The K*BMD: A verification data structure

Drechsler, Rolf; Becker, Bernd; Ruppertz, Stefan

doi:10.1109/54.587742

Cited by 48 publications

(18 citation statements)

References 15 publications

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“…WLDDs are graph-based representations for functions with a Boolean domain and an integer range [5]. Furthermore, Binary Moment Diagrams (BMD), Multiplicative BMD (*BMD) and Kronecker *BMD (K*BMD) provide representations of integer-valued functions defined over bit-vectors and attempt to make the decomposition more efficient in terms of the graph size [7]. However, they fail to represent Boolean functions that can easily be represented using BDD.…”

Section: Related Workmentioning

confidence: 99%

“…The goal of this section is to introduce a graph-based representation called HED [1] for functions with a mixed Boolean and integer domain and an integer range to represent arithmetic operations at a high level of abstraction, while other proposed Word Level Decision Diagrams (WLDDs) [5], [7] are graph-based representations for functions with a Boolean domain and an integer range. In HED, functions to be represented are maintained as a single graph in canonical form.…”

Section: Horner Expansion Diagram (Hed)mentioning

confidence: 99%

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A Unified Framework for Equivalence Verification of Datapath Oriented Applications

Alizadeh

Fujita

2009

IEICE Trans. Inf. & Syst.

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SUMMARYIn this paper, we introduce a unified framework based on a canonical decision diagram called Horner Expansion Diagram (HED) [1] for the purpose of equivalence checking of datapath oriented hardware designs in various design stages from an algorithmic description to the gatelevel implementation. The HED is not only able to represent and manipulate algorithmic specifications in terms of polynomial expressions with modulo equivalence but also express bit level adder (BLA) description of gate-level implementations. Our HED can support modular arithmetic operations over integer rings of the form Z 2 n . The proposed techniques have successfully been applied to equivalence checking on industrial benchmarks. The experimental results on different applications have shown the significant advantages over existing bit-level and also word-level equivalence checking techniques.

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Section: Related Workmentioning

confidence: 99%

Section: Horner Expansion Diagram (Hed)mentioning

confidence: 99%

A Unified Framework for Equivalence Verification of Datapath Oriented Applications

Alizadeh

Fujita

2009

IEICE Trans. Inf. & Syst.

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“…We give a brief overview on Decision Diagrams (DDs). (For more details see [18,13] For MTBDD [9,2], BMD [6], HDD [10], EVBDD [20], *BMD [6] and K*BMD [14], the corresponding functions f e are given in Table 1 (a; m are integer numbers). …”

Section: Word-level Decision Diagramsmentioning

confidence: 99%

“…Examples of WLDDs are e.g. EVBDDs [20], MTBDDs [9,2], *BMDs [6], HDDs [10], and K*BMDs [14]. In the meantime WLDDs have been integrated in verifications tools [1,8] and are also used for symbolic model checking [11,7].…”

Section: Introductionmentioning

confidence: 99%

Formal verification of word-level specifications

Höreth

Drechsler

1999

Proceedings of the Conference on Design, Automation and Test in Europe

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“…Canonic graph-based representations, such as Binary Decision Diagrams (BDDs) [1], Binary Moment Diagrams (BMDs) [2], and their variants (PHDDs [3], K*BMDs [4], etc.) play an important role in the development of computer-aided verification tools.…”

mentioning

confidence: 99%

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

Ciesielski

Kalla

Askar

2006

IEEE Trans. Comput.

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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.

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The K*BMD: A verification data structure

Cited by 48 publications

References 15 publications

A Unified Framework for Equivalence Verification of Datapath Oriented Applications

A Unified Framework for Equivalence Verification of Datapath Oriented Applications

Formal verification of word-level specifications

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

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