Symbolic Simulation with Approximate Values

Symbolic methods such as model checking using binary decision diagrams (BDDs) have had limited success in verifying large designs because BDD sizes regularly exceed memory capacity. Symbolic simulation is a method that controls BDD size by allowing the user to specify the number of symbolic variables in a test. However, BDDs still may blow up when using symbolic simulation in large designs with a large number of symbolic variables. This paper describes techniques for limiting the size of the internal representation of values in symbolic simulation no matter how many symbolic variables are present. The basic idea is to use approximate values on internal nodes; an approximate value is one that consists of combinations of the values 0, 1, and X. If an internal node is known not to aaect the functionality being tested, then the simulator can output a value of X for this node, reducing the amount of time and memory required to represent the value of this node. Our algorithm uses categorization of the symbolic input variables to determine which node values can be more approximate and which can be more exact.