Decomposition techniques for efficient ROBDD construction

Abstract

In this paper, we address the problem of memory-efficient construction of ROBDDs for a given Boolean network. We show that for a large number of applications, it is more efficient to construct the ROBDD by a suitable combination of top-down and bottom-up approaches than a purely bottom-up approach. We first build a decomposed ROBDD of the target function and then follow it by a symbolic composition to get the final ROBDD. We propose two heuristic algorithms for decomposition. One is based on a topological analysis of the given netlist, while the other is purely functional, making no assumptions about the underlying circuit topology. We demonstrate the utility of our methods on standard benchmark circuits as well as some hard industrial circuits. Our results show that this method requires significantly less memory than the conventional bottom-up construction. In many cases, we are able to build the ROBDDs of outputs for which the conventional method fails. In addition, in most cases this memory reduction is accompanied by a significant speed up in the ROBDD construction process.

Logic synthesis for large pass transistor circuits

“…These intermediate variables are called decomposition points and the resulting set of BDDs (BDDs of the decomposition points, and the BDD of the target function in terms of the primary inputs and decomposition points) is called a decomposed BDD [8]. An example of a decomposed BDD is shown in Fig.…”

“…Finally, we would like to mention that the idea of introducing intermediate variables to control the size of BDDs has previously been used in [8][9] for unrelated problems. In these papers decomposition was used in a different context -In [8] decomposition was used to reduce the intermediate memory requirements during BDD construction and in [9] it was used for cycle-based simulation.…”

“…In these papers decomposition was used in a different context -In [8] decomposition was used to reduce the intermediate memory requirements during BDD construction and in [9] it was used for cycle-based simulation. In this work, we apply decomposition to construct a compact, decomposed BDD representation of the target logic function which can be directly mapped to a PTL network.…”

“…This is similar to [8]. When building the BDD depthfirst from inputs to outputs, a decomposition point is introduced whenever the BDD size increases by a disproportionate amount.…”

Towards scalable system-level reliability analysis

“…A smorgasbord of approaches for early quantification is available like [12,19] with [7] being the most closely related approach. In comparison, the approach proposed in the work at hand uses a divide-and-conquer heuristic based on finding cuts in a graph-based representation of the dependencies between relations.…”