A multiple-valued logic approach to the design and verification of hardware circuits

Abstract

We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are performed in the more informative MVL setting reveal details which are either invisible or harder to detect through binary or ternary simulations. In equivalence verification, detecting different behavior under MVL simulations may lead to the discovery of a genuine binary non-equivalence or to a qualitative gap between two designs. The value of a variable in a simulation may hold information about its degree of truth and its “place of birth” and “date of birth”. Applications include equivalence verification, initialization, assertions generation and verification, partial control on the flow of data by prioritizing and block-oriented simulations. Much of the paper is devoted to theoretical aspects behind the MVL approach, including the reason for choosing a specific algebra for computations and the introduction of the notions of De Morgan Canonical Form and of verification complexity of Boolean expressions. Two basic simulation-based algorithms are presented, one for satisfying and verifying combinational designs and the other for equivalence verification of sequential designs.