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

Abstract

Abstract-A Taylor Expansion Diagram (TED) is a compact, word-level, canonical representation for data flow computations that can be expressed as multivariate polynomials. TEDs are based on a decomposition scheme using Taylor series expansion that allows one to model word-level signals as algebraic symbols. This power of abstraction, combined with the 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 an HDL design specification and discusses the application of TEDs in proving the 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. Index Terms-Register transfer level-design aids, verification; arithmetic and logic structures-verification; symbolic and algebraic manipulation.

A Unified Framework for Equivalence Verification of Datapath Oriented Applications

“…Thus these techniques are not able to handle these designs due to the large number of Boolean variables. The latest word-level representation in the literature, i.e., Taylor Expansion Diagram (TED), supports multiplication and is able to represent functions with an integer domain and range [8]. It uses the Taylor series expansion as its decomposition method to represent a multivariate polynomial expression.…”

Data-Flow Transformations using Taylor Expansion Diagrams

“…Taylor Expansion Diagram [12] is a canonical, word-level data structure that offers an efficient way to represent computation in a compact, factored form. It is particularly suitable for algorithm-oriented applications, such as signal and image processing, with computations modeled as polynomial expressions.…”

“…In contrast, this paper presents a systematic method to perform behavioral transformations, based on a canonical representation of the computation, called Taylor Expansion Diagram (TED) [12]. Being a canonical representation, TED can capture an entire class of structural solutions, rather than a single DFG.…”

Approximate Bisimulation for High-Level Datapaths in Intelligent Transportation Systems

“…There are several equivalent verification tools for circuits, but most of these tools are only suited for circuit verification at a low level, for example, binary decision diagrams (BDDs) [1], word-level decision diagrams (WLDDs) [2], and Taylor expansion diagrams (TEDs) [3]. These tools were all defined on standardized graphs, which have large exponential spaces and time complexities.…”