Ordinary differential equations (ODEs) are widespread in many natural sciences including chemistry, ecology, and systems biology, and in disciplines such as control theory and electrical engineering. Building on the celebrated molecules-as-processes paradigm, they have become increasingly popular in computer science, with high-level languages and formal methods such as Petri nets, process algebra, and rule-based systems that are interpreted as ODEs.
We consider the problem of comparing and minimizing ODEs automatically. Influenced by traditional approaches in the theory of programming, we propose differential equivalence relations. We study them for a basic intermediate language, for which we have decidability results, that can be targeted by a class of high-level specifications. An ODE implicitly represents an uncountable state space, hence reasoning techniques cannot be borrowed from established domains such as probabilistic programs with finite-state Markov chain semantics. Instead we provide novel procedures to check an equivalence and compute the largest one via partition refinement algorithms that use satisfiability modulo theories.
We illustrate the generality of our framework by showing that differential equivalences include (i) well-known notions for the minimization of continuous-time Markov chains (lumpability), (ii) bisimulations for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics. With a prototype implementation we are able to detect equivalences in biochemical models from the literature that cannot be reduced using competing automatic techniques.
Wed 20 JanDisplayed time zone: Guadalajara, Mexico City, Monterrey change
14:20 - 16:00
|Query-Guided Maximum Satisfiability|
Xin Zhang Georgia Tech, Ravi Mangal Georgia Institute of Technology, Aditya Nori Microsoft Research, UK, Mayur Naik Georgia TechFile Attached
|String Solving with Word Equations and Transducers: Decidability and Applications to Detecting Mutation XSS|
Research PapersMedia Attached
|Symbolic Computation of Differential Equivalences|
Luca Cardelli Microsoft Research and University of Oxford, Mirco Tribastone IMT Institute for Advanced Studies Lucca, Italy, Max Tschaikowski IMT Institute for Advanced Studies Lucca, Italy, Andrea Vandin IMT Institute for Advanced Studies Lucca, ItalyMedia Attached
|Unboundedness and Downward Closures of Higher-Order Pushdown Automata|
Matthew Hague Royal Holloway University of London, UK, Jonathan Kochems Department of Computer Science, University of Oxford, C.-H. Luke Ong University of Oxford, UKMedia Attached