Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Template abstract domains allow to express more interesting properties than classical abstract domains. Hover, template generation is a challenging problem when one uses template abstract domains for program analysis. ,  relate template generation with the program properties that  want to prove.  focus on one-loop programs with nested conditional branches.  formally define the notion of ll-representative template basis with respect to such programs and a given property. The definition relies on the fact that template abstract domains produce inductive invariants.  show that these invariants can be obtained by solving certain systems of functional inequalities. Then, such systems can be strengthened using a hierarchy of sum-of-squares (SOS) problems when  consider programs written in polynomial arithmetic. Each step of the SOS hierarchy can possibly provide a solution which in turn yields an invariant together with a certificate that the desired property holds. The interest of this approach is illustrated on nontrivial program examples in polynomial arithmetic.
['Assalé Adjé', 'Victor Magron']
I am writing a research paper on a idea Polynomial Template Generation using Sum-of-Squares Programming
[{"from": "human", "value": "I am writing a research paper on a idea Polynomial Template Generation using Sum-of-Squares Programming"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Template abstract domains allow to express more interesting properties than classical abstract domains. Hover, template generation is a challenging problem when one uses template abstract domains for program analysis. ,  relate template generation with the program properties that  want to prove.  focus on one-loop programs with nested conditional branches.  formally define the notion of ll-representative template basis with respect to such programs and a given property. The definition relies on the fact that template abstract domains produce inductive invariants.  show that these invariants can be obtained by solving certain systems of functional inequalities. Then, such systems can be strengthened using a hierarchy of sum-of-squares (SOS) problems when  consider programs written in polynomial arithmetic. Each step of the SOS hierarchy can possibly provide a solution which in turn yields an invariant together with a certificate that the desired property holds. The interest of this approach is illustrated on nontrivial program examples in polynomial arithmetic."}]