Umans, Christopher (1998) The Minimum Equivalent DNF Problem and Shortest Implicants. In: 39th Annual Symposium on Foundations of Computer Science. Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society , Los Alamitos, CA, pp. 556-563. ISBN 0-8186-9172-7. https://resolver.caltech.edu/CaltechAUTHORS:20120119-070934161
Full text is not posted in this repository. Consult Related URLs below.
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20120119-070934161
Abstract
We prove that the Minimum Equivalent DNF problem is _Σ2 ^(p-)complete, resolving a conjecture due to L.J. Stockmeyer (1976). The proof involves as an intermediate step a variant of a related problem in logic minimization, namely, that of finding the shortest implicant of a Boolean function. We also obtain certain results concerning the complexity of the shortest implicant problem that may be of independent interest. When the input is a formula, the shortest implicant problem is Σ_2^(p-)complete, and Σ_2^(p-)hard to approximate to within an n^(1/2-ε) factor. When the input is a circuit, approximation is Σ_2^(p-)hard to within an n^(1-ε) factor. However, when the input is a DNF formula, the shortest implicant problem cannot be Σ_2^(p-)complete unless Σ_2^p=NP[log^2_n]^(NP).
| Item Type: | Book Section | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Related URLs: |
| |||||||||
| Additional Information: | © 1998 IEEE. Issue Date: Nov 1998. Date of Current Version: 06 August 2002. Supported by NSF grant CCR-9626361 and an NSF Graduate Research Fellowship. We would like to thank Christos Papadimitriou for suggesting this problem, and many useful discussions. | |||||||||
| Funders: |
| |||||||||
| Other Numbering System: |
| |||||||||
| Series Name: | Annual IEEE Symposium on Foundations of Computer Science | |||||||||
| DOI: | 10.1109/SFCS.1998.743506 | |||||||||
| Record Number: | CaltechAUTHORS:20120119-070934161 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120119-070934161 | |||||||||
| Official Citation: | Umans, C.; , "The minimum equivalent DNF problem and shortest implicants," Foundations of Computer Science, 1998. Proceedings.39th Annual Symposium on , vol., no., pp.556-563, 8-11 Nov 1998 doi: 10.1109/SFCS.1998.743506 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=743506&isnumber=15971 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 28844 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 19 Jan 2012 15:56 | |||||||||
| Last Modified: | 09 Nov 2021 17:01 |
Repository Staff Only: item control page
