Equivalence checking of partial designs using dependency quantified Boolean formulae

Gitina, Karina; Reimer, Sven; Sauer, Matthias; Wimmer, Ralf; Scholl, Christoph; Becker, Bernd

doi:10.1109/iccd.2013.6657071

Cited by 32 publications

(19 citation statements)

References 12 publications

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“…In order to be able to express the dependencies correctly, one has to resort to DQBF ( [36], see also Section 2.3). It is able to express arbitrary dependencies and therefore constitutes a complete decision method for arbitrary incomplete combinational circuits.…”

Section: Complete Methodsmentioning

confidence: 99%

“…The approach of [32,33] solves the PEC problem exactly, but it is restricted to problem instances of moderate sizes, since the black boxes are replaced by function tables using an exponential number of Boolean variables. A more efficient complete approach, based on solving dependency quantified Boolean formulas (DQBFs) was presented in [36].…”

Section: Unknown Values In Verificationmentioning

confidence: 99%

See 1 more Smart Citation

Modeling Unknown Values in Test and Verification

Becker

Sauer

Scholl

et al. 2015

Formal Modeling and Verification of Cyber-Physical Systems

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Abstract.With increasing complexities and a component-based design style the handling of unknown values (e. g., at the interface of components) becomes more and more important in electronic design automation (EDA) and production processes. Tools are required that allow an accurate modeling of unknowns in combination with algorithms balancing exactness of representation and efficiency of calculation. In the following, state-ofthe-art approaches are described that enable an efficient and successful handling of unknown values using formal techniques in the areas of Test and Verification.

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Section: Complete Methodsmentioning

confidence: 99%

Section: Unknown Values In Verificationmentioning

confidence: 99%

Modeling Unknown Values in Test and Verification

Becker

Sauer

Scholl

et al. 2015

Formal Modeling and Verification of Cyber-Physical Systems

Self Cite

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“…All of them encode partial equivalence checking (PEC) problems, i.e., circuits containing some "black boxes" compared against full circuits. This benchmark set includes the benchmarks of the 3-bit arithmetic circuits adder and the 16-bit arbiter implementations bitcell and lookahead from [11], and also the circuit family pec_xor from [16] about comparing the XOR of input bits against a random Boolean function. We converted those benchmarks to DQDIMACS format, and then ran iDQ on them.…”

Section: Resultsmentioning

confidence: 99%

“…This includes, e.g., partial information non-cooperative games [32] or certain bit-vector logics [25,38] used in the context of Satisfiability Modulo Theories (SMT). More recently, also applications in the area of equivalence for partial implementations [15,16] and synthesis for fragments of linear temporal logic [9] have been discussed and translations to DQBF have been proposed.…”

Section: Introductionmentioning

confidence: 99%

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iDQ: Instantiation-Based DQBF Solving

Fröhlich¹,

Kovásznai²,

Biere³

et al.

EPiC Series in Computing

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Dependency Quantified Boolean Formulas (DQBF) are obtained by adding Henkin quantifiers to Boolean formulas and have seen growing interest in the last years. Since deciding DQBF is NExpTime-complete, efficient ways of solving it would have many practical applications. Still, there is only few work on solving this kind of formulas in practice. In this paper, we present an instantiation-based technique to solve DQBF efficiently. Apart from providing a theoretical foundation, we also propose a concrete implementation of our algorithm. Finally, we give a detailed experimental analysis evaluating our prototype iDQ on several DQBF as well as QBF benchmarks.

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Rectification of Arithmetic Circuits with Craig Interpolants in Finite Fields

Gupta

Ilioaea

Rao

et al. 2019

VLSI-SoC: Design and Engineering of Electronics Systems Based on New Computing Paradigms

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When formal verification of arithmetic circuits identifies the presence of a bug in the design, the task of rectification needs to be performed to correct the function implemented by the circuit so that it matches the given specification. In our recent work [26], we addressed the problem of rectification of buggy finite field arithmetic circuits. The problems are formulated by means of a set of polynomials (ideals) and solutions are proposed using concepts from computational algebraic geometry. Single-fix rectification is addressed -i.e. the case where any set of bugs can be rectified at a single net (gate output). We determine if single-fix rectification is possible at a particular net, formulated as the Weak Nullstellensatz test and solved using Gröbner bases. Subsequently, we introduce the concept of Craig interpolants in polynomial algebra over finite fields and show that the rectification function can be computed using algebraic interpolants. This article serves as an extension to our previous work, provides a formal definition of Craig interpolants in finite fields using algebraic geometry and proves their existence. We also describe the computation of interpolants using elimination ideals with Gröbner bases and prove that our procedure computes the smallest interpolant. As the Gröbner basis algorithm exhibits high computational complexity, we further propose an efficient approach to compute interpolants. Experiments are conducted over a variety of finite field arithmetic circuits which demonstrate the superiority of our approach against SAT-based approaches.

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Equivalence checking of partial designs using dependency quantified Boolean formulae

Cited by 32 publications

References 12 publications

Modeling Unknown Values in Test and Verification

Modeling Unknown Values in Test and Verification

iDQ: Instantiation-Based DQBF Solving

Rectification of Arithmetic Circuits with Craig Interpolants in Finite Fields

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