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Author Stockmeyer, Larry ♦ Meyer, Albert R.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2002
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Circuit complexity ♦ WS1S ♦ Computational complexity ♦ Decision problem ♦ Logic ♦ Lower bound ♦ Practical undecidability
Abstract An exponential lower bound on the circuit complexity of deciding the weak monadic second-order theory of one successor (WS1S) is proved. Circuits are built from binary operations, or 2-input gates, which compute arbitrary Boolean functions. In particular, to decide the truth of logical formulas of length at most 610 in this second-order language requires a circuit containing at least $10^{125}$ gates. So even if each gate were the size of a proton, the circuit would not fit in the known universe. This result and its proof, due to both authors, originally appeared in 1974 in the Ph.D. thesis of the first author. In this article, the proof is given, the result is put in historical perspective, and the result is extended to probabilistic circuits.*
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2002-11-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 49
Issue Number 6
Page Count 32
Starting Page 753
Ending Page 784

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Source: ACM Digital Library