Symbolic Analysis by Determinant Decision Diagrams and Applications

Symbolic analysis traditionally suffers circuit size problems as the number of symbolic terms generated can grow exponentially with the circuit size. This problem has been partially mitigated by a graph-based approach, called Determinant Decision Diagram (DDDs) [1], where the symbolic terms are implicitly represented in a graph, which has been inspired by the success of Binary Decision Diagram (BDDs) [2] as an enabling technology for industrial use of symbolic analysis and formal verification in digital logic design. DDD-based symbolic analysis enables the exact symbolic analysis of many analog circuits substantially larger than the previous methods and open new applications for symbolic analysis. DDD-based symbolic analysis still remains the most efficient symbolic analysis technique. This chapter will present basic concept of DDDs, the most efficient DDD construction method based on logic operation, s-expanded DDDs for generating s-expanded polynomials and transfer functions. We will also show how DDDs and s-expanded DDDs can be used for constructing simplified symbolic expressions.

Keywords: Symbolic analysis, determinant decision diagrams, analog circuits, modeling, simulation and analysis, binary decision diagrams, compact modeling