Luca
Bortolussi
Markov chain
network
time-inhomogeneous discrete-time Markov chain
accuracy
space
number
probabilistic reachability
temporal properties
reachability probabilities
chapter
semantics
inequality
Approximation of Probabilistic Reachability for Chemical Reaction Networks Using the Linear Noise Approximation
reachability region
time-bounded reachability probabilities
reaction networks
restriction
number of species
https://doi.org/10.1007/978-3-319-43425-4_5
continuous space Gaussian process
noise approximation
https://scigraph.springernature.com/explorer/license/
terms
original Gaussian process
abstraction
study
true
2016-08-03
properties
region
algorithm
state space
computation
scalable computation
probability
reachability
space Gaussian process
species
process
72-88
case study
time-bounded probabilistic reachability
reachability properties
approximation
chapters
chemical reaction networks
complex temporal properties
linear noise approximation
discrete-time Markov chain
linear inequalities
approximate computation
stochastic semantics
problem
2016-08-03
en
Gaussian process
intersection
explosion problem
space explosion problem
discrete stochastic semantics
2022-01-01T19:24
chain
We study time-bounded probabilistic reachability for Chemical Reaction Networks (CRNs) using the Linear Noise Approximation (LNA). The LNA approximates the discrete stochastic semantics of a CRN in terms of a continuous space Gaussian process. We consider reachability regions expressed as intersections of finitely many linear inequalities over the species of a CRN. This restriction allows us to derive an abstraction of the original Gaussian process as a time-inhomogeneous discrete-time Markov chain (DTMC), such that the dimensionality of its state space is independent of the number of species of the CRN, ameliorating the state space explosion problem. We formulate an algorithm for approximate computation of time-bounded reachability probabilities on the resulting DTMC and show how to extend it to more complex temporal properties. We implement the algorithm and demonstrate on two case studies that it permits fast and scalable computation of reachability properties with controlled accuracy.
dimensionality
state space explosion problem
Laurenti
Luca
Computation Theory and Mathematics
Cardelli
Luca
dimensions_id
pub.1020794792
Department of Computer Science, University of Oxford, Oxford, UK
Department of Computer Science, University of Oxford, Oxford, UK
Microsoft Research, Cambridge, UK
Springer Nature
Agha
Gul
Marta
Kwiatkowska
Department of Mathematics and Geosciences, University of Trieste, Trieste, Italy
Department of Mathematics and Geosciences, University of Trieste, Trieste, Italy
978-3-319-43424-7
978-3-319-43425-4
Quantitative Evaluation of Systems
Information and Computing Sciences
Van Houdt
Benny
Springer Nature - SN SciGraph project
10.1007/978-3-319-43425-4_5
doi