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Monotone Complexity (1990)
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by Michelangelo Grigni , Michael Sipser
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2825 - 11 self
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Citations
387
Relationship between nondeterministic and deterministic tape classes.
- Savitch - 1970
329
Algebraic methods in the theory of lower bounds for Boolean circuit complexity.
- Smolensky - 1987
277
Almost optimal lower bounds for small depth circuits,”
- Hastad - 1986
270
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1.
- Barrington - 1989
262
Nondeterministic space is closed under complementation.
- Immerman - 1988
245
Languages that capture complexity classes,
- Immerman - 1987
241
An O(n log n) sorting network,”
- Ajtai, Komlos, et al. - 1983
213
Separating the polynomial-time hierarchy by oracles (preliminary version).
- Yao - 1985
207
Matching is as easy as matrix inversion.
- MULMULEY, VAZIRANI, et al. - 1987
184
The complexity of finite functions, in:
- Boppana, Sipser - 1990
176
The synthesis of two-terminal switching circuits.
- Shannon - 1949
174
Completeness classes in algebra.
- Valiant - 1979
168
Monotone circuits for connectivity require super-logarithmic depth.
- Karchmer, Wigderson - 1990
163
On uniform circuit complexity,
- Ruzzo - 1981
158
Lower bounds on the monotone complexity of some Boolean function.
- Razborov - 1985
147
Complexity classes in communication complexity theory. In:
- Babai, Frankl, et al. - 1986
144
The monotone circuit complexity of Boolean functions.
- Alon, Boppana - 1987
123
Parity, Circuits and the Polynomial Time Hierarchy
- Furst, Saxe, et al. - 1984
101
Reliable circuits using less reliable relays.
- Moore, Shannon - 1956
97
Short monotone formulae for the majority function.
- Valiant - 1984
87
1-formulae on finite structures.
- Ajtai - 1983
82
Monotone Circuits for Matching require Linear Depth.
- Raz, Wigderson - 1992
81
On determinants, matchings, and random algorithms.
- Lovász - 1979
79
The Boolean formula value problem is in ALOGTIME
- Buss - 1987
71
Tree–size bounded alternation.
- Ruzzo - 1980
64
The gap between monotone and non-monotone circuit complexity is exponential.
- Tardos - 1987
62
Two applications of inductive counting for complementation problems
- Borodin, Cook, et al. - 1989
61
Properties that characterize LOGCFL.
- Venkateswaran - 1991
58
A complexity theory based on boolean algebra.
- Skyum, Valiant - 1985
55
The method of forcing for nondeterministic automata
- Szelepcsényi - 1987
51
On a method for obtaining lower bounds for the complexity of individual monotone functions.
- Andreev - 1985
47
Fast parallel matrix and GCD computations
- Borodin, Gathen, et al. - 1982
45
On time-hardware complexity tradeoffs for boolean functions.
- Spira - 1971
43
Finite monoids and the fine structure of NC
- Barrington, Therien - 1988
39
Monotone versus positive
- Ajtai, Gurevich - 1987
38
A lower bound on the monotone network complexity of the logical permanent.
- Razborov - 1985
30
Symmetric complementation
- Reif - 1982
22
Probabilistic communication complexity of Boolean relations.
- Raz, Wigderson - 1989
22
Circuits and Local Computation,
- Yao - 1989
22
bounds on the size of bounded depth networks over a complete basis with logical addition. Mathematicheskie Zametki
- Lower - 1987
21
Communication Complexity: A New Approach to Circuit Depth
- Karchmer - 1989
20
Lower bounds to the complexity of symmetric boolean functions. Theoretical Computer Science 74(3):313–323
- Babai, Pudlák, et al. - 1990
12
Constructing a maximum matching is in Random NC
- Karp, Upfal, et al. - 1986
9
Monotone separation of logspace from NC
- Grigni, Sipser - 1991
8
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