ERODE: A tool for the evaluation and reduction of ordinary differential equations

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

We present ERODE, a multi-platform tool for the solution and exact reduction of systems of ordinary differential equations (ODEs). ERODE supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence yields a self-consistent aggregate system where each ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class. Backward differential equivalence identifies variables that have identical solutions whenever starting from the same initial conditions. As back-end ERODE uses the well-known Z3 SMT solver to compute the largest equivalence that refines a given initial partition of ODE variables. In the special case of ODEs with polynomial derivatives of degree at most two (covering affine systems and elementary chemical reaction networks), it implements a more efficient partition-refinement algorithm in the style of Paige and Tarjan. ERODE comeswitharich development environment based on the Eclipse plug-in framework offering: (i) seamless project management; (ii) a fully-featured text editor; and (iii) importing-exporting capabilities.

Original languageEnglish
Title of host publicationTools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings
Number of pages19
Volume10206 LNCS
PublisherSpringer Verlag
Publication date2017
Pages310-328
ISBN (Print)9783662545799
DOIs
Publication statusPublished - 2017
Externally publishedYes
Event23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017 - Uppsala, Sweden
Duration: 22 Apr 201729 Apr 2017

Conference

Conference23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017
CountrySweden
City Uppsala
Period22/04/201729/04/2017
SeriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10206 LNCS
ISSN0302-9743

Cite this

Cardelli, L., Tribastone, M., Tschaikowski, M., & Vandin, A. (2017). ERODE: A tool for the evaluation and reduction of ordinary differential equations. In Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings (Vol. 10206 LNCS, pp. 310-328). Springer Verlag. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol.. 10206 LNCS https://doi.org/10.1007/978-3-662-54580-5_19
Cardelli, Luca ; Tribastone, Mirco ; Tschaikowski, Max ; Vandin, Andrea. / ERODE : A tool for the evaluation and reduction of ordinary differential equations. Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings. Vol. 10206 LNCS Springer Verlag, 2017. pp. 310-328 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10206 LNCS).
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abstract = "We present ERODE, a multi-platform tool for the solution and exact reduction of systems of ordinary differential equations (ODEs). ERODE supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence yields a self-consistent aggregate system where each ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class. Backward differential equivalence identifies variables that have identical solutions whenever starting from the same initial conditions. As back-end ERODE uses the well-known Z3 SMT solver to compute the largest equivalence that refines a given initial partition of ODE variables. In the special case of ODEs with polynomial derivatives of degree at most two (covering affine systems and elementary chemical reaction networks), it implements a more efficient partition-refinement algorithm in the style of Paige and Tarjan. ERODE comeswitharich development environment based on the Eclipse plug-in framework offering: (i) seamless project management; (ii) a fully-featured text editor; and (iii) importing-exporting capabilities.",
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Cardelli, L, Tribastone, M, Tschaikowski, M & Vandin, A 2017, ERODE: A tool for the evaluation and reduction of ordinary differential equations. in Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings. vol. 10206 LNCS, Springer Verlag, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10206 LNCS, pp. 310-328, 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, 22/04/2017. https://doi.org/10.1007/978-3-662-54580-5_19

ERODE : A tool for the evaluation and reduction of ordinary differential equations. / Cardelli, Luca; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea.

Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings. Vol. 10206 LNCS Springer Verlag, 2017. p. 310-328 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10206 LNCS).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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T1 - ERODE

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AU - Cardelli, Luca

AU - Tribastone, Mirco

AU - Tschaikowski, Max

AU - Vandin, Andrea

PY - 2017

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N2 - We present ERODE, a multi-platform tool for the solution and exact reduction of systems of ordinary differential equations (ODEs). ERODE supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence yields a self-consistent aggregate system where each ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class. Backward differential equivalence identifies variables that have identical solutions whenever starting from the same initial conditions. As back-end ERODE uses the well-known Z3 SMT solver to compute the largest equivalence that refines a given initial partition of ODE variables. In the special case of ODEs with polynomial derivatives of degree at most two (covering affine systems and elementary chemical reaction networks), it implements a more efficient partition-refinement algorithm in the style of Paige and Tarjan. ERODE comeswitharich development environment based on the Eclipse plug-in framework offering: (i) seamless project management; (ii) a fully-featured text editor; and (iii) importing-exporting capabilities.

AB - We present ERODE, a multi-platform tool for the solution and exact reduction of systems of ordinary differential equations (ODEs). ERODE supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence yields a self-consistent aggregate system where each ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class. Backward differential equivalence identifies variables that have identical solutions whenever starting from the same initial conditions. As back-end ERODE uses the well-known Z3 SMT solver to compute the largest equivalence that refines a given initial partition of ODE variables. In the special case of ODEs with polynomial derivatives of degree at most two (covering affine systems and elementary chemical reaction networks), it implements a more efficient partition-refinement algorithm in the style of Paige and Tarjan. ERODE comeswitharich development environment based on the Eclipse plug-in framework offering: (i) seamless project management; (ii) a fully-featured text editor; and (iii) importing-exporting capabilities.

U2 - 10.1007/978-3-662-54580-5_19

DO - 10.1007/978-3-662-54580-5_19

M3 - Article in proceedings

AN - SCOPUS:85017511925

SN - 9783662545799

VL - 10206 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 310

EP - 328

BT - Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings

PB - Springer Verlag

ER -

Cardelli L, Tribastone M, Tschaikowski M, Vandin A. ERODE: A tool for the evaluation and reduction of ordinary differential equations. In Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings. Vol. 10206 LNCS. Springer Verlag. 2017. p. 310-328. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10206 LNCS). https://doi.org/10.1007/978-3-662-54580-5_19