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.

Abstract-Communication-centric design is a key paradigm for systems-on-chips (SoCs), where most computing blocks are predesigned IP cores. Due to the problems with distributing a clock across a large die, future system designs will be more asynchronous or self-timed. For portable, battery-run applications, power and pin efficiency is an important property of a communication system where the cost of a signal transition on a global interconnect is much greater than for internal wires in logic blocks. The paper addresses this issue by designing an asynchronous communication system aimed at power and pin efficiency. Another important issue of SoC design is design productivity. It demands new methods and tools, particularly for designing communication protocols and interconnects. The design of a self-timed communication system is approached employing formal techniques supported by verification and synthesis tools. The protocol is formally specified and verified with respect to deadlockfreedom and delay-insensitivity using a Petri-net-based model-checking tool. A protocol controller has been synthesized by a direct mapping of the Petri net model derived from the protocol specification. The logic implementation was analyzed using the Cadence toolkit. The results of SPICE simulation show the advantages of the direct mapping method compared to logic synthesis.

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Abstract-This paper presents an algorithm for disjointsupport decomposition of Boolean functions which combines functional and structural approaches. First, a set of proper cut points is identified in the circuit by using dominator relations (structural method). Then, the circuit is partitioned along these cut points and a BDD-based decomposition is applied to the resulting smaller functions (functional method). Previous work on Boolean decomposition used only single methods and did not integrate a combined strategy. The experimental results show that the presented technique is more robust than a pure BDD-based approach and produces better-quality decompositions.

The growing complexity of today's system designs requires fast and robust verification methods. Existing BDD, SAT or ATPG-based techniques do not provide sufficient solutions for many verification instances. Boolean function hashing is a probabilistic verification approach which can complement existing formal methods in a number of applications such as equivalence checking, biased random simulation, power analysis and power optimization. The proposed hashing technique is based on the arithmetic transform, which maps a Boolean function onto a probabilistic hash value for a given input assignment. The presented algorithm uses multiple-vertex dominators in circuit graphs to progressively simplify intermediate hashing steps. The experimental results on benchmark circuits demonstrate the robustness of our approach.