Shallow multiplication circuits and wise financial investments

Michael S. Paterson, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Paterson, Pippenger and Zwick have recently obtained a general theory that describes the optimal way in which given carry-save adders can be combined into carry-save networks. Their work produces, in particular, multiplication circuits of depth 3.711og2n (these circuits put out two numbers whose sum is the result of the multiplication). In this work an extension of the above general theory is obtained. We now consider carry-save adders that may receive inputs and produce outputs using several different representation methods. We describe the optimal way of utilising any such collection of carry-save adders. The optimality proof uses the min-max theorem of game theory. By using several different representation standards, the depth of multiplication circuits can be surprisingly reduced to 3.48 log2 n (again two output numbers are produced). We introduce bit level redundancy by using a novel coding scheme in which each bit is distributed over four wires. Interestingly, the information on these four wires is usually not transmitted simultaneously. Finally, an analogy is made between the optimisation problem faced by the circuit designer and the optimisation problem faced by an investor, offered a collection of financial investment plans, each involving perhaps several different currencies. This analogy is used to obtain intuitive explanations of the results obtained.

Original languageEnglish
Title of host publicationProceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Electronic)0897915119
StatePublished - 1 Jul 1992
Event24th Annual ACM Symposium on Theory of Computing, STOC 1992 - Victoria, Canada
Duration: 4 May 19926 May 1992

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F129722
ISSN (Print)0737-8017


Conference24th Annual ACM Symposium on Theory of Computing, STOC 1992


FundersFunder number
European Commission3075


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