Lower bounds for (MOD p - MOD m) circuits

Vince Grolmusz, G. Tardos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Modular gates are known to be immune for the random restriction techniques of Ajtai, Furst, Saxe, Sipser, Yao and Hadstad. We demonstrate here a random clustering technique which overcomes this difficulty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Therien, Krause and Pudlak, and others, characterizing symmetric functions computable by small (MODp, ANDt, MODm) circuits. Applying a degree-decreasing technique together with random restriction methods for the AND gates at the bottom level, we also prove a hard special case of the Constant Degree Hypothesis of Barrington, Straubing, Therien, and other related lower bounds for certain (MODp, MODm, AND) circuits. Most of the previous lower bounds on circuits with modular gates used special definitions of the modular gates (i.e., the gate outputs one if the sum of its inputs is divisible by m, or is not divisible by m), and were not valid for more general MODm gates. Our methods are applicable - and our lower bounds are valid - for the most general modular gates as well.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science - Proceedings
Editors Anon
PublisherIEEE Comp Soc
Pages279-288
Number of pages10
Publication statusPublished - 1998
EventProceedings of the 1998 39th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA
Duration: Nov 8 1998Nov 11 1998

Other

OtherProceedings of the 1998 39th Annual Symposium on Foundations of Computer Science
CityPalo Alto, CA, USA
Period11/8/9811/11/98

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Networks (circuits)

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Grolmusz, V., & Tardos, G. (1998). Lower bounds for (MOD p - MOD m) circuits. In Anon (Ed.), Annual Symposium on Foundations of Computer Science - Proceedings (pp. 279-288). IEEE Comp Soc.

Lower bounds for (MOD p - MOD m) circuits. / Grolmusz, Vince; Tardos, G.

Annual Symposium on Foundations of Computer Science - Proceedings. ed. / Anon. IEEE Comp Soc, 1998. p. 279-288.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Grolmusz, V & Tardos, G 1998, Lower bounds for (MOD p - MOD m) circuits. in Anon (ed.), Annual Symposium on Foundations of Computer Science - Proceedings. IEEE Comp Soc, pp. 279-288, Proceedings of the 1998 39th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, USA, 11/8/98.
Grolmusz V, Tardos G. Lower bounds for (MOD p - MOD m) circuits. In Anon, editor, Annual Symposium on Foundations of Computer Science - Proceedings. IEEE Comp Soc. 1998. p. 279-288
Grolmusz, Vince ; Tardos, G. / Lower bounds for (MOD p - MOD m) circuits. Annual Symposium on Foundations of Computer Science - Proceedings. editor / Anon. IEEE Comp Soc, 1998. pp. 279-288
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