License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TIME.2017.5
URN: urn:nbn:de:0030-drops-79203
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7920/
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Behaegel, Jonathan ; Comet, Jean-Paul ; Folschette, Maxime

Constraint Identification Using Modified Hoare Logic on Hybrid Models of Gene Networks

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LIPIcs-TIME-2017-5.pdf (0.7 MB)

Abstract

We present a new hybrid Hoare logic dedicated for a class of linear hybrid automata well suited to model gene regulatory networks. These automata rely on Thomas' discrete framework in which qualitative parameters have been replaced by continuous parameters called celerities. The identification of these parameters remains one of the keypoints of the modelling process, and is difficult especially because the modelling framework is based on a continuous time. We introduce Hoare triples which handle biological traces and pre/post-conditions. Observed chronometrical biological traces play the role of an imperative program for classical Hoare logic and our hybrid Hoare logic, defined by inference rules, is proved to be sound. Furthermore, we present a weakest precondition calculus (a la Dijkstra) which leads to constraints on dynamical parameters. Finally, we illustrate our "constraints generator" with a simplified circadian clock model describing the rhythmicity of cells in mammals on a 24-hour period.

BibTeX - Entry

@InProceedings{behaegel_et_al:LIPIcs:2017:7920,
  author =	{Jonathan Behaegel and Jean-Paul Comet and Maxime Folschette},
  title =	{{Constraint Identification Using Modified Hoare Logic on Hybrid Models of Gene Networks}},
  booktitle =	{24th International Symposium on Temporal Representation and Reasoning (TIME 2017)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-052-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{90},
  editor =	{Sven Schewe and Thomas Schneider and Jef Wijsen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7920},
  URN =		{urn:nbn:de:0030-drops-79203},
  doi =		{10.4230/LIPIcs.TIME.2017.5},
  annote =	{Keywords: Hoare logic, weakest precondition, linear hybrid automata, constraint synthesis, gene networks}
}

Keywords: Hoare logic, weakest precondition, linear hybrid automata, constraint synthesis, gene networks
Collection: 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)
Issue Date: 2017
Date of publication: 25.09.2017

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