On the construction of Gröbner bases using syzygies
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial methods for component matching and verification
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Polynomial methods for allocating complex components
DATE '99 Proceedings of the conference on Design, automation and test in Europe
Polynomial circuit models for component matching in high-level synthesis
IEEE Transactions on Very Large Scale Integration (VLSI) Systems - System Level Design
Synthesis of saturation arithmetic architectures
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Computer algebra handbook
Energy Efficient Hardware Synthesis of Polynomial Expressions
VLSID '05 Proceedings of the 18th International Conference on VLSI Design held jointly with 4th International Conference on Embedded Systems Design
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
Some properties of Gröbner-bases for polynomial ideals
ACM SIGSAM Bulletin
Factoring and eliminating common subexpressions in polynomial expressions
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Improved use of the carry-save representation for the synthesis of complex arithmetic circuits
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
MiBench: A free, commercially representative embedded benchmark suite
WWC '01 Proceedings of the Workload Characterization, 2001. WWC-4. 2001 IEEE International Workshop
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Towards the automatic exploration of arithmetic-circuit architectures
Proceedings of the 43rd annual Design Automation Conference
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Groebner bases computation in Boolean rings for symbolic model checking
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
Optimization of Arithmetic Datapaths with Finite Word-Length Operands
ASP-DAC '07 Proceedings of the 2007 Asia and South Pacific Design Automation Conference
A Gröbner basis approach to CNF-formulae preprocessing
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Application of symbolic computer algebra in high-level data-flow synthesis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Optimizing Polynomial Expressions by Algebraic Factorization and Common Subexpression Elimination
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Polynomial datapath optimization using partitioning and compensation heuristics
Proceedings of the 46th Annual Design Automation Conference
Improved heuristics for finite word-length polynomial datapath optimization
Proceedings of the 2009 International Conference on Computer-Aided Design
Modular datapath optimization and verification based on modular-HED
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Tradeoff between Approximation Accuracy and Complexity for Range Analysis using Affine Arithmetic
Journal of Signal Processing Systems
Polynomial datapath optimization using constraint solving and formal modelling
Proceedings of the International Conference on Computer-Aided Design
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Polynomial computations over fixed-size bit-vectors are found in many practical datapath designs. For efficient RTL synthesis, it is important to identify good decompositions of the polynomial into smaller/simpler units. Symbolic computer algebra algorithms and tools have been used for this purpose. However, fixed-size (m) bit-vector arithmetic is polynomial algebra over the finite integer ring Z2m, which is a non-unique factorization domain (non-UFD). While non-UFDs provide an extra freedom to search for decompositions, they complicate polynomial manipulation as traditional division-based algorithms are inapplicable. This paper presents new mathematical concepts for polynomial decomposition over Z2m, for RTL synthesis over fixed-size m-bit vectors. Given a polynomial, we identify a specific set of linear expressions and compute the Gröbner bases of their ideal (over non-UFD Z2m) using syzygies. This basis serves as good building-blocks for the given computation. A decomposition is identified by subsequent Gröbner basis reduction. Experimental results demonstrate significant area savings due to our approach, as compared against contemporary datapath synthesis techniques.