We consider the language of constraint formula involving Boolean connectives, and relational, logical, and arithmetic operations on bit vectors. An example of a formula in this language is F=((A+B)<C)∧(A+D)∧((A+D)⩽E)∧(<(G&H)) where A through H are bit vectors, and & denotes bit-wise and. We address the problem of generating the satisfying set of formulas such as F in the parametric form; in other words, corresponding to the Boolean variable υi (O⩽i<N) used in F, we seek to find an expression εi over new variables pi (O⩽i<N+log2(M)), where M is the cardinality of the satisfying set of F. The pi are called parametric variables, and for each value assignment to them, the vector of εis satisfy F when substituted for υi (O⩽i<N). This problem arises in a number of occasions, typically during the generation of symbolic vectors for use in symbolic simulation based verification. We propose a new method to obtain the parametric solutions εi such that both their sizes as well as variations in their sizes is small. Small sizes and small variations in sizes of parametric expressions prove to be important for verifying many practical examples through symbolic simulation

### Published in:

Computer Design: VLSI in Computers and Processors, 1993. ICCD '93. Proceedings., 1993 IEEE International Conference on

3-6 Oct 1993