=> Définir comment implanter les SAN

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Selon The Kronecker product and stochastic automata networks de Amy N. Langville et William J. Stewart https://www.sciencedirect.com/science/article/pii/S0377042703009312 "One remedy for this storage problem is SANs, which store the infinitesimal generator of the Markov chain in compact form using Kronecker products." La représentation compacte des SANs s'appuie sur les SAN descriptors de Plateau.

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Voir le code produit avec chatGPT dans le paquetage jKendrick.sans

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Tiré du papier cité plus haut.

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ChatGPT provided some information about the San descriptors: Yes, Brigitte Plateau's work on Stochastic Automata Networks (SANs) often involves efficient representations of the Q-matrix using descriptors. These descriptors capture the local interactions among automata and can significantly reduce the memory requirements for storing the Q-matrix, especially when the system has a large number of states or automata.

Using SAN Descriptors Local Event Descriptors (LED): These describe the local events in each automaton. They contain the rates of transitions that are local to an automaton.

Synchronization Event Descriptors (SED): These describe the events that synchronize multiple automata. They contain the rates of transitions that involve more than one automaton.

Functional Transition Descriptors (FTD): These describe transitions whose rates are functions of the states of one or more automata.

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ChatGPT propose ce code public class LocalEventDescriptor { int fromState; int toState; double rate; // ... }

public class SynchronizationEventDescriptor { int[] fromStates; int[] toStates; double rate; // ... }

public class FunctionalTransitionDescriptor { int fromState; int toState; RateFunction rateFunction; // ... }

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See https://graal.ens-lyon.fr/~abenoit/papers/RR-4259.pdf Memory Ecient Iterative Methods for Stochastic Automata Networks

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Un papier intéressant discute de l'implantation efficace du produit de Kronecker pour les SANs https://link.springer.com/chapter/10.1007/978-3-540-24611-4_8 Kronecker Based Matrix Representations for Large Markov Models

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See the PRISM tool https://www.prismmodelchecker.org/casestudies/index.php