We consider reasoning and minimization in systems of polynomial ordinary differential equations (ODEs). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow polynomials with a transition system structure based on the concept of Lie derivative, thus inducing a notion of -bisimulation. Two states (variables) are proven -bisimilar if and only if they correspond to the same solution in the ODEs system. We then characterize -bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest -bisimulation containing all valid identities that are instances of a user-specified template. A specific largest -bisimulation can be used to build a reduced system of ODEs, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations.

Algebra, coalgebra, and minimization in polynomial differential equations / Boreale, Michele*. - STAMPA. - (2017), pp. 71-87. [10.1007/978-3-662-54458-7_5]

### Algebra, coalgebra, and minimization in polynomial differential equations

#### Abstract

We consider reasoning and minimization in systems of polynomial ordinary differential equations (ODEs). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow polynomials with a transition system structure based on the concept of Lie derivative, thus inducing a notion of -bisimulation. Two states (variables) are proven -bisimilar if and only if they correspond to the same solution in the ODEs system. We then characterize -bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest -bisimulation containing all valid identities that are instances of a user-specified template. A specific largest -bisimulation can be used to build a reduced system of ODEs, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations.
##### Scheda breve Scheda completa Scheda completa (DC) 2017
9783662544570
Foundations of Software Science and Computation Structures - 20th International Conference, {FOSSACS} 2017, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
71
87
Boreale, Michele*
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/1113069`
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