eprintid: 3435
rev_number: 8
eprint_status: archive
userid: 69
dir: disk0/00/00/34/35
datestamp: 2016-04-13 08:26:32
lastmod: 2016-04-13 08:26:32
status_changed: 2016-04-13 08:26:32
type: conference_item
metadata_visibility: show
creators_name: Cardelli, Luca
creators_name: Tribastone, Mirco
creators_name: Tschaikowski, Max
creators_name: Vandin, Andrea
creators_id: 
creators_id: mirco.tribastone@imtlucca.it
creators_id: max.tschaikowski@imtlucca.it
creators_id: andrea.vandin@imtlucca.it
title: Symbolic Computation of Differential Equivalences
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: public
pres_type: paper
keywords: Quantitative Equivalence Relations, Satisfiability Mod-ulo Theory, Ordinary Differential Equations, Partition Refinement
abstract: 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.
date: 2016
date_type: published
publisher: ACM
pagerange: 137-150
event_title: 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
event_location: St. Petersburg, FL, USA
event_dates: January 20 - 22, 2016
event_type: conference
id_number: 10.1145/2837614.2837649
refereed: TRUE
isbn: 978-1-4503-3549-2
book_title: Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
official_url: http://dx.doi.org/10.1145/2837614.2837649
related_url_url: http://dl.acm.org/citation.cfm?id=2837614&picked=formats&CFID=770048590&CFTOKEN=77197608
related_url_type: pub
citation:   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)  
document_url: http://eprints.imtlucca.it/3435/1/z3-popl16.pdf