BibTeX
@MISC{Grigni90monotonecomplexity,
author = {Michelangelo Grigni and Michael Sipser},
title = {Monotone Complexity},
year = {1990}
}
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Abstract
We give a general complexity classification scheme for monotone computation, including monotone space-bounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple notion of monotone reducibility and exhibit complete problems. This provides a framework for stating existing results and asking new questions. We show that mNL (monotone nondeterministic log-space) is not closed under complementation, in contrast to Immerman's and Szelepcs 'enyi's nonmonotone result [Imm88, Sze87] that NL = co-NL; this is a simple extension of the monotone circuit depth lower bound of Karchmer and Wigderson [KW90] for st-connectivity. We also consider mBWBP (monotone bounded width branching programs) and study the question of whether mBWBP is properly contained in mNC 1 , motivated by Barrington's result [Bar89] that BWBP = NC 1 . Although we cannot answer t...
Keyphrases
monotone circuit depth simple notion turing machine model monotone computation exhibit complete problem general complexity classification scheme nl co-nl result bar89 monotone complexity class monotone reducibility wigderson kw90 nonmonotone result imm88 new question bwbp nc nondeterministic log-space simple extension
