TY - GEN

T1 - Shallow multiplication circuits and wise financial investments

AU - Paterson, Michael S.

AU - Zwick, Uri

N1 - Publisher Copyright:
© 1992 ACM.

PY - 1992/7/1

Y1 - 1992/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027004050&partnerID=8YFLogxK

U2 - 10.1145/129712.129753

DO - 10.1145/129712.129753

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AN - SCOPUS:0027004050

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 429

EP - 437

BT - Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992

PB - Association for Computing Machinery

T2 - 24th Annual ACM Symposium on Theory of Computing, STOC 1992

Y2 - 4 May 1992 through 6 May 1992

ER -