Andrew Sogokon

A Method for Invariant Generation for Polynomial Continuous Systems

This paper presents a method for generating semi-algebraic invariants for systems governed by non-linear polynomial ordinary differential equations under semi-algebraic evolution constraints. Based on the notion of discrete abstraction, our method eliminates unsoundness and unnecessary coarseness found in existing approaches for computing abstractions for non-linear continuous systems and is able to construct invariants with intricate boolean structure, in contrast to invariants typically generated using template-based methods. In order to tackle the state explosion problem associated with discrete abstraction, we present invariant generation algorithms that exploit sound proof rules for safety verification, such as differential cut

A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets

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Direct Formal Verification of Liveness Properties in Continuous and Hybrid Dynamical Systems

, and a new proof rule that we call differential divide-and-conquer

Vector Barrier Certificates and Comparison Systems

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Operational Models for Piecewise-Smooth Systems

, which splits the verification problem into smaller sub-problems. The resulting invariant generation method is observed to be much more scalable and efficient than the naive approach, exhibiting orders of magnitude performance improvement on many of the problems.

Verifying Hybrid Systems Involving Transcendental Functions

This paper studies sound proof rules for checking positive invariance of algebraic and semi-algebraic sets, that is, sets satisfying polynomial equalities and those satisfying finite boolean combinations of polynomial equalities and inequalities, under the flow of polynomial ordinary differential equations. Problems of this nature arise in formal verification of continuous and hybrid dynamical systems, where there is an increasing need for methods to expedite formal proofs. We study the trade-off between proof rule generality and practical performance and evaluate our theoretical observations on a set of benchmarks. The relationship between increased deductive power and running time performance of the proof rules is far from obvious; we discuss and illustrate certain classes of problems where this relationship is interesting.