|
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
| |
Aj83
|
M. AJTAI, #-formulae on finite structures, Annals of Pure and Applied Logic 24, 1-48, 1983.
|
| |
AB87
|
|
| |
An85
|
A.E. ANDREEV, On a method for obtaining lower bounds for the complexity of individual monotone functions, Doklady Akademii Nauk SSSR 282:5, 1033-1037 (in Russian). English translation in Soviet Mathematics DoUady 31:3, 530-534, 1985.
|
| |
As55
|
G. ASSER, Das Repr#entatenproblem im PrKdikatenkalkiil der ersten Stufe mit identit#t, Zeitschrift fiir Matemitische Logic und Grundlagen der Mathematik, 1, 252-263, 1955.
|
| |
BGS75
|
T. P. BAKER, J. GILL, AND R. SOLOVAY, Relativizations of the P=?NP question, SIAM Journal on Computing 4:4, 431-442, 1975.
|
| |
Ba86a
|
|
| |
Ba86a
|
D.A. BARRINQTON, A note on a theorem of Razborov, manuscript, 1986.
|
| |
BH91
|
S. BEN-DAVID AND S. HALEVI, On the independence of P versus NP, Tech. Report #699, Technion, 1991.
|
| |
Be82
|
S.J. BERKOWITZ, On some relationships between monotone and non-monotone circuit complexity, Technical Report, Computer Science Department, University of Toronto, 1982.
|
 |
Bl67
|
|
| |
Bl84
|
N. BLUM, A Boolean function requiring 3n network size, Theoretical Computer Science 28, 337-345, 1984.
|
| |
Bo86
|
|
| |
BS90
|
|
| |
Bu86
|
S.R. Buss, Bounded Arilhmetic, Bibliopolis, 1986.
|
| |
Co64
|
A. COBHAM, The intrinsic computational difficulty of functions, Proc. of the 196# international Congress for Logic, Methodology, and lhe Philosophy of Science, edited by Y. Bar- Hillel, North-Holland, 24-30, 1964.
|
| |
CSV84
|
A. K. CHANDRA, L. J. STOCKMEYER, AND U. VISHKIN, Constant depth reducibility, SIAM Journal on Compufiug 13:2, 423-439, 1984.
|
 |
Co71
|
|
 |
Co75
|
|
| |
CU88
|
S.A. COOK AND A. URQUHART, Functional interpretations of feasibly constructive arithmetic, Technical Report 210/88, Computer Science Department, University of Toronto, 1988.
|
 |
DL79
|
|
| |
Du88
|
|
| |
Ed65
|
J. EDMONDS, Paths, trees, and flowers, Canadian Journal of Mathematics, 17, 449- 467, 1965.
|
| |
Ed65b
|
J. EDMONDS, Minimum partition of a matroid into independent sets, Journal of Research of the National Bureau of Standards (B), 69, 67-72,
|
| |
EIRS91
|
|
| |
Fa74
|
R. FAaIN, Generalized first-order spectra and polynomial-time recognizable sets, Complexity of Computation, SIAM-AMS Proceedings 7, 43-73, 1974.
|
| |
FS88
|
|
| |
FSS84
|
M. FURST, J. SAX#., AND M. SIr'SER, Parity, circuits and the polynomial time hierarchy, Mathematical Systems Theory 17, 13-27, 1984.
|
| |
Ga77
|
Z. GALm, On the complexity of regular resolution and the Davis-Putnam procedure, Theoretical Computer Science 4, 23-46, 1977.
|
| |
GJ79
|
|
| |
GH89
|
M. Goldmann, J. Hhstad, A lower bound for monotone clique using a communication game, manuscript, 1989.
|
| |
GS90
|
|
| |
GS91
|
M. GrUGNI AND M. SIPSZR, Monotone separation of N C1 from logspaee, Proceedings of the 6th Annual Symposium on Structure in Complexity Theory, 294-298, 1991.
|
| |
HS72
|
L.H. HARPER AND J. E. SAVAGE, The complexity of the marriage problem, Advances in Mathematics 9, 299-312, 1972.
|
| |
Ha89
|
J. HARTMANIS, GSdel, von Neumann and the P=?NP Problem, Bulletin of the European Association for Theoretical Computer Science, 101-107, June 1989.
|
 |
HH76
|
|
| |
HS65
|
J. HARTMANIS AND P#. E. STEARNS, On the computational complexity of algorithms, Transactions of the AMS 117, 285-306, 1965.
|
| |
Ha85
|
A. HAKe, N, The intractability of resolution, Theoretical Computer Science 39, 297-308, 1985.
|
| |
Hå86
|
|
| |
HW91
|
J. H),STAD, A. WmD#.RSON, Composition of the Universal Relation, manuscript, 1991.
|
| |
HU79
|
|
| |
Im87
|
|
| |
Im88
|
|
| |
JS74
|
N.D. JONES AND A. L. SELMAN, Turing machines and the spectra of first-order formulas, Journal of Symbolic Logic 39, 139-150, 1974.
|
| |
KS87
|
B. KALYANASUNDARAM AND G. SCHNIT- GER, The probabilistic communication complexity of set intersection, Proceedings of #he Second Annual Conference on Structure in Complexity Theory, 41-49, 1987.
|
| |
KRW91
|
M. KARCHMER, R. RAZ, A. WIGDERSON, On proving super-logarithmic depth lower bounds via the direct sum in communication complexity, Proceedings of the Sixth Annual Conference on Structure in Complexity Theory, 1991.
|
 |
KW88
|
|
| |
Ka72
|
R.M. KARP, Reducibility among combinatorim problems, Complexity of Computer Computations, Plenum Press, 85-103, 1972.
|
| |
Ko77
|
D. KOZEN, Lower bounds for natural proof systems, Proceedings of the 18th Annual Symposium on Foundations of Computer Science, 254-266, 1977.
|
| |
LJK87
|
|
| |
Le05
|
H. L#.B#.SGU#., Sur les fonetions repr#sentables analytiquement, Journal de Math. 6# serie 1, 139-216, 1905.
|
| |
Le73
|
L. LEVIN, Universal sequential search problems, Probl. Pered. Inform. IX 3, 1973; translation in Problems of Information Trans 9, 3, 265--266; corrected translation in Trakhtenxbrot {Tr84}.
|
| |
Li78
|
R.J. LIPTON, Model theoretic aspects of complexity theory, Proceeding of the 19th Annual Symposium on Foundations of Computer Science, 193-200, 1978.
|
 |
LFKN90
|
|
| |
MS72
|
A. R,. MEYER, AND L. J. STOCKMEYER, The equivalence problem for regular expressions with squaring requires exponential time, Proceedings of #he 13th Annual Symposium on Switching and Automata Theory, 125-129, 1972.
|
| |
Mo80
|
Y.N. MOSCHOVAKIS, Descriptive Set Theory, North-Holland, 1980.
|
| |
Mu56
|
D. E. MULLER, Complexity in electronic switching circuits, IRE Transactions on Electronic Computers 5, 15-19, 1956.
|
| |
Pa76
|
M. S. PATERSON, An introduction to Boolean function complexity, Astgrisque 38- 39, 183-201, 1976.
|
| |
Ra60
|
M.O. I#BIN, Degree of diflieutly of computing a function and a partial ordering of reeursive sets, Teeh. Rep. No. 2, Hebrew University, 1960.
|
| |
Ra66
|
M.O. tL#BIN, Mathematical theory of automata, Proceedings of 19th A CM Symposium in Applied Mathematics, 153-175, 1966.
|
 |
RW90
|
|
| |
Ra85a
|
A. A. RAZBOROV, A lower bound on the monotone network complexity of the logical permanent, Matematicheskie gametki 37:6, 887-900 (in Russian). En/#lish translation in Mathematical Notes of the Academy of Sciences of the USSR 37:6, 485-493, 1985.
|
| |
Ra85b
|
A. A. RAZBOROV, A lower bound on the monotone network complexity of the logical permanent, Matema#icheskie Zametki 37:6, 887-900 (in Russian). English translation in Mathematical Notes of the Academy of Sciences of the USSR 37:6, 485--493, 1985.
|
| |
Ra87
|
A.A. RAZBOROV, Lower bounds on the size of bounded depth networks over a complete basis with logical addition, Matematicheskie Zametki 41:4, 598-607 (in Russian). English translation in Mathematical Notes of the Academy of Sciences of the USSR 41:4, 333- 338, 1987.
|
 |
Ra89
|
|
| |
Ra90a
|
|
| |
Ra90b
|
A. A. RAZBOROV, Applications of matrix methods for the theory of lower bounds in computational complexity, Combinalorica 10, 81-93, 1990.
|
 |
Sa72
|
|
| |
Sa80
|
|
| |
Sc52
|
H. SCHOLZ, Problem #1, Journal of Symbolic Logic, 17, 160, 1952.
|
 |
Sh90
|
|
| |
Sh49
|
C.E. SHANNON, The synthesis of twoterminal switching circuits, Bell Systems Technical Journal 28:1, 59-98, 1949.
|
| |
Si81
|
M. SIPSZR, On polynomial vs. exponential growth, unpubfished, 1981.
|
 |
Si83
|
|
| |
Si84
|
M. SIPSER, A topological view of some problems in complexity theory, Colloquia Mathematica Societatis Jdno8 Bolyai 44, 387-391, 1984.
|
 |
Sm87
|
|
| |
Sz88
|
|
| |
Ta88
|
TARDOS, The gap between monotone and non-monotone circuit complexity is exponential, Combinatorica 8:1, 141-142, 1988.
|
| |
Tr84
|
B.A. TRAKHTBNBROT, A survey of Russian approaches to Perebor (brute-force search) algorithms, Annals of the History of Computing 6, no. 4, 384-400, 1984.
|
| |
Ts62
|
G.S. TSI#ITIN, On the complexity of derivation in propositional calculus, Studies in Constructive Mathematics and Mathematical Logic, Part 2, Consultants Bureau, New Youk-London, 115-125, 1962.
|
| |
Va90
|
|
| |
Vo53
|
J. VON NEUMANN, A certain zero-sum twoperson game equivalent to the optimal assignment problem, Contributions to the Theory of Games $, 5-12, 1953.
|
| |
We87
|
|
| |
Ya59a
|
S. YABLONSKI, The algorithmic difficulties of synthesizing minimal switching circuits, Prob. lemy Kibernetiki 2, Moscow, Fizmatgiz, 75- 121, 1959; translation in Problems of Cybernetics 2, Pergamon Press, 401-457, 1961.
|
| |
Ya59b
|
S. YABLONSKI, On the impossibility of eliminating brute force search in solving some problems of circuit theory, Doklady, AN SSSR 124, 44-47, 1959.
|
| |
Ya85
|
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