Formal Aspects of Computing

, Volume 25, Issue 3, pp 345–363 | Cite as

A Hoare logic for linear systems

  • Rob ArthanEmail author
  • Ursula Martin
  • Paulo Oliva
Original Article


We consider reasoning about linear systems expressed as block diagrams that give a graphical representation of a system of differential equations or recurrence equations. We use the notion of additive relation borrowed from homological algebra to give a convenient framework in which all diagrams have a semantic value. We give a sound system of Hoare-style rules for the block diagram constructors that singles out a tractable subset of the block diagram language in which all diagrams represent total functions. We show these rules in action on some simple examples from a variety of applications domains.


Hoare logic Formal verification Linear systems Control systems 


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Copyright information

© British Computer Society 2011

Authors and Affiliations

  1. 1.School of Electronic Engineering and Computer Science, Queen MaryUniversity of LondonLondonUK

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