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Verification of a Multiplier: 64 Bits and beyond
, 1993
"... Verifying a 64bit multiplier has a computational complexity that puts it beyond the grasp of current finitestate algorithms, including those based upon homomorphic reduction, the induction principle, and bdd fixedpoint algorithms. Theorem proving, while not bound by the same computational constra ..."
Abstract

Cited by 35 (6 self)
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Verifying a 64bit multiplier has a computational complexity that puts it beyond the grasp of current finitestate algorithms, including those based upon homomorphic reduction, the induction principle, and bdd fixedpoint algorithms. Theorem proving, while not bound by the same computational constraints, may not be feasible for routinely coping with the complex, lowlevel details of a real multiplier. We show how to verify such a multiplier by applying COSPAN, a modelchecking algorithm, to verify local properties of the complex lowlevel circuit, and using TLP, a theorem prover based on the Temporal Logic of Actions, to prove that these properties imply the correctness of the multiplier. Both verification steps are automated, and we plan to mechanize the translation between the languages of TLP and COSPAN.
Modular Verification of SRT Division
, 1996
"... . We describe a formal specification and mechanized verification in PVS of the general theory of SRT division along with a specific hardware realization of the algorithm. The specification demonstrates how attributes of the PVS language (in particular, predicate subtypes) allow the general theory to ..."
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Cited by 16 (1 self)
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. We describe a formal specification and mechanized verification in PVS of the general theory of SRT division along with a specific hardware realization of the algorithm. The specification demonstrates how attributes of the PVS language (in particular, predicate subtypes) allow the general theory to be developed in a readable manner that is similar to textbook presentations, while the PVS table construct allows direct specification of the implementation's quotient lookup table. Verification of the derivations in the SRT theory and for the data path and lookup table of the implementation are highly automated and performed for arbitrary, but finite precision; in addition, the theory is verified for general radix, while the implementation is specialized to radix 4. The effectiveness of the automation stems from the tight integration in PVS of rewriting with decision procedures for equality, linear arithmetic over integers and rationals, and propositional logic. This example demonstrates t...
Mechanically Verifying a Family of Multiplier Circuits
 Proc. Computer Aided Veri (CAV'96
, 1996
"... . A methodology for mechanically verifying a family of parameterized multiplier circuits, including many wellknown multiplier circuits such as the linear array, the Wallace tree and the 73 multiplier is proposed. A top level specification for these multipliers is obtained by abstracting the co ..."
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Cited by 14 (6 self)
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. A methodology for mechanically verifying a family of parameterized multiplier circuits, including many wellknown multiplier circuits such as the linear array, the Wallace tree and the 73 multiplier is proposed. A top level specification for these multipliers is obtained by abstracting the commonality in their behavior. The behavioral correctness of any multiplier in the family can be mechanically verified by a uniform proof strategy. Proofs of properties are done by rewriting and induction using an automated theorem prover RRL (Rewrite Rule Laboratory). The behavioral correctness of the circuits is established with respect to addition and multiplication on numbers. The automated proofs involve minimal user intervention in terms of intermediate lemmas required. Generic hardware components are used to segregate the specification and the implementation aspects, enabling verification of circuits in terms of behavioral constraints that can be realized in different ways. Th...
Under consideration for publication in Formal Aspects of Computing Proof producing synthesis of
"... arithmetic and cryptographic ..."
Hierarchical Verification of TwoDimensional HighSpeed Multiplication in PVS: A Case Study
 FORMAL METHODS IN COMPUTERAIDED DESIGN, VOLUME 1166 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1996
"... It is shown how to use the PVS specification language and proof checker to present a hierarchical formalization of a twodimensional, highspeed integer multiplier on the gate level. We first give an informal description of iterative array multiplier circuits together with a natural refinement in ..."
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It is shown how to use the PVS specification language and proof checker to present a hierarchical formalization of a twodimensional, highspeed integer multiplier on the gate level. We first give an informal description of iterative array multiplier circuits together with a natural refinement into vertical and horizontal stages, and then show how the various features of PVS can be used to obtain a readable, highlevel specification. The verification exploits the tight integration between rewriting, arithmetic decision procedures, and equality that is present in PVS. Altogether, this case study demonstrates that the resources of an expressive specification language and of a generalpurpose theorem prover permit highly automated verification in this domain, and can contribute to clarity, generality, and reuse.
Aided Verification Verification of a Multiplier: 64 Bits and Beyond
, 1993
"... Abstract. Verifying a 64bit multiplier has a computational complexity that puts it beyond the grasp of current finitestate algorithms, including those based upon homomorphic reduction, the induction principle, and bdd fixedpoint algorithms. Theorem proving, while not bound by the same computation ..."
Abstract
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Abstract. Verifying a 64bit multiplier has a computational complexity that puts it beyond the grasp of current finitestate algorithms, including those based upon homomorphic reduction, the induction principle, and bdd fixedpoint algorithms. Theorem proving, while not bound by the same computational constraints, may not be feasible for routinely coping with the complex, lowlevel details of a real multiplier. We show how to verify such a multiplier by applying COSPAN, a modelchecking algorithm, to verify local properties of the complex lowlevel circuit, and using TLP, a theorem prover based on the Temporal Logic of Actions, to prove that these properties imply the correctness of the multiplier. Both verification steps are automated, and we plan to mechanize the translation between the languages of TLP and COSPAN. 1