A Hoare logic for linear systems


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.

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Correspondence to Rob Arthan.

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Jonathan P. Bowen, Michael Butler, Mike Hinchey, Steve Reeves and Jim Woodcock

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Arthan, R., Martin, U. & Oliva, P. A Hoare logic for linear systems. Form Asp Comp 25, 345–363 (2013). https://doi.org/10.1007/s00165-011-0180-9

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  • Hoare logic
  • Formal verification
  • Linear systems
  • Control systems