Fast algorithm for computing spectral transforms of Boolean and multiple-valued functions on circuit representation

Abstract

In this paper we present a fast algorithm for computing the value of a spectral transform of Boolean or multiplevalued functions for a given assignment of input variables. Our current implementation is for arithmetic transform, because our work is primarily aimed at optimizing the performance of probabilistic verification methods. However, the presented technique is equally applicable for other discrete transforms, e.g. Walsh or Reed-Muller transforms. Previous methods for computing spectral transforms used truth tables, sum-of-product expressions, or various derivatives of decision diagrams. They were fundamentally limited by the excessive memory requirements of these data structures. We present a new algorithm that partitions the computation of the spectral transform based on the dominator relations of the circuit graph representing the function to be transformed. As a result, the presented algorithm can handle larger functions than previously possible.

Robust Evaluation of Weighted Random Logic BIST Structures in Industrial Designs

“…As discussed above, the brute-for Parker and McCluskey [12] genera polynomial, which might grow expo as shown in [16], by using effic packages to represent the Boole medium size circuits, this approac complete BDD-based circuit repres that every BDD-path is evaluated in signal probability of the circuit, th simply added.…”

<title>Computing a perfect input assignment for probabilistic verification</title>

“…As an alternative, in 21 an algorithm for computing the arithmetic transform directly on a circuit representation was presented. This algorithm uses an extension of the classical Lengauer-Tarjan algorithm for finding dominators 22 to determine correlations between nodes of the circuit due to re-convergent fan-outs.…”

“…We get It is important to point out that, during the computation of hash values, e.g. by the algorithm, 21 the intermediate results will be hash values of some functions of up to n variables computed for the perfect input assignment. Therefore, the intermediate results can only be multiples of δ n and can be represented as k · δ n as well, where k ∈ {0, 1,...,2 2 n − 1}.…”

Spectral Response of Ternary Logic Netlists

“…Past work in the direct computation of a spectrum from a netlist includes that reported in [10] [11]. In [10] a method was described that allowed for a single spectral coefficient to be obtained but required augmenting the structure of a netlist and then traversing it for each spectral coefficient.…”

“…In [10] a method was described that allowed for a single spectral coefficient to be obtained but required augmenting the structure of a netlist and then traversing it for each spectral coefficient. In [11] a method was described where spectral coefficients can be obtained directly from a netlist, however the resulting coefficients are based upon a specific variable assignment. Here, a method for computation of the spectrum by traversing a structural netlist representation without modifying the netlist or performing a specific variable assignment is developed.…”