Lower bounds for (MOD p - MOD m) circuits

Vince Grolmusz, Gabor Tardos

Research output: Contribution to journalConference article

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
Pages (from-to)279-288
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
Publication statusPublished - Dec 1 1998
EventProceedings of the 1998 39th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA
Duration: Nov 8 1998Nov 11 1998

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ASJC Scopus subject areas

  • Hardware and Architecture

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