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Hyperstream processing systems: nonstandard modeling of continuous-time signals

Published:23 January 2013Publication History
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Abstract

We exploit the apparent similarity between (discrete-time) stream processing and (continuous-time) signal processing and transfer a deductive verification framework from the former to the latter. Our development is based on rigorous semantics that relies on nonstandard analysis (NSA).

Specifically, we start with a discrete framework consisting of a Lustre-like stream processing language, its Kahn-style fixed point semantics, and a program logic (in the form of a type system) for partial correctness guarantees. This stream framework is transferred as it is to one for hyperstreams---streams of streams, that typically arise from sampling (continuous-time) signals with progressively smaller intervals---via the logical infrastructure of NSA. Under a certain continuity assumption we identify hyperstreams with signals; our final outcome thus obtained is a deductive verification framework of signals. In it one verifies properties of signals using the (conventionally discrete) proof principles, like fixed point induction.

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References

  1. S. Abramsky and A. Jung. Domain theory. In S. Abramsky, D. M. Gabbai, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, volume 3, pages 1--168. Oxford Univ. Press, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theor. Comp. Sci., 138(1): 3--34, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. R. Beauxis and S. Mimram. A non-standard semantics for Kahn networks in continuous time. In M. Bezem, editor, CSL, volume 12 of LIPIcs, pages 35--50. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2011. ISBN 978-3-939897-32-3.Google ScholarGoogle Scholar
  4. A. Benveniste, T. Bourke, B. Caillaud, and M. Pouzet. Divide and recycle: types and compilation for a hybrid synchronous language. In J. Vitek and B. D. Sutter, editors, LCTES, pages 61--70. ACM, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. A. Benveniste, T. Bourke, B. Caillaud, and M. Pouzet. Non-standard semantics of hybrid systems modelers. J. Comput. Syst. Sci., 78 (3): 877--910, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. S. Bliudze and D. Krob. Modelling of complex systems: Systems as dataflow machines. Fundam. Inform., 91 (2): 251--274, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. O. Bouissou and A. Chapoutot. An operational semantics for Simulink's simulation engine. In R. Wilhelm, H. Falk, and W. Yi, editors, LCTES, pages 129--138. ACM, 2012. ISBN 978--1--4503--1212--7. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. M. L. Bujorianu and J. Lygeros. Theoretical foundations of stochastic hybrid systems. In International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004), 2004.Google ScholarGoogle Scholar
  9. P. Caspi, D. Pilaud, N. Halbwachs, and J. Plaice. Lustre: A declarative language for programming synchronous systems. In POPL, pages 214--227. ACM Press, 1987. ISBN 0--89791--215--2. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. A. Chapoutot and M. Martel. Abstract simulation: A static analysis of simulink models. In T. Chen, D. N. Serpanos, and W. Taha, editors, ICESS, pages 83--92. IEEE, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. A. Gamatié and L. Gonnord. Static analysis of synchronous programs in signal for efficient design of multi-clocked embedded systems. In J. Vitek and B. D. Sutter, editors, LCTES, pages 71--80. ACM, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. R. Goldblatt. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer-Verlag, 1998.Google ScholarGoogle Scholar
  13. I. Hasuo and K. Suenaga. Exercises in phNonstandard Static Analysis of hybrid systems. In P. Madhusudan and S. A. Seshia, editors, CAV, volume 7358 of Lect. Notes Comp. Sci., pages 462--478. Springer, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. A. E. Hurd and P. A. Loeb. An Introduction to Nonstandard Real Analysis. Academic Press, 1985.Google ScholarGoogle Scholar
  15. G. Kahn. The semantics of simple language for parallel programming. In IFIP Congress, pages 471--475, 1974.Google ScholarGoogle Scholar
  16. N. R. Krishnaswami and N. Benton. Ultrametric semantics of reactive programs. In LICS, pages 257--266. IEEE Computer Society, 2011. ISBN 978-0--7695--4412-0. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. E. A. Lee and H. Zheng. Operational semantics of hybrid systems. IncitetDBLP:conf/hybrid/2005, pages 25--53. ISBN 3--540--25108--1. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, 1995. ISBN 978-0--387--94459--3. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. M. Morari and L. Thiele, editors. Hybrid Systems: Computation and Control, 8th International Workshop, HSCC 2005, Zurich, Switzerland, March 9--11, 2005, Proceedings, volume 3414 of Lecture Notes in Computer Science, 2005. Springer. ISBN 3--540--25108--1. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. H. Nakano. A modality for recursion. In LICS, pages 255--266. IEEE Computer Society, 2000. ISBN 0--7695-0725--5. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. A. Platzer. Logical Analysis of Hybrid Systems--Proving Theorems for Complex Dynamics. Springer, 2010. ISBN 978--3--642--14508--7. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. A. Platzer. Stochastic differential dynamic logic for stochastic hybrid programs. In N. Bjørner and V. Sofronie-Stokkermans, editors, CADE, volume 6803 of Lecture Notes in Computer Science, pages 446--460. Springer, 2011. ISBN 978--3--642--22437--9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. A. Platzer. The complete proof theory of hybrid systems. In LICS, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. A. Robinson. Non-standard analysis. Princeton Univ. Press, 1996.Google ScholarGoogle Scholar
  25. E. Rodríguez-Carbonell and A. Tiwari. Generating polynomial invariants for hybrid systems. IncitetDBLP:conf/hybrid/2005, pages 590--605. ISBN 3--540--25108--1. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. S. Sankaranarayanan. Automatic invariant generation for hybrid systems using ideal fixed points. In K. H. Johansson and W. Yi, editors, HSCC, pages 221--230. ACM, 2010. ISBN 978--1--60558--955--8. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. S. Sankaranarayanan, H. B. Sipma, and Z. Manna. Constructing invariants for hybrid systems. Formal Meth. in Sys. Design, 32 (1): 25--55, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. P. Schrammel and B. Jeannet. From hybrid data-flow languages to hybrid automata: a complete translation. In T. Dang and I. M. Mitchell, editors, HSCC, pages 167--176. ACM, 2012. ISBN 978--1--4503--1220--2. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. R. Stephens. A survey of stream processing. Acta Inf., 34 (7): 491--541, 1997.Google ScholarGoogle Scholar
  30. K. Suenaga and I. Hasuo. Programming with infinitesimals: A while-language for hybrid system modeling. In L. Aceto, M. Henzinger, and J. Sgall, editors, ICALP (2), volume 6756 of Lect. Notes Comp. Sci., pages 392--403. Springer, 2011. ISBN 978--3--642--22011--1. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. K. Suenaga, H. Sekine, and I. Hasuo. Hyperstream processing systems: Nonstandard modeling of continuous signal processing. Extended version with proofs, 2013.www-mmm.is.s.u-tokyo.ac.jp/ ichiro/papers.htmlGoogle ScholarGoogle Scholar
  32. T. Terauchi. Dependent types from counterexamples. In M. V. Hermenegildo and J. Palsberg, editors, POPL, pages 119--130. ACM, 2010. ISBN 978--1--60558--479--9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. S. Tripakis, C. Sofronis, P. Caspi, and A. Curic. Translating discrete-time simulink to Lustre. ACM Trans. Embedded Comput. Syst., 4 (4): 779--818, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Z. Wan and P. Hudak. Functional reactive programming from first principles. In M. S. Lam, editor, PLDI, pages 242--252. ACM, 2000. ISBN 1--58113--199--2. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. K. R. Wicks. Nonstandard analysis of ordered sets. Order, 12: 265--293, 1995.Google ScholarGoogle ScholarCross RefCross Ref

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        • Published in

          cover image ACM SIGPLAN Notices
          ACM SIGPLAN Notices  Volume 48, Issue 1
          POPL '13
          January 2013
          561 pages
          ISSN:0362-1340
          EISSN:1558-1160
          DOI:10.1145/2480359
          Issue’s Table of Contents
          • cover image ACM Conferences
            POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
            January 2013
            586 pages
            ISBN:9781450318327
            DOI:10.1145/2429069

          Copyright © 2013 ACM

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          • Published: 23 January 2013

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