Expansion Diagrams: A Canonical Representation for Verification of Data Flow Designs

Taylor Expansion Diagram (TED) is a compact, wordlevel, canonical representation for data flow computations that can be expressed as multi-variate polynomials. TEDs are based on a decomposition scheme using Taylor series expansion that allows to model word-level signals as algebraic symbols. This power of abstraction, combined with canonicity and compactness of TED, makes it applicable to equivalence verification of dataflow designs. The paper describes the theory of TEDs and proves their canonicity. It shows how to construct a TED from a HDL design specification and discusses application of TEDs in proving equivalence of such designs. Experiments were performed with a variety of designs to observe the potential and limitations of TEDs for dataflow design verification. Application of TEDs to algorithmic and behavioral verification is demonstrated. I