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A method for generating polynomial invariants of imperative programs is presented using the abstract interpretation framework. It is shown that for programs with polynomial assignments, an invariant consisting of a conjunction of polynomial equalities can be automatically generated for each program point. The proposed approach takes into account tests in conditional statements as well as in loops,...
We present a novel static analysis for approximating the algebraic relational semantics of imperative programs. Our method is based on abstract interpretation in the lattice of polynomial pseudo ideals of bounded degree – finite-dimensional vector spaces of polynomials of bounded degree which are closed under bounded degree products. For a fixed bound, the space complexity of our approach and the...
An interesting area in static analysis is the study of numeric properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numeric abstract...
We describe data structures and algorithms for performing a path-sensitive program analysis to discover equivalences of expressions involving linear arithmetic or uninterpreted functions. We assume that conditionals are abstracted as boolean variables, which may be repeated to reflect equivalent conditionals. We introduce free conditional expression diagrams (FCEDs), which extend binary decision diagrams...
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