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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...
Extending Decision Procedures with Induction Schemes
 Proc. CADE17, LNAI 1831
, 2000
"... Families of function definitions and conjectures based in quantifierfree decidable theories are identified for which inductive validity of conjectures can be decided by the cover set method, a heuristic implemented in a rewritebased induction theorem prover Rewrite Rule Laboratory (RRL) for me ..."
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Cited by 10 (8 self)
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Families of function definitions and conjectures based in quantifierfree decidable theories are identified for which inductive validity of conjectures can be decided by the cover set method, a heuristic implemented in a rewritebased induction theorem prover Rewrite Rule Laboratory (RRL) for mechanizing induction. Conditions characterizing definitions and conjectures are syntactic, and can be easily checked, thus making it possible to determine a priori whether a given conjecture can be decided. The concept of a T based function definition is introduced that consists of a finite set of terminating complete rewrite rules of the form f(s1 ; \Delta \Delta \Delta ; sm) ! r, where s1 ; \Delta \Delta \Delta ; sm are interpreted terms from a decidable theory T , and r is either an interpreted term or has nonnested recursive calls to f with all other function symbols from T . Two kinds of conjectures are considered. Simple conjectures are of the form f(x1 ; \Delta \Delta \Delta xm ) = t, where f is T based, x i 's are distinct variables, and t is interpreted in T .
Defthms about zip and tie: Reasoning about powerlists in ACL2
 Univ. of Texas Comp. Sci. Tech. Rep
, 1997
"... In [Mis94], Misra introduced the powerlist data structure, which is well suited to express recursive, dataparallel algorithms. Moreover, Misra and other researchers have shown how powerlists can be used to prove the correctness of several algorithms. This success has encouraged some researchers to ..."
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Cited by 8 (3 self)
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In [Mis94], Misra introduced the powerlist data structure, which is well suited to express recursive, dataparallel algorithms. Moreover, Misra and other researchers have shown how powerlists can be used to prove the correctness of several algorithms. This success has encouraged some researchers to pursue automated proofs of theorems about powerlists[Kap97, KS95a, KS95b]. In this paper, we show how ACL2 can be used to verify theorems about powerlists. We depart from previous approaches in two significant ways. First, the powerlists we use are not the regular structures defined by Misra; that is, we do not require powerlists to be balanced trees. As we will see, this complicates some of the proofs, but on the other hand it allows us to state theorems that are otherwise beyond the language of powerlists. Second, we wish to prove the correctness of powerlist algorithms as much as possible within the logic of powerlists. Previous approaches have relied
Rewriting, decision procedures and lemma speculation for automated hardware verification
 Proc. 10th Intl. Conf. Theorem Proving in Higher Order Logics, LNCS 1275
, 1997
"... The use of a rewritebased, induction theorem prover, Rewrite Rule Laboratory (RRL) [13] is discussed for verifying arithmetic circuits at the gate level. It ..."
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Cited by 4 (3 self)
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The use of a rewritebased, induction theorem prover, Rewrite Rule Laboratory (RRL) [13] is discussed for verifying arithmetic circuits at the gate level. It
Automatic Generation of Simple Lemmas from Recursive Definitions Using Decision Procedures
 Proc. ASIAN 2003, LNCS
, 2003
"... Using recent results on integrating induction schemes into decidable theories, a method for generating lemmas useful for reasoning about Tbased function definitions is proposed. The method relies on terms in a decidable theory admitting a (finite set of) canonical form scheme(s) and ability to so ..."
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Cited by 2 (1 self)
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Using recent results on integrating induction schemes into decidable theories, a method for generating lemmas useful for reasoning about Tbased function definitions is proposed. The method relies on terms in a decidable theory admitting a (finite set of) canonical form scheme(s) and ability to solve parametric equations relating two canonical form schemes with parameters. Using nontrivial examples, it is shown how the method can be used to automatically generate many simple lemmas; these lemmas are likely to be found useful in automatically proving other nontrivial properties of Tbased functions, thus unburdening the user of having to provide many simple intermediate lemmas. During the formalization of a problem, after a user inputs Tbased definitions, the method can be employed in the background to explore a search space of possible conjectures which can be attempted, thus building a library of lemmas as well as false conjectures. This investigation was motivated by our attempts to automatically generate lemmas arising in proofs of generic, arbitrary datawidth parameterized arithmetic circuits. The scope of applicability of the proposed method is broader, however, including generating proofs for proofcarrying codes, certification of proofcarrying code as well as in reasoning about distributed computation algorithms.