Using GF(2) matrices in Simulation and Logic Synthesis
Maurer, Peter M.
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GF(2) matrices are matrices of ones and zeros under modulo 2 arithmetic. Like the GF(2) polynomials used in error detection and correction, they have many potential uses in Electronic Design Automation (EDA). Non-singular matrices can be used to define new classes of symmetry called conjugate symmetries. Conjugate symmetries have been used to speed up certain kinds of functional-level simulations, and have other potential uses. GF(2) matrices can also be used to transform Boolean vector spaces and simplify Boolean functions. Although matrix transformations can be complex, simpler single-bit matrices can be used instead of general matrices. This simplifies the approach without loss of generality. Singular matrices can be used to reduce the complexity of certain functions, beyond what is normally possible with conventional simplification techniques. GF(2) matrices can also be used to define exotic symmetries called strange symmetries and collapsed symmetries. These exotic symmetries may prove useful in future EDA applications.