Conference paper Open Access

Synthesizing Invariants by Solving Solvable Loops

de Oliveira, Steven; Bensalem, Saddek; Prevosto, Virgile


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    <subfield code="a">Automated Technology for Verification and Analysis</subfield>
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    <subfield code="a">Synthesizing Invariants by Solving Solvable Loops</subfield>
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    <subfield code="a">VERIFICATION ENGINEERING OF SAFETY AND SECURITY CRITICAL DYNAMIC INDUSTRIAL APPLICATIONS</subfield>
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    <subfield code="a">&lt;p&gt;Formal program verification faces two problems. The first&lt;br&gt;
problem is related to the necessity of having automated solvers that are&lt;br&gt;
powerful enough to decide whether a formula holds for a set of proof obli-&lt;br&gt;
gations as large as possible, whereas the second manifests in the need of&lt;br&gt;
finding sufficiently strong invariants to obtain correct proof obligations.&lt;br&gt;
This paper focuses on the second problem and describes a new method&lt;br&gt;
for the automatic generation of loop invariants that handles polynomial&lt;br&gt;
and non deterministic assignments. This technique is based on the eigen-&lt;br&gt;
vector generation for a given linear transformation and on the polynomial&lt;br&gt;
optimization problem, which we implemented on top of the open-source&lt;br&gt;
tool Pilat.&lt;br&gt;
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