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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 ... (Update)
Context of citations to this paper: More
...game. Razborov [Ra90b] and Goldmann and Hastad [GH89] obtained additional lower bounds using the communication game. Grigni and Sipser [GS90] point out that many of the results in monotone complexity can be viewed in terms of monotone analogs, mP, mNP, etc. of the familiar...
.... Mainz Swansea Abstract Continuing a line of research opened up by Grigni and Sipser in [4] and further pursued in [10] we show that a wide variety of equivalent characterizations of P still remain equivalent when restricted to be positive. All these restrictions thus define...
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2: On the method of approximation, Proc. of the 21th ACM Symp (context) - Razborov - 1989
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BibTeX entry: (Update)
M. Grigni and M. Sipser, Monotone complexity, Proceedings of LMS workshop on Boolean Function Complexity, Durham, edited by M. S. Paterson, Cambridge University Press, 1990. http://citeseer.ist.psu.edu/grigni90monotone.html More
@inproceedings{ grigni92monotone,
author = "Grigni and Sipser",
title = "Monotone Complexity",
booktitle = "{PATBOOL}: Paterson (Ed.), Boolean Function Complexity",
publisher = "London Mathematical Society Lecture Note Series 169, Cambridge University Press",
year = "1992",
url = "citeseer.ist.psu.edu/grigni90monotone.html" }
Citations (may not include all citations):170 Nondeterministic space is closed under complementation - Immerman - 1988
141 The complexity of finite functions (context) - Boppana, Sipser - 1990
114 Bounded-width polynomial-size branching programs recognize e.. (context) - Barrington - 1989
87 Sorting Network (context) - Ajtai, Komlos et al. - 1983
84 Mathematical Systems Theory (context) - Furst, Saxe et al. - 1984
83 The monotone circuit complexity of boolean functions (context) - Alon, Boppana - 1987
82 Monotone circuits for connectivity require super-logarithmic.. (context) - Karchmer, Wigderson - 1990
82 Lower bounds on the monotone complexity of some Boolean func.. (context) - Razborov - 1985
70 The Boolean formula value problem is in ALOGTIME - Buss - 1987
66 Complexity classes in communication complexity theory (context) - Babai, Frankl et al. - 1986
56 Finite monoids and the fine structure of NC (context) - Barrington, Th'erien - 1988
48 Two applications of inductive counting for complementation p.. (context) - Borodin, Cook et al. - 1989
48 A complexity theory based on boolean algebra (context) - Skyum, Valiant - 1985
44 Short monotone formulae for the majority function (context) - Valiant - 1984
44 Monotone circuits for matching require linear depth - Raz, Wigderson - 1990
41 Properties that Characterize LOGCFL (context) - Venkateswaran - 1987
34 The gap between monotone and nonmonotone circuit complexity .. (context) - Tardos - 1988
31 a method for obtaining lower bounds for the complexity of in.. (context) - Andreev - 1985
29 The method of forcing for nondeterministic automata (context) - Szelepcs'enyi - 1987
26 Monotone versus positive (context) - Ajtai, Gurevich - 1987
25 Reliable circuits using less reliable relays (context) - Moore, Shannon - 1956
20 A lower bound on the monotone network complexity of the logi.. (context) - Razborov - 1985
19 Circuits and local computation (context) - Yao - 1989
13 Monotone separation of logspace from NC (context) - Grigni, Sipser - 1991
13 Probabilistic communication complexity of boolean relations - Raz, Wigderson - 1989
3 Massachusetts Institute of Technology (context) - Grigni - 1991
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