The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A hybrid SAT-based decision procedure for separation logic with uninterpreted functions
Proceedings of the 40th annual Design Automation Conference
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Equivalence verification of arithmetic datapaths with multiple word-length operands
Proceedings of the conference on Design, automation and test in Europe: Proceedings
Formal verification at higher levels of abstraction
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Efficient E-Matching for SMT Solvers
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
A lazy and layered SMT(BV) solver for hard industrial verification problems
CAV'07 Proceedings of the 19th international conference on Computer aided verification
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Equivalence Verification of Polynomial Datapaths Using Ideal Membership Testing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Normalization Method for Arithmetic Data-Path Verification
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
The Gröbner basis of the ideal of vanishing polynomials
Journal of Symbolic Computation
Algebraic approach to arithmetic design verification
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Efficient gröbner basis reductions for formal verification of galois field multipliers
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
Proof logging for computer algebra based SMT solving
Proceedings of the International Conference on Computer-Aided Design
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This paper proposes a new approach for proving arithmetic correctness of data paths in System-on-Chip modules. It complements existing techniques which are, for reasons of complexity, restricted to verifying only the control behavior. The circuit is modeled at the arithmetic bit level (ABL) so that our approach is well adapted to current industrial design styles for high performance data paths. Normalization at the ABL is combined with the techniques of computer algebra. We compute normal forms with respect to Gröbner bases over rings 茂戮驴/$\left\langle{2^n}\right\rangle$. Our approach proves tractable for industrial data path designs where standard property checking techniques fail.