Combinatorial Methods In Boolean Function Complexity

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Combinatorial Methods In Boolean Function Complexity (1995) (Make Corrections) (5 citations)
Anna Gal

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Abstract: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Complexity of Boolean functions . . . . . . . . . . . . . . . . . . 1 1.1.1. The basic model: Boolean circuits . . . . . . . . . . . . . . 1 1.1.2. The complexity classes NC and AC . . . . . . . . . . . . 2 1.1.3. Boolean formulas . . . . . . . . . . . . . . . . . . . . . . . 3 1.2. Fault tolerance of Boolean circuits . . . . . . . . ... (Update)

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...= f , f 1 = f # and M 0 = M. It is then su#cient to find M 1 computing f 1 = f # so that the pair M 0 , M 1 satisfies equation (1) In [21] a construction is presented which, given an MSP N = K, N,#) of size d computing f (and with target vector (1, 1) yields a dual...

.... holds: calculating a function defined by a polynomial size MSP is in N ) The most relevant references for this question are [BGK 96] and [Gal95] 3. No results have so far been published which extend threshold results other than [GMW] BOGW] CCD] RBO] Of particular...

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BibTeX entry: (Update)

A. Gal, Combinatorial methods in Boolean function complexity, Ph.D.-thesis, University of Chicago, 1995. http://citeseer.ist.psu.edu/gal95combinatorial.html More

@techreport{ gal95combinatorial,
    author = "Anna Gal",
    title = "Combinatorial Methods in Boolean Function Complexity",
    number = "TR-95-08",
    month = "30,",
    year = "1995",
    url = "citeseer.ist.psu.edu/gal95combinatorial.html" }

Citations (may not include all citations):
403 Proof verification and hardness of approximation problems - Arora, Lund et al. - 1992
202 The Complexity of Boolean Functions - Wegener - 1987
189 Algebraic methods in the theory of lower bounds for Boolean .. (context) - Smolensky - 1987
168 A taxonomy of problems with fast parallel algorithms (context) - Cook - 1985
163 NP is as easy as detecting unique solutions (context) - Valiant, Vazirani - 1986
125 On uniform circuit complexity (context) - Ruzzo - 1981
106 Matching is as easy as matrix inversion (context) - Mulmuley, Vazirani et al. - 1987
103 Almost optimal lower bounds for small depth circuits - Hastad - 1989
85 Upper and lower bounds on first order expressibility (context) - Immerman - 1982
83 The monotone circuit complexity of Boolean functions (context) - Alon, Boppana - 1987
82 Monotone circuits for connectivity require superlogarithmic .. (context) - Karchmer, Wigderson - 1990
82 Lower bounds for the monotone complexity of some Boolean fun.. (context) - Razborov - 1985
69 On span programs (context) - Karchmer, Wigderson - 1993
68 On lower bounds for read-k-times branching programs (context) - Borodin, Razborov et al. - 1993
67 The synthesis of two-terminal switching circuits (context) - Shannon - 1949
66 On simultaneous resource bounds (context) - Pippenger - 1979
62 Lower bounds for deterministic and nondeterministic branchin.. - Razborov - 1991
60 On computing the determinant in small parallel time using a .. (context) - Berkowitz - 1984
53 A fast parallel algorithm to compute the rank of a matrix ov.. (context) - Mulmuley - 1987
51 Probabilistic logics and the synthesis of reliable organisms.. (context) - von Neumann - 1956
51 the tape complexity of deterministic context-free languages (context) - Sudborough - 1978
51 Lower bounds for the size of circuits of bounded depth with .. (context) - Razborov - 1987
49 Tree-size bounded alternation (context) - Ruzzo - 1980
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 - 1981
45 Parity, circuits and the polynomial time hierarchy (context) - Furst, Saxe et al. - 1984
44 CREW PRAMs and decision trees (context) - Nisan - 1989
44 Monotone circuits for matching require linear depth - Raz, Wigderson - 1990
41 Properties that characterize LOGCFL (context) - Venkateswaran - 1987
37 Probabilistic checking of proofs (context) - Arora, Safra - 1992
32 On networks of noisy gates (context) - Pippenger - 1985
31 A theorem on probabilistic constant depth computations (context) - Ajtai, Ben-Or - 1984
31 a method for obtaining lower bounds for the complexity of in.. (context) - Andreev - 1985
29 A lower bound for integer multiplication with read-once bran.. - Ponzio - 1995
25 the method of approximation (context) - Razborov - 1989
25 Structure and importance of the logspace-mod class (context) - Buntrock, Damm et al. - 1992
24 Entropy of contact circuits and lower bound on their complex.. (context) - Jukna - 1988
23 A new lower bound theorem for read-only-once branching progr.. (context) - Simon, Szegedy - 1993
22 Computing with unreliable information (context) - Feige, Peleg et al. - 1990
22 Upper bound for the redundancy of selfcorrecting arrangement.. (context) - Dobrushin, Ortyukov - 1977
22 Two lower bounds for branching programs - Ajtai, Babai et al. - 1986
21 Reliable Computation with Noisy Circuits and Decision Trees .. (context) - Reischuk, Schmeltz - 1991
21 Lower Bounds for the Complexity of Reliable Boolean Circuits.. - G'acs, G'al - 1994
21 Lower Bounds for the Complexity of Reliable Boolean Circuits.. - G'al - 1991
19 a lower bound for the redundancy of reliable networks with n.. (context) - Pippenger, Stamoulis et al. - 1991
19 Lower bound for the redundancy of selfcorrecting arrangement.. (context) - Dobrushin, Ortyukov - 1977
17 An O(n log n) sorting network (context) - Ajtai, Koml'os et al. - 1983
17 Transparent proofs and limits to approximation - Babai - 1993
16 Fault tolerant sorting network (context) - Assaf, Upfal - 1990
16 Lower bounds for monotone span programs - Beimel, G'al et al. - 1994
16 Lower bounds for monotone span programs - Beimel, G'al et al.
16 An exponential lower bound for one time only branching porgr.. (context) - Zak - 1984
16 Halvers and expanders (context) - Ajtai, Koml'os et al. - 1992
15 On proving lower bounds for circuit size (context) - Karchmer - 1993
14 Complexity in electronic switching circuits (context) - Muller - 1956
14 The fusion method for lower bounds in circuit complexity - Wigderson - 1993
12 Universally ideal secret sharing schemes - Beimel, Chor - 1994
12 Characterizing non-deterministic circuit size (context) - Karchmer, Wigderson - 1993
12 On time-hardware complexity tradeoffs for Boolean functions (context) - Spira - 1971
12 Depth reduction for noncommutative arithmetic circuits - Allender, Jiao - 1993
11 The dealer's random bits in perfect secret sharing schemes - Csirmaz - 1994
10 Personal communication (context) - Tardos
10 Information theory and noisy computation - Evans - 1994
10 a method of circuit synthesis (context) - Lupanov - 1958
10 Separating the polynomial hierarchy by oracles (context) - Yao - 1985
10 Information theory and noisy computation - Evans, Schulman - 1995
8 Personal communication (context) - Nisan
7 the synthesis of self-correcting schemes from functional ele.. (context) - Uhlig - 1974
7 A Boolean function requiring 3n network size (context) - Blum - 1984
7 The Synthesis of Reliable Organisms from Unreliable Componen.. (context) - Pippenger, in - 1990
5 A simple lower bound for monotone clique using a communicati.. (context) - Goldman, Hastad - 1992
5 P 1 1 -formulae on finite structures (context) - Ajtai - 1983
5 A simple function that requires exponential size read-once b.. (context) - G'al
5 the design of reliable Boolean circuits that contain partial.. (context) - Kleitman, Leighton et al. - 1994
4 Space complexity of computations (context) - Pudlak, Zak - 1983
4 Synthesis of self-correcting schemes from functional element.. (context) - Kirienko - 1970
4 On self-correcting schemes from functional elements (context) - Kirienko - 1964
4 A lower bound for read-once branching programs (context) - Babai, Hajnal et al. - 1987
4 Reliable networks from unreliable gates with almost minimal .. (context) - Uhlig - 1987
4 Sensitivity vs. block sensitivity of Boolean functions (context) - Rubinstein - 1995
4 A note on read-k-times branching programs - Jukna - 1992
3 Personal communication (context) - Venkateswaran
3 Exponential lower bounds on the complexity of real time and .. (context) - Krause - 1988
3 Personal communication (context) - Lund, Spielmann
3 Fault tolerant circuits and probabilistically checkable proo.. - G'al, Szegedy - 1995
3 Signal propagation with application to a lower bound on the .. - Evans, Schulman - 1993
2 Circuit synthesis in complete monotone basis (context) - Andreev - 1988
2 NL=poly ` \PhiL=poly (context) - Wigderson - 1994
2 lower bound on the combinatorial complexity of Boolean funct.. (context) - Paul, n- - 1977
2 Semi-unbounded fan-in circuits: Boolean vs. arithmetic - G'al - 1995
2 A linear construction of perfect secret sharing schemes (context) - van Dijk - 1994
1 the combinatorial complexity of certain symmetric Boolean fu.. (context) - Stockmeyer - 1977
1 Relationships among complexity measures (context) - Pippenger, Fischer - 1977
1 a problem of K. Zarankiewicz (context) - Kov'ari, S'os et al. - 1954
1 Boolean complexity classes vs. their arithmetic analogs (context) - G'al, Wigderson
1 Ideal Secret Sharing Schemes (context) - Beimel - 1992
1 the complexity of branching porgrams and decision trees for .. (context) - Wegener - 1988
1 Lower bounds on the complexity of 1-time only branching prog.. (context) - Dunne - 1985
1 On another Boolean matrix (context) - Pippenger - 1980
1 A 4n lower bound on the combinatorial complexity over U 2 = .. (context) - Zwick - 1991

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