Journal ArticleDOI
Toward Verifying Nonlinear Integer Arithmetic
Paul Beame,Vincent Liew +1 more
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TLDR
NO(1) size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and nO(log n) size proofs for these identities on Wallace tree multipliers are given.Abstract:
We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give nO(1) size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and nO(log n) size proofs for these identities on Wallace tree multipliers.read more
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Book ChapterDOI
Towards Verifying Nonlinear Integer Arithmetic
Paul Beame,Vincent Liew +1 more
TL;DR: A key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers is eliminated, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits.
Journal ArticleDOI
Formal verification of multiplier circuits using computer algebra
TL;DR: This thesis examines and develops automated reasoning approaches based on computer algebra and provides an algebraic proof calculus in this thesis that allows obtaining certificates as a by-product of circuit verification in order to boost confidence in the outcomes of automated reasoning tools.
Proceedings ArticleDOI
SAT, Computer Algebra, Multipliers
TL;DR: This paper focuses on the implementation details of the implementation of the new dedicated reduction engine, which not only allows fully automated adder substitution, but also employs polynomial reduction efficiently.
Proceedings ArticleDOI
Automated Synthesis of Quantum Circuits Using Symbolic Abstractions and Decision Procedures
TL;DR: A new methodology called Quantum Automated Synthesizer (QUASH) that can automatically synthesize quantum circuits using decision procedures that perform symbolic reasoning for combinatorial search and is a step towards the automation of quantum algorithm design.
Journal ArticleDOI
Verifying Whiley Programs with Boogie
TL;DR: In this article , the authors explore the use of Boogie as an intermediate verification language for verifying programs in Whiley, and demonstrate that the resulting verification tool can verify significantly more programs than the native Whiley verifier.
References
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Journal ArticleDOI
Graph-Based Algorithms for Boolean Function Manipulation
TL;DR: In this paper, the authors present a data structure for representing Boolean functions and an associated set of manipulation algorithms, which have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large.
Book ChapterDOI
Z3: an efficient SMT solver
TL;DR: Z3 is a new and efficient SMT Solver freely available from Microsoft Research that is used in various software verification and analysis applications.
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A machine program for theorem-proving
TL;DR: The programming of a proof procedure is discussed in connection with trial runs and possible improvements.
Proceedings ArticleDOI
Chaff: engineering an efficient SAT solver
TL;DR: The development of a new complete solver, Chaff, is described which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy.
Journal ArticleDOI
A Computing Procedure for Quantification Theory
Martin Davis,Hilary Putnam +1 more
TL;DR: In the present paper, a uniform proof procedure for quantification theory is given which is feasible for use with some rather complicated formulas and which does not ordinarily lead to exponentiation.