Polynomial Constants Are Decidable
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Constant propagation aims at identifying expressions that always yield a unique constant value at run-time. It is well-known that constant propagation is undecidable for programs working on integers even if guards are ignored as in non-deterministic flow graphs. We show that polynomial constants are decidable in non-deterministic flow graphs. In polynomial constant propagation, assignment statements that use the operators +, -,* are interpreted exactly but all assignments that use other operators are conservatively interpreted as non-deterministic assignments.
We present a generic algorithm for constant propagation via a symbolic weakest precondition computation and show how this generic algorithm can be instantiated for polynomial constant propagation by exploiting techniques from computable ring theory.
KeywordsConstant Propagation Polynomial Ring Assignment Statement Abstract Interpretation Start Node
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