Andre Platzer - The Structure of Differential Invariants and Differential Cut Elimination

lmcs:809 - Logical Methods in Computer Science, November 21, 2012, Volume 8, Issue 4 - https://doi.org/10.2168/LMCS-8(4:16)2012
The Structure of Differential Invariants and Differential Cut EliminationArticle

Authors: Andre Platzer ORCID

    The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more scalable verification. Search procedures for these proof certificates are still rather ad-hoc, though, because the problem structure is only understood poorly. We investigate differential invariants, which define an induction principle for differential equations and which can be checked for invariance along a differential equation just by using their differential structure, without having to solve them. We study the structural properties of differential invariants. To analyze trade-offs for proof search complexity, we identify more than a dozen relations between several classes of differential invariants and compare their deductive power. As our main results, we analyze the deductive power of differential cuts and the deductive power of differential invariants with auxiliary differential variables. We refute the differential cut elimination hypothesis and show that, unlike standard cuts, differential cuts are fundamental proof principles that strictly increase the deductive power. We also prove that the deductive power increases further when adding auxiliary differential variables to the dynamics.


    Volume: Volume 8, Issue 4
    Published on: November 21, 2012
    Imported on: April 10, 2011
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Classical Analysis and ODEs,Mathematics - Dynamical Systems,Mathematics - Logic,math.CA
    Funding:
      Source : OpenAIRE Graph
    • CAREER: Logical Foundations of Cyber-Physical Systems; Funder: National Science Foundation; Code: 1054246
    • CPS: Small: Compositionality and Reconfiguration for Distributed Hybrid Systems; Funder: National Science Foundation; Code: 0931985
    • Collaborative Research: Next-Generation Model Checking and Abstract Interpretation with a Focus on Embedded Control and Systems Biology; Funder: National Science Foundation; Code: 0926181

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