An algebraic approach for proving data correctness in arithmetic data paths

Abstract

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 ℤ/ 〈2n〉. Our approach proves tractable for industrial data path designs where standard property checking techniques fail. © 2008 Springer-Verlag.