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Automata Based Symbolic Reasoning in Hardware Verification
, 1998
"... . We present a new approach to hardware verification based on describing circuits in Monadic Secondorder Logic (M2L). We show how to use this logic to represent generic designs like nbit adders, which are parameterized in space, and sequential circuits, where time is an unbounded parameter. M2L ad ..."
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Cited by 20 (11 self)
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. We present a new approach to hardware verification based on describing circuits in Monadic Secondorder Logic (M2L). We show how to use this logic to represent generic designs like nbit adders, which are parameterized in space, and sequential circuits, where time is an unbounded parameter. M2L admits a decision procedure, implemented in the Mona tool [17], which reduces formulas to canonical automata. The decision problem for M2L is nonelementary decidable and thus unlikely to be usable in practice. However, we have used Mona to automatically verify, or find errors in, a number of circuits studied in the literature. Previously published machine proofs of the same circuits are based on deduction and may involve substantial interaction with the user. Moreover, our approach is orders of magnitude faster for the examples considered. We show why the underlying computations are feasible and how our use of Mona generalizes standard BDDbased hardware reasoning. 1. Introduction Correctnes...
Parametric Circuit Representation Using Inductive Boolean Functions
 In Computer Aided Verification, CAV '93, LNCS 697
, 1993
"... . We have developed a methodology based on symbolic manipulation of inductive Boolean functions (IBFs) for formal verification of inductivelydefined hardware. This methodology combines the techniques of reasoning by induction and symbolic tautologychecking in an automated and potentially efficient ..."
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Cited by 17 (2 self)
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. We have developed a methodology based on symbolic manipulation of inductive Boolean functions (IBFs) for formal verification of inductivelydefined hardware. This methodology combines the techniques of reasoning by induction and symbolic tautologychecking in an automated and potentially efficient way. In this paper, we describe a component of this methodology that regards various mechanisms used to represent inductivelydefined circuits in the form of IBFs. The focus is on general parameterization issues, such as multiple parameter functions, multiple output functions, interaction of different parameters for supporting compositions etc. These mechanisms, which may be useful in other applications involving parametric circuit descriptions, are illustrated through practical circuit examples along with preliminary results. We also describe an application of our formal verification methodology, where a proof by induction is performed by automatic symbolic manipulation of parametric circuit...
Representation and Symbolic Manipulation of Linearly Inductive Boolean Functions
 In Proceedings of the IEEE International Conference on ComputerAided Design. IEEE Computer
, 1993
"... We consider a class of practically useful Boolean functions, called Linearly Inductive Functions (LIFs), and present a canonical representation as well as algorithms for their automatic symbolic manipulation. LIFs can be used to capture structural induction in parameterized circuit descriptions, whe ..."
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Cited by 10 (1 self)
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We consider a class of practically useful Boolean functions, called Linearly Inductive Functions (LIFs), and present a canonical representation as well as algorithms for their automatic symbolic manipulation. LIFs can be used to capture structural induction in parameterized circuit descriptions, whereby our LIF representation provides a fixedsized representation for all size instances of a circuit. Furthermore, since LIFs can naturally capture the temporal induction inherent in sequential system descriptions, our representation also provides a canonical form for sequential functions. This allows for a wide range of applications of symbolic LIF manipulation in the verification and synthesis of digital systems. We also present practical results from a preliminary implementation of a general purpose LIF package. 1 Introduction Symbolic manipulation of Boolean functions has found numerous applications in the area of VLSI design automation [5]. These applications are greatly facilitated ...
Beyond the Finite in Automatic Hardware Verification
, 1996
"... We present a new approach to hardware verification based on describing circuits in Monadic Secondorder Logic (M2L). We show how to use this logic to represent generic designs like nbit adders, which are parameterized in space, and sequential circuits, where time is an unbounded parameter. M2L admi ..."
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We present a new approach to hardware verification based on describing circuits in Monadic Secondorder Logic (M2L). We show how to use this logic to represent generic designs like nbit adders, which are parameterized in space, and sequential circuits, where time is an unbounded parameter. M2L admits a decision procedure, implemented in the Mona tool [16], which reduces formulas to canonical automata. The decision problem for M2L is nonelementary decidable and thus unlikely to be usable in practice. However, we have used Mona to automatically verify, or find errors in, a number of circuits studied in the literature. Previously published machine proofs of the same circuits are based on deduction and may involve substantial interaction with the user. Moreover, our approach is orders of magnitude faster for the examples considered. We show why the underlying computations are feasible and how our use of Mona generalizes standard BDDbased hardware reasoning.
Extending VLSI Design with HigherOrder Logic
"... Extending VLSI CAD with higherorder logic integrates formal verification with synthesis. The benefits of doing so are: 1) relating instructionset descriptions to implementations, 2) designing at a higher level of abstraction than at the level of schematics, 3) verifying by proof, 4) reusing verifi ..."
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Extending VLSI CAD with higherorder logic integrates formal verification with synthesis. The benefits of doing so are: 1) relating instructionset descriptions to implementations, 2) designing at a higher level of abstraction than at the level of schematics, 3) verifying by proof, 4) reusing verified parameterized designs, 5) automatically compiling designs in higherorder logic to parameterized cell generators and layouts, and 6) validating electrical and functional properties by simulation. Such an integration is demonstrated by linking the Cambridge HigherOrder Logic (HOL) theoremprover with the Mentor Graphics GDT design environment. We illustrate its application by creating a parameterized macrocell generator for an nbit Am2910 microprogram sequencer, whose design is formally verified with respect to its instructionset architecture specification. 1 Introduction This paper reports on our experience integrating formal verification with VLSI design. Our long term goal is to ex...