research-article

Hyperstream processing systems: nonstandard modeling of continuous-time signals

Authors:

Hiroyoshi Sekine, and

Ichiro HasuoAuthors Info & Claims

ACM SIGPLAN Notices, Volume 48, Issue 1

Pages 417 - 430

https://doi.org/10.1145/2480359.2429120

Published: 23 January 2013 Publication History

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.

Supplementary Material

MP4 File (r1d3_talk4.mp4)

Download
113.30 MB

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.

Digital 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.

Digital 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.

[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.

Digital 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.

Digital Library

[6]

S. Bliudze and D. Krob. Modelling of complex systems: Systems as dataflow machines. Fundam. Inform., 91 (2): 251--274, 2009.

Digital 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.

Digital 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.

[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.

Digital 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.

Digital 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.

Digital Library

[12]

R. Goldblatt. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer-Verlag, 1998.

[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.

Digital Library

[14]

A. E. Hurd and P. A. Loeb. An Introduction to Nonstandard Real Analysis. Academic Press, 1985.

[15]

G. Kahn. The semantics of simple language for parallel programming. In IFIP Congress, pages 471--475, 1974.

[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.

Digital 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.

Digital Library

[18]

Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, 1995. ISBN 978-0--387--94459--3.

Digital 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.

Digital Library

[20]

H. Nakano. A modality for recursion. In LICS, pages 255--266. IEEE Computer Society, 2000. ISBN 0--7695-0725--5.

Digital Library

[21]

A. Platzer. Logical Analysis of Hybrid Systems--Proving Theorems for Complex Dynamics. Springer, 2010. ISBN 978--3--642--14508--7.

Digital 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.

Digital Library

[23]

A. Platzer. The complete proof theory of hybrid systems. In LICS, 2012.

Digital Library

[24]

A. Robinson. Non-standard analysis. Princeton Univ. Press, 1996.

[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.

Digital 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.

Digital 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.

Digital 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.

Digital Library

[29]

R. Stephens. A survey of stream processing. Acta Inf., 34 (7): 491--541, 1997.

[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.

Digital 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.html

[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.

Digital 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.

Digital 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.

Digital Library

[35]

K. R. Wicks. Nonstandard analysis of ordered sets. Order, 12: 265--293, 1995.

Cited By

Hasuo I(2019)Nonstandard Static Analysis: Literal Transfer of Deductive Verification Frameworks from Discrete to HybridCyber Physical Systems. Design, Modeling, and Evaluation10.1007/978-3-030-17910-6_1(3-7)Online publication date: 13-Apr-2019
https://doi.org/10.1007/978-3-030-17910-6_1
Hasuo I(2017)Metamathematics for Systems DesignNew Generation Computing10.1007/s00354-017-0023-135:3(271-305)Online publication date: 15-Jul-2017
https://doi.org/10.1007/s00354-017-0023-1
Nakamura HKojima KSuenaga KIgarashi A(2017)A Nonstandard Functional Programming LanguageProgramming Languages and Systems10.1007/978-3-319-71237-6_25(514-533)Online publication date: 19-Nov-2017
https://doi.org/10.1007/978-3-319-71237-6_25
Show More Cited By

Index Terms

Hyperstream processing systems: nonstandard modeling of continuous-time signals
1. Theory of computation
  1. Logic
    1. Programming logic
  2. Semantics and reasoning
    1. Program reasoning
    2. Program semantics
      1. Denotational semantics

Recommendations

Hyperstream processing systems: nonstandard modeling of continuous-time signals
POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

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 ...
Read More
Coriolis mass flowmeter signal processing system based on time-varying signal model

In order to improve the signal processing effect and efficiency of Coriolis mass flowmeter, a signal processing system of Coriolis mass flowmeter based on time-varying signal model is designed. Based on the analysis of the structure and working ...
Read More
Input-to-state stability of impulsive and switching hybrid systems with time-delay

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov-Krasovskii functionals. It is shown that, even if all ...
Read More

Comments

Information & Contributors

Information

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

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
General Chair:
Roberto Giacobazzi
Università di Verona, Italy
,
Program Chair:
Radhia Cousot
École normale supérieure CNRS & INRIA, France

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 January 2013

Published in SIGPLAN Volume 48, Issue 1

Check for updates

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

20
Total Citations
View Citations
386
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)0

Other Metrics

View Author Metrics

Citations

Cited By

Hasuo I(2019)Nonstandard Static Analysis: Literal Transfer of Deductive Verification Frameworks from Discrete to HybridCyber Physical Systems. Design, Modeling, and Evaluation10.1007/978-3-030-17910-6_1(3-7)Online publication date: 13-Apr-2019
https://doi.org/10.1007/978-3-030-17910-6_1
Hasuo I(2017)Metamathematics for Systems DesignNew Generation Computing10.1007/s00354-017-0023-135:3(271-305)Online publication date: 15-Jul-2017
https://doi.org/10.1007/s00354-017-0023-1
Nakamura HKojima KSuenaga KIgarashi A(2017)A Nonstandard Functional Programming LanguageProgramming Languages and Systems10.1007/978-3-319-71237-6_25(514-533)Online publication date: 19-Nov-2017
https://doi.org/10.1007/978-3-319-71237-6_25
Kido KChaudhuri SHasuo I(2016)Abstract Interpretation with InfinitesimalsProceedings of the 17th International Conference on Verification, Model Checking, and Abstract Interpretation - Volume 958310.1007/978-3-662-49122-5_11(229-249)Online publication date: 17-Jan-2016
https://dl.acm.org/doi/10.1007/978-3-662-49122-5_11
Bartenstein TLiu Y(2014)Rate types for stream programsACM SIGPLAN Notices10.1145/2714064.266022549:10(213-232)Online publication date: 15-Oct-2014
https://dl.acm.org/doi/10.1145/2714064.2660225
Kolčák JDubut JHasuo IKatsumata SSprunger DYamada A(2020)Relational Differential Dynamic LogicTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-45190-5_11(191-208)Online publication date: 17-Apr-2020
https://doi.org/10.1007/978-3-030-45190-5_11
Suenaga KIshizawa T(2020)Generalized Property-Directed Reachability for Hybrid SystemsVerification, Model Checking, and Abstract Interpretation10.1007/978-3-030-39322-9_14(293-313)Online publication date: 16-Jan-2020
https://dl.acm.org/doi/10.1007/978-3-030-39322-9_14
Hasuo I(2019)Nonstandard Static Analysis: Literal Transfer of Deductive Verification Frameworks from Discrete to HybridCyber Physical Systems. Design, Modeling, and Evaluation10.1007/978-3-030-17910-6_1(3-7)Online publication date: 13-Apr-2019
https://doi.org/10.1007/978-3-030-17910-6_1
Benveniste ABourke TCaillaud BColaco JPasteur CPouzet M(2018)Building a Hybrid Systems Modeler on Synchronous Languages PrinciplesProceedings of the IEEE10.1109/JPROC.2018.2858016106:9(1568-1592)Online publication date: Sep-2018
https://doi.org/10.1109/JPROC.2018.2858016
Bourke TCarcenac FColaço JPagano BPasteur CPouzet M(2017)A Synchronous Look at the Simulink Standard LibraryACM Transactions on Embedded Computing Systems10.1145/312651616:5s(1-24)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126516
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents