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Bound-set preserving ROBDD variable orderings may not be optimum
KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.
KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.
KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.ORCID iD: 0000-0001-7382-9408
2005 (English)In: I.E.E.E. transactions on computers (Print), ISSN 0018-9340, E-ISSN 1557-9956, Vol. 54, no 2, 236-237 p.Article in journal (Refereed) Published
Abstract [en]

This paper reports a result concerning the relation between the best variable orderings of an ROBDD G(f) and the decomposition structure of the Boolean function f represented by G(f). It was stated in [1] that, if f has a decomposition of type f(X) = g(h(1)(Y-1), h(2)(Y-2), ..., h(k)(Y-k)), where {Y-i}, i is an element of {1, 2, ..., k}, is a partition of X, then one of the orderings which keeps the variables within the sets {Y-i} adjacent is a best ordering for G(f). Using a counterexample, we show that this statement is incorrect.

Place, publisher, year, edition, pages
2005. Vol. 54, no 2, 236-237 p.
Keyword [en]
ROBDD, variable ordering, bound set
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-14429DOI: 10.1109/TC.2005.17ISI: 000225715900015Scopus ID: 2-s2.0-14844342353OAI: oai:DiVA.org:kth-14429DiVA: diva2:332470
Note

QC 20100525

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2018-01-12Bibliographically approved
In thesis
1. Advances in Functional Decomposition: Theory and Applications
Open this publication in new window or tab >>Advances in Functional Decomposition: Theory and Applications
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing.

This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient.

The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering.

The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time.

The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function.

The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches.

Finally we present two publications that resulted from the many detours we have taken along the winding path of our research.

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. xi,176 p.
Series
Trita-ICT-ECS AVH, ISSN 1653-6363 ; 06:06
Keyword
computer science, electronic system design, Boolean decomposition, binary decision diagram, logic synthesis, graph algorithm
National Category
Computer Sciences
Identifiers
urn:nbn:se:kth:diva-4135 (URN)
Public defence
2006-10-12, E, KTH Forum, Isafjordsgatan 39, Kista, 09:00
Opponent
Supervisors
Note
QC 20100909Available from: 2006-10-09 Created: 2006-10-09 Last updated: 2018-01-13Bibliographically approved

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Dubrova, Elena

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