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Symbolic Computation of Differential Equivalences

Cardelli, Luca and Tribastone, Mirco and Tschaikowski, Max and Vandin, Andrea Symbolic Computation of Differential Equivalences. In: 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, January 20 - 22, 2016, St. Petersburg, FL, USA pp. 137-150. ISBN 978-1-4503-3549-2. (2016)

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Ordinary differential equations (ODEs) are widespread in manynatural 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. We provide novel symbolic 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 proposedby 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 thatcannot be reduced using competing automatic techniques.

Item Type: Conference or Workshop Item (Paper)
Identification Number: 10.1145/2837614.2837649
Uncontrolled Keywords: Quantitative Equivalence Relations, Satisfiability Mod-ulo Theory, Ordinary Differential Equations, Partition Refinement
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 13 Apr 2016 08:26
Last Modified: 13 Apr 2016 08:26
URI: http://eprints.imtlucca.it/id/eprint/3435

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