Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
An Efficient Method of Computing Generalized Reed-Muller Expansions from Binary Decision Diagram
IEEE Transactions on Computers
Applying coding theory to sparse interpolation
SIAM Journal on Computing
Boolean matching using generalized Reed-Muller forms
DAC '94 Proceedings of the 31st annual Design Automation Conference
Error control systems for digital communication and storage
Error control systems for digital communication and storage
Verification of arithmetic circuits with binary moment diagrams
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Cryptography and network security (2nd ed.): principles and practice
Cryptography and network security (2nd ed.): principles and practice
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
Fast Algorithms for Digital Signal Processing
Fast Algorithms for Digital Signal Processing
A Multiple-Valued Reed-Muller Transform for Incompletely Specified Functions
IEEE Transactions on Computers
A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields
IEEE Transactions on Computers
Circuit Design from Kronecker Galois Field Decision Diagrams for Multiple-Valued Functions
ISMVL '97 Proceedings of the 27th International Symposium on Multiple-Valued Logic
On the Construction of Multiple-Valued Decision Diagrams
ISMVL '02 Proceedings of the 32nd International Symposium on Multiple-Valued Logic
Optimization of GF(4) Expressions Using the Extended Dual Polarity Property
ISMVL '03 Proceedings of the 33rd International Symposium on Multiple-Valued Logic
Proceedings of the conference on Design, automation and test in Europe
Functional Decision Diagrams for Multiple-Valued Functions
ISMVL '95 Proceedings of the 25th International Symposium on Multiple-Valued Logic
High-Speed, Low-Complexity Systolic Designs of Novel Iterative Division Algorithms in GF(2^m)
IEEE Transactions on Computers
MODD: A New Decision Diagram and Representation for Multiple Output Binary Functions
Proceedings of the conference on Design, automation and test in Europe - Volume 2
Design Verification by Test Vectors and Arithmetic Transform Universal Test Set
IEEE Transactions on Computers
Error Control Coding, Second Edition
Error Control Coding, Second Edition
Mathematical framework for representing discrete functions as word-level polynomials
HLDVT '03 Proceedings of the Eighth IEEE International Workshop on High-Level Design Validation and Test Workshop
Reed-Muller Like Canonic Forms for Multivalued Functions
IEEE Transactions on Computers
A Theory of Galois Switching Functions
IEEE Transactions on Computers
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
| Hi-index | 14.98 |
This paper presents the generalized theory and an efficient graph-based technique for the calculation and representation of coefficients of multivariate canonic polynomials over arbitrary finite fields in any polarity. The technique presented for computing coefficients is unlike polynomial interpolation or matrix-based techniques and takes into consideration efficient graph-based forms which can be available as an existing resource during synthesis, verification, or simulation of digital systems. Techniques for optimization of the graph-based forms for representing the coefficients are also presented. The efficiency of the algorithm increases for larger fields. As a test case, the proposed technique has been applied to benchmark circuits over GF2. The experimental results show that the proposed technique can significantly speed up execution time.