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SAS04: Abstract for Paper 53
Path-Sensitive Analysis for Linear Arithmetic and Uninterpreted Functions
We describe data structures and algorithms for performing a path-sensitive 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 (BDDs) with internal nodes corresponding to linear arithmetic operators or uninterpreted functions. FCEDs can be used to represent values of expressions in a program involving conditionals and linear arithmetic (or uninterpreted functions). We show how to construct them easily from a program, and we present a randomized linear time algorithm (or quadratic time for uninterpreted functions) for comparing FCEDs for equality. These algorithms are simple, but their probabilistic soundness proofs are involved. FCEDs are compact due to maximal representation sharing for portions of the program with independent conditionals. They inherit from BDDs the precise reasoning about boolean expressions needed to handle dependent conditionals.