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Continuity of Thresholded Mode-Switched ODEs and Digital Circuit Delay Models

Authors:

Arman Ferdowsi,

Matthias Függer,

Thomas Nowak,

Ulrich SchmidAuthors Info & Claims

HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

Article No.: 10, Pages 1 - 11

https://doi.org/10.1145/3575870.3587125

Published: 09 May 2023 Publication History

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Abstract

Thresholded mode-switched ODEs are restricted dynamical systems that switch ODEs depending on digital input signals only, and produce a digital output signal by thresholding some internal signal. Such systems arise in recent digital circuit delay models, where the analog signals within a gate are governed by ODEs that change depending on the digital inputs.

We prove the continuity of the mapping from digital input signals to digital output signals for a large class of thresholded mode-switched ODEs. This continuity property is known to be instrumental for ensuring the faithfulness of the model w.r.t. propagating short pulses. We apply our result to several instances of such digital delay models, thereby proving them to be faithful.

References

[1]

Manuel J. Bellido-Díaz, Jorge Juan-Chico, and Manuel Valencia. 2006. Logic-Timing Simulation and the Degradation Delay Model. Imperial College Press, London.

Google Scholar

[2]

Maxence Bouvier, Alexandre Valentian, Thomas Mesquida, Francois Rummens, Marina Reyboz, Elisa Vianello, and Edith Beigne. 2019. Spiking Neural Networks Hardware Implementations and Challenges: A Survey. ACM Journal on Emerging Technologies in Computing Systems 15, 2, Article 22 (2019), 35 pages.

Digital Library

Google Scholar

[3]

Liang-Chi Chen, S. K. Gupta, and M. A. Breuer. 2001. A new gate delay model for simultaneous switching and its applications. In Proceedings of the 38th Design Automation Conference. 289–294. https://doi.org/10.1109/DAC.2001.156153

Digital Library

Google Scholar

[4]

Arman Ferdowsi, Jürgen Maier, Daniel Öhlinger, and Ulrich Schmid. 2022. A Simple Hybrid Model for Accurate Delay Modeling of a Multi-Input Gate. In Proceedings of the 2022 Design, Automation & Test in Europe Conference & Exhibition.

Crossref

Google Scholar

[5]

Arman Ferdowsi, Ulrich Schmid, and Josef Salzmann. 2022. An Accurate Hybrid Delay Model for Multi-Input Gates. arXiv preprint arXiv:2211.10628 (2022).

Google Scholar

[6]

A. F. Filippov. 1988. Differential Equations with Discontinuous Righthand Sides. Springer, Heidelberg.

Google Scholar

[7]

Matthias Függer, Thomas Nowak, and Ulrich Schmid. 2016. Unfaithful Glitch Propagation in Existing Binary Circuit Models. IEEE Trans. Comput. 65, 3 (2016), 964–978. https://doi.org/10.1109/TC.2015.2435791

Digital Library

Google Scholar

[8]

M. Függer, R. Najvirt, T. Nowak, and U. Schmid. 2020. A Faithful Binary Circuit Model. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39, 10 (2020), 2784–2797. https://doi.org/10.1109/TCAD.2019.2937748

Crossref

Google Scholar

[9]

Thomas A Henzinger. 2000. The theory of hybrid automata. In Verification of Digital and Hybrid Systems. Springer, Heidelberg, 265–292.

Crossref

Google Scholar

[10]

Nancy Lynch, Roberto Segala, and Frits Vaandrager. 2003. Hybrid I/O automata. Information and Computation 185, 1 (2003), 105–157.

Digital Library

Google Scholar

[11]

Walter Rudin. 1976. Principles of Mathematical Analysis. McGraw-Hill, New York.

Google Scholar

[12]

H. Shichman and D. A. Hodges. 1968. Modeling and simulation of insulated-gate field-effect transistor switching circuits. IEEE Journal of Solid-State Circuits 3, 3 (1968), 285–289. https://doi.org/10.1109/JSSC.1968.1049902

Crossref

Google Scholar

[13]

Gerald Teschl. 2012. Ordinary Differential Equations and Dynamical Systems. American Mathematical Society, Providence.

Google Scholar

[14]

Daniel Öhlinger, Jürgen Maier, Matthias Függer, and Ulrich Schmid. 2021. The Involution Tool for Accurate Digital Timing and Power Analysis. Integration 76 (2021), 87–98. https://doi.org/10.1016/j.vlsi.2020.09.007

Crossref

Google Scholar

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Ferdowsi AFügger MNowak TSchmid UDrmota M(2025)Faithful dynamic timing analysis of digital circuits using continuous thresholded mode-switched ODEsNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2024.10157256(101572)Online publication date: May-2025
https://doi.org/10.1016/j.nahs.2024.101572
Ferdowsi ASchmid USalzmann J(2023)Accurate Hybrid Delay Models for Dynamic Timing Analysis2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)10.1109/ICCAD57390.2023.10323646(1-9)Online publication date: 28-Oct-2023
https://doi.org/10.1109/ICCAD57390.2023.10323646

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HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

May 2023

239 pages

ISBN:9798400700330

DOI:10.1145/3575870

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

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Published: 09 May 2023

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HSCC '23: 26th ACM International Conference on Hybrid Systems: Computation and Control

May 9 - 12, 2023

TX, San Antonio, USA

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Ferdowsi AFügger MNowak TSchmid UDrmota M(2025)Faithful dynamic timing analysis of digital circuits using continuous thresholded mode-switched ODEsNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2024.10157256(101572)Online publication date: May-2025
https://doi.org/10.1016/j.nahs.2024.101572
Ferdowsi ASchmid USalzmann J(2023)Accurate Hybrid Delay Models for Dynamic Timing Analysis2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)10.1109/ICCAD57390.2023.10323646(1-9)Online publication date: 28-Oct-2023
https://doi.org/10.1109/ICCAD57390.2023.10323646

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Continuity and pullback attractors for a non-autonomous reaction-diffusion equation in R N

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Continuity and pullback attractors for a non-autonomous reaction-diffusion equation in R N

Singular boundary value problems for ODEs

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

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