Efficient Local Computation of Differential Bisimulations via Coupling and Up-to Methods

We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems acros...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 14
Main Authors: Bacci, Giorgio, Bacci, Giovanni, Larsen, Kim G., Tribastone, Mirco, Tschaikowski, Max, Vandin, Andrea
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Couplings
Differential equations
Heuristic algorithms
Probabilistic logic
Prototypes
Runtime
Systems biology
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when disproving equivalences between Markov chains.
DOI:10.1109/LICS52264.2021.9470555