISoLA). doi: 10.1007/978-3-030-89159-6_15.CrossRefGoogle Scholar
Martin, T, Real-Time Programing Language PEARL - Concept and Characteristics. In Computer Software and Applications Conference (COMPSAC), Chicago, 1978, pp. 301–306.Google Scholar
Mok, AK (1987) Annotating ADA for real-time program synthesis. In IEEE Conference on Computer Assurance (COMPASS), IEEE.Google Scholar
Henzinger, TA, Horowitz, B and Kirsch, CM (2003) Giotto: A time-triggered language for embedded programming. Proceedings of IEEE, 91, 84–99. doi: 10.1109/JPROC.2002.805825.CrossRefGoogle Scholar
Andalam, S, Roop, PS and Girault, A (2010) Predictable multithreading of embedded applications using PRET-C. In Formal Methods and Models for Codesign (MEMOCODE), Grenoble, France, June 4. IEEE/ACM, pp. 159–168. doi: 10.1109/MEMCOD.2010.5558636.Google Scholar
Elmqvist, H, Otter, M and Mattsson, SE (2012) Fundamentals of Synchronous Control in Modelica. In International Modelica Conference, Munich Germany, September 3–5. doi: 10.3384/ecp1207615.CrossRefGoogle Scholar
Natarajan, S and Broman, D (2018) Timed C: An extension to the C Programming language for real-time systems. In Real-Time and Embedded Technology and Applications Symposium (RTAS), Porto, Portugal, April 11–13, pp. 227–239. doi: 10.1109/RTAS.2018.00031.CrossRefGoogle Scholar
Lohstroh, M, Menard, C, Bateni, S and Lee, EA (2021) Toward a Lingua Franca for deterministic concurrent systems. ACM Transactions on Embedded Computing Systems (TECS), 20, Article 36. doi: 10.1145/3448128.CrossRefGoogle Scholar
Manna, Z and Pnueli, A (1993) Verifying hybrid systems. Hybrid Systems, LNCS, vol. 736, pp. 4–35.CrossRefGoogle Scholar
Clarke, EM and Emerson, EA (1981). Design and Synthesis of Synchronization Skeletons using Branching-Time Temporal Logic. In Workshop on Logic of Programs, LNCS, vol. 131. Springer-Verlag.Google Scholar
Matsikoudis, E, Stergiou, C and Lee, EA (2013) On the schedulability of real-time discrete-event systems. In International Conference on Embedded Software (EMSOFT), Montreal, Canada, September 29–October 4. ACM. doi: 10.1109/EMSOFT.2013.6658590.CrossRefGoogle Scholar
Sirjani, M, Lee, EA and Khamespanah, E (2020) Verification of cyberphysical systems. Mathematics, 8. doi: 10.3390/math8071068.CrossRefGoogle Scholar
Galison, P (2003) Einstein’s Clocks, Poincaré's Maps. New York: W. W. Norton & Company.Google Scholar
Muller, RA (2016) Now – The Physics of Time. W. W. Norton and Company.Google Scholar
Rovelli, C (2018) The Order of Time. New York: Riverhead Books.Google Scholar
Kopetz, H and Bauer, G (2003) The time-triggered architecture. Proceedings of the IEEE, 91, 112–126.CrossRefGoogle Scholar
Wilhelm, R (2003) Run-time guarantees for real-time systems. In Formal Modeling and Analysis of Timed Systems (FORMATS), LNCS, vol. 2791. Springer, pp. 166–167.CrossRefGoogle Scholar
Thiele, L and Wilhelm, R (2004) Design for timing predictability. Real-Time Systems, 28, 157–177. doi: 10.1023/B:TIME.0000045316.66276.6e.CrossRefGoogle Scholar
Edwards, SA and Lee, EA (2007) The Case for the Precision Timed (PRET) Machine. In Design Automation Conference (DAC), San Diego, CA, June 4–8.Google Scholar
Wilhelm, R et al. (2008) The worst-case execution-time problem - overview of methods and survey of tools, ACM Transactions on Embedded Computing Systems (TECS), 7, 1–53.CrossRefGoogle Scholar
Wilhelm, R, Grund, D, Reineke, J, Schlickling, M, Pister, M and Ferdinand, C (2009) Memory hierarchies, pipelines, and buses for future architectures in time-critical embedded systems. IEEE Transactions on Computer Aided Design, 28, 966–978. doi: 10.1109/TCAD.2009.2013287.CrossRefGoogle Scholar
Schoeberl, M (2009) Time-predictable computer architecture. EURASIP Journal on Embedded Systems, Article ID 758480, 17 pages. doi: 10.1155/2009/758480.Google Scholar
Lee, EA, Reineke, J and Zimmer, M (2017) Abstract PRET machines. In IEEE Real-Time Systems Symposium (RTSS), Paris, France.CrossRefGoogle Scholar