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Monotone Complexity (1990)
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by Michelangelo Grigni , Michael Sipser
Citations:
2802 - 11 self
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Citations
385
Relationships between nondeterministic and deterministic tape complexities
- Savitch - 1970
323
Algebraic methods in the theory of lower bounds for boolean circuit complexity
- Smolensky - 1987
273
Almost optimal lower bounds for small depth circuits
- H˚astad - 1989
268
Bounded-width polynomial-size branching programs recognize exactly those languages in NC
- Barrington - 1989
259
Nondeterministic space is closed under complementation
- Immerman - 1988
241
Languages that capture complexity classes
- Immerman - 1987
238
An O(n log n) sorting network
- Ajtai, Komlos, et al. - 1983
212
Separating the polynomial–time hierarchy by oracles
- Yao - 1985
207
Matching is as easy as matrix inversion
- Mulmuley, Vazirani, et al. - 1987
183
The complexity of finite functions
- Boppana, Sipser - 1990
174
The synthesis of two-terminal switching circuits
- Shannon - 1949
170
Completeness classes in algebra
- Valiant - 1979
164
and Avi Wigderson. Monotone circuits for connectivity require superlogarithmic depth
- Karchmer - 1990
162
On uniform circuit complexity
- Ruzzo - 1981
156
Lower bounds on the monotone complexity of some boolean functions
- Razborov - 1985
145
Complexity classes in communication complexity theory
- Babai, Frankl, et al. - 1986
141
The monotone circuit complexity of boolean functions
- Alon, Boppana - 1987
123
Parity, circuits, and the polynomial time hierarchy
- Furst, Saxe, et al. - 1984
100
Reliable circuits using less reliable relays, part I
- Moore, Shannon
98
Short monotone formulae for the majority function
- Valiant - 1984
86
1 -Formulae on Finite Structures
- Ajtái - 1983
82
Monotone circuits for matching require linear depth
- Raz, Wigderson - 1990
80
The Boolean Formula Value Problem is in ALOGTIME
- Buss - 1987
80
On determinants, matchings, and random algorithms
- Lovász - 1979
71
Tree-size bounded alternation
- Ruzzo - 1980
63
The gap between monotone and non-monotone circuit complexity is exponential
- Tardos - 1988
62
Two applications of inductive counting for complementation problems
- Borodin, Cook, et al. - 1989
60
Properties that characterize LOGCFL
- Venkateswaran - 1991
57
A complexity theory based on Boolean algebra
- Skyum, Valiant - 1981
56
The method of forcing for nondeterministic automata
- Szelepcsényi - 1987
49
On a method for obtaining lower bounds for the complexity of individual monotone functions
- Andreev - 1985
48
Fast parallel matrix and gcd computations
- Borodin, Gathen, et al. - 1982
43
Finite monoids and the fine structure of NC
- Barrington, Therien - 1988
43
On time hardware complexity of tradeoffs for boolean functions
- Spira - 1971
39
Monotone versus positive
- Ajtai, Gurevich - 1987
37
Lower bounds on monotone network complexity of the logical permanent
- Razborov - 1985
30
Symmetric complementation
- Reif - 1982
22
bounds on the size of bounded depth networks over a complete basis with logical addition. Mathematicheskie Zametki
- Lower - 1987
21
Wigderson A,, “Probabilistic Communication Complexity of Boolean Relations
- Raz - 1989
21
Circuits and local computation
- Yao - 1989
21
Communication Complexity: A New Approach to Circuit Depth
- Karchmer - 1989
20
Lower bounds to the complexity of symmetric Boolean functions, preprint
- BABAI, PIJDLK, et al.
12
Constructing a maximum matching is in Random NC
- Karp, Upfal, et al. - 1986
9
Monotone separation of logspace from NC
- Grigni, Sipser - 1991
7
Relating monotone formula size and monotone depth of Boolean functions
- Wegener - 1983
5
Random walks, traversal sequences, and the complexity of maze problems
- Aleliunas, Karp, et al. - 1979
4
theory and lower bounds for branching programs
- Meanders - 1986
2
Minimal relay-diode bipoles for monotonic symmetric functions, Problems of Cybernetics 8
- Markov - 1964
1
Amplification of probabilistic Boolean functions
- Boppana - 1990
1
Lower bounds for small-depth monotone threshold circuits
- Hastad - 1989