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Fast algorithm for computing spectral transforms of boolean and multiple-valued functions on circuit representation
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.ORCID iD: 0000-0001-7382-9408
2003 (English)In: 33RD INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC, PROCEEDINGS, 2003, 334-339 p.Conference paper, Published paper (Other academic)
Abstract [en]

In this paper we present a fast algorithm for computing the value of a spectral transform of Boolean or multiple-valued 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.

Place, publisher, year, edition, pages
2003. 334-339 p.
Series
International symp on multiple-valued logic - proceedings, ISSN 0195-623X
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-6854DOI: 10.1109/ISMVL.2003.1201426ISI: 000183282100050OAI: oai:DiVA.org:kth-6854DiVA: diva2:11678
Conference
33rd International Symposium on Multiple-Valued Logic (ISMVL 2003) MEIJI UNIV, TOKYO, JAPAN, MAY 16-19, 2003
Note
QC 20110215Available from: 2007-03-01 Created: 2007-03-01 Last updated: 2012-08-22Bibliographically approved
In thesis
1. Graph dominators in logic synthesis and verification
Open this publication in new window or tab >>Graph dominators in logic synthesis and verification
2004 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This work focuses on the usage of dominators in circuit graphs in order to reduce the complexity of synthesis and verification tasks. One of the contributions of this thesis is a new algorithm for computing multiple-vertex dominators in circuit graphs. Previous algorithms, based on single-vertex dominators suffer from their rare appearance in many circuits. The presented approach searches efficiently for multiple-vertex dominators in circuit graphs. It finds dominator relations, where algorithms for computing single-vertex dominators fail. Another contribution of this thesis is the application of dominators for combinational equivalence checking based on the arithmetic transform. Previous algorithms rely on representations providing an explicit or implicit disjoint function cover, which is usually excessive in memory requirements. The new algorithm allows a partitioned evaluation of the arithmetic transform directly on the circuit graph using dominator relations. The results show that the algorithm brings significant improvements in memory consumption for many benchmarks. Proper cuts are used in many areas of VLSI. They provide cut points, where a given problem can be split into two disjoint sub-problems. The algorithm proposed in this thesis efficiently detects proper cuts in a circuit graph and is based on a novel concept of a reduced dominator tree. The runtime of the algorithm is less than 0.4 seconds for the largest benchmark circuit. The final contribution of this thesis is the application of the proper cut algorithm as a structural method to decompose a Boolean function, represented by a circuit graph. In combination with a functional approach, it outperforms previous methods, which rely on functional decomposition only.

Series
Trita-IMIT. LECS, ISSN 1651-4076 ; 2004:04
Keyword
formal verification, logic synthesis, dominators, equivalence checking, decomposition
National Category
Computer Science
Identifiers
urn:nbn:se:kth:diva-4293 (URN)
Available from: 2007-03-01 Created: 2007-03-01 Last updated: 2012-03-20

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Dubrova, Elena

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Output format
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