Practical policy iterations

Roux, Pierre Le; Garoche, Pierre-Löıc

doi:10.1007/s10703-015-0230-7

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…For the lead-lag controllers (programs Lead-lag, Lead-lag-reset and Lead-lagsaturated from [21]), none of the abstract domains could find an inductive invariant before timeout. The case of the dampened oscillators [21] fails similarly.…”

Section: Methodsmentioning

confidence: 99%

Combining Zonotope Abstraction and Constraint Programming for Synthesizing Inductive Invariants

Kabi

Goubault

Miné

et al. 2020

Lecture Notes in Computer Science

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We propose to extend an existing framework combining abstract interpretation and continuous constraint programming for numerical invariant synthesis, by using more expressive underlying abstract domains, such as zonotopes. The original method, which relies on iterative refinement, splitting and tightening a collection of abstract elements until reaching an inductive set, was initially presented in combination with simple underlying abstract elements: boxes and octagons. The novelty of our work is to use zonotopes, a sub-polyhedric domain that shows a good compromise between cost and precision. As zonotopes are not closed under intersection, we had to extend the existing framework, in addition to designing new operations on zonotopes, such as a novel splitting algorithm based on paving zonotopes by sub-zonotopes and parallelotopes. We implemented this method on top of the APRON library, and tested it on programs with non-linear loops that present complex, possibly non-convex, invariants. We present some results demonstrating both the interest of this splitting-based algorithm to synthesize invariants on such programs, and the good compromise presented by its use in combination with zonotopes with respect to its use with both simpler domains such as boxes and octagons, and more expressive domains such as polyhedra.

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Section: Methodsmentioning

confidence: 99%

Combining Zonotope Abstraction and Constraint Programming for Synthesizing Inductive Invariants

Kabi

Goubault

Miné

et al. 2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis

2020

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We present an automated procedure for synthesizing sound inductive invariants for floating-point numerical loops. Our procedure generates invariants of the form of a convex polynomial inequality that tightly bounds the values of loop variables. Such invariants are a prerequisite for reasoning about the safety and roundoff errors of floating-point programs. Unlike previous approaches that rely on policy iteration, linear algebra or semi-definite programming, we propose a heuristic procedure based on simulation and counterexample-guided refinement. We observe that this combination is remarkably effective and general and can handle both linear and nonlinear loop bodies, nondeterministic values as well as conditional statements. Our evaluation shows that our approach can efficiently synthesize loop invariants for existing benchmarks from literature, but that it is also able to find invariants for nonlinear loops that today’s tools cannot handle.

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Practical policy iterations

Cited by 2 publications

References 39 publications

Combining Zonotope Abstraction and Constraint Programming for Synthesizing Inductive Invariants

Combining Zonotope Abstraction and Constraint Programming for Synthesizing Inductive Invariants

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis

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