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.
Supplemental Material
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- S. Bliudze and D. Krob. Modelling of complex systems: Systems as dataflow machines. Fundam. Inform., 91 (2): 251--274, 2009. Google Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- R. Goldblatt. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer-Verlag, 1998.Google Scholar
- 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 Scholar
Digital Library
- A. E. Hurd and P. A. Loeb. An Introduction to Nonstandard Real Analysis. Academic Press, 1985.Google Scholar
- G. Kahn. The semantics of simple language for parallel programming. In IFIP Congress, pages 471--475, 1974.Google Scholar
- 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 Scholar
Digital Library
- E. A. Lee and H. Zheng. Operational semantics of hybrid systems. IncitetDBLP:conf/hybrid/2005, pages 25--53. ISBN 3--540--25108--1. Google Scholar
Digital Library
- Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, 1995. ISBN 978-0--387--94459--3. Google Scholar
Digital Library
- 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 Scholar
Digital Library
- H. Nakano. A modality for recursion. In LICS, pages 255--266. IEEE Computer Society, 2000. ISBN 0--7695-0725--5. Google Scholar
Digital Library
- A. Platzer. Logical Analysis of Hybrid Systems--Proving Theorems for Complex Dynamics. Springer, 2010. ISBN 978--3--642--14508--7. Google Scholar
Digital Library
- 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 Scholar
Digital Library
- A. Platzer. The complete proof theory of hybrid systems. In LICS, 2012. Google Scholar
Digital Library
- A. Robinson. Non-standard analysis. Princeton Univ. Press, 1996.Google Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- S. Sankaranarayanan, H. B. Sipma, and Z. Manna. Constructing invariants for hybrid systems. Formal Meth. in Sys. Design, 32 (1): 25--55, 2008. Google Scholar
Digital Library
- 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 Scholar
Digital Library
- R. Stephens. A survey of stream processing. Acta Inf., 34 (7): 491--541, 1997.Google Scholar
- 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 Scholar
Digital Library
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- K. R. Wicks. Nonstandard analysis of ordered sets. Order, 12: 265--293, 1995.Google Scholar
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Hyperstream processing systems: nonstandard modeling of continuous-time signals
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