-
1
-
-
0023985196
-
RSA and Rabin functions: Certain parts are as hard as the whole
-
Alexi W. B., Chor, B., Goldreich, O., and Schnorr C. P. (1988), RSA and Rabin functions: Certain parts are as hard as the whole, SIAM J. Comp. 17, 194-209.
-
(1988)
SIAM J. Comp.
, vol.17
, pp. 194-209
-
-
Alexi, W.B.1
Chor, B.2
Goldreich, O.3
Schnorr, C.P.4
-
2
-
-
0031481402
-
Lower bounds for cutting planes proofs with small coefficients
-
Bonet, M. L., Pitassi, T., and Raz, R. (1997), Lower bounds for cutting planes proofs with small coefficients, J. Symbolic Logic 62(3), 708-728.
-
(1997)
J. Symbolic Logic
, vol.62
, Issue.3
, pp. 708-728
-
-
Bonet, M.L.1
Pitassi, T.2
Raz, R.3
-
4
-
-
0029720065
-
Using the Groebner basis algorithm to find proofs of unsatisfiability
-
Assoc. Comput. Mach., New York
-
Clegg, M., Edmonds, J., and Implagliazzo, R. (1996), Using the Groebner basis algorithm to find proofs of unsatisfiability, in "Proc. the 28th Annual ACM Symposium on Theory of Computing," pp. 174-183, Assoc. Comput. Mach., New York.
-
(1996)
Proc. the 28th Annual ACM Symposium on Theory of Computing
, pp. 174-183
-
-
Clegg, M.1
Edmonds, J.2
Implagliazzo, R.3
-
5
-
-
85055637708
-
Feasibly constructive proofs and the propositional calculus
-
Assoc. Comput. Mach., New York
-
Cook, S. A. (1975), Feasibly constructive proofs and the propositional calculus, in "Proc. 7th Annual ACM Symposium on Theory of Computing," pp. 83-97, Assoc. Comput. Mach., New York.
-
(1975)
Proc. 7th Annual ACM Symposium on Theory of Computing
, pp. 83-97
-
-
Cook, S.A.1
-
6
-
-
0001601465
-
The relative efficiency of propositional proof systems
-
Cook, S. A., and Reckhow, A. R. (1979), The relative efficiency of propositional proof systems, J. Symbolic Logic 44(1), -50.
-
(1979)
J. Symbolic Logic
, vol.44
, Issue.1
, pp. 50
-
-
Cook, S.A.1
Reckhow, A.R.2
-
7
-
-
0009309925
-
Fragments of bounded arithmetic and bounded query classes
-
Krajíček, J. (1993), Fragments of bounded arithmetic and bounded query classes, Trans. Amer. Math. Soc. 338(2), 587-598.
-
(1993)
Trans. Amer. Math. Soc.
, vol.338
, Issue.2
, pp. 587-598
-
-
Krajíček, J.1
-
8
-
-
0009942942
-
Lower bounds to the size of constant-depth propositional proofs
-
Krajíček, J. (1994), Lower bounds to the size of constant-depth propositional proofs, J. Symbolic Logic 59(1), 73-86.
-
(1994)
J. Symbolic Logic
, vol.59
, Issue.1
, pp. 73-86
-
-
Krajíček, J.1
-
9
-
-
0003235615
-
Bounded arithmetic, propositional logic and complexity theory
-
Cambridge Univ. Press, Cambridge, UK/New York/Melbourne
-
Krajíček, J. (1995), Bounded arithmetic, propositional logic and complexity theory, in "Encyclopedia of Mathematics and Its Applications," Vol. 60, Cambridge Univ. Press, Cambridge, UK/New York/Melbourne.
-
(1995)
Encyclopedia of Mathematics and Its Applications
, vol.60
-
-
Krajíček, J.1
-
10
-
-
0031478484
-
Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic
-
Krajíček, J. (1997), Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic, J. Symbolic Logic 62(2), 457-486.
-
(1997)
J. Symbolic Logic
, vol.62
, Issue.2
, pp. 457-486
-
-
Krajíček, J.1
-
11
-
-
0013556631
-
Discretely ordered modules as a first-order extension of the cutting planes proof system
-
to appear
-
Krajíček, J., Discretely ordered modules as a first-order extension of the cutting planes proof system, J. Symbolic Logic, to appear.
-
J. Symbolic Logic
-
-
Krajíček, J.1
-
13
-
-
0040785904
-
On methods for proving lower bounds in propositional logic
-
995, "The Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence (August 19-25)" (M. L. Dalla Chiara, K. Dotes, D. Mundici, and J. van Benthem, Eds.), Kluwer Academic, Dordrecht
-
Krajíček, J. ((995), On methods for proving lower bounds in propositional logic, in "The Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence (August 19-25)" (M. L. Dalla Chiara, K. Dotes, D. Mundici, and J. van Benthem, Eds.), Vol. 1 (Logic and Scientific Methods), pp. 69-83, Kluwer Academic, Dordrecht.
-
Logic and Scientific Methods
, vol.1
, pp. 69-83
-
-
Krajíček, J.1
-
14
-
-
0001579141
-
Propositional proof systems, the consistency of first order theories and the complexity of computations
-
Krajíček, J., and Pudlák, P. (1989), Propositional proof systems, the consistency of first order theories and the complexity of computations, J. Symbolic Logic 54(3), 1063-1079.
-
(1989)
J. Symbolic Logic
, vol.54
, Issue.3
, pp. 1063-1079
-
-
Krajíček, J.1
Pudlák, P.2
-
15
-
-
0007208937
-
Quantified propositional calculi and fragments of bounded arithmetic
-
Krajíček, J. (1990), Quantified propositional calculi and fragments of bounded arithmetic, Z. Math. Logik Grundlagen Math. 36(1), 29-46.
-
(1990)
Z. Math. Logik Grundlagen Math.
, vol.36
, Issue.1
, pp. 29-46
-
-
Krajíček, J.1
-
16
-
-
0000919087
-
Bounded arithmetic and the polynomial hierarchy
-
Krajíček, J., Pudlák, P., and Takeuti, G. (1991), Bounded arithmetic and the polynomial hierarchy, Ann. Pure Appl. Logic 52, -153.
-
(1991)
Ann. Pure Appl. Logic
, vol.52
, pp. 153
-
-
Krajíček, J.1
Pudlák, P.2
Takeuti, G.3
-
17
-
-
0343670930
-
Complexity of Craig's interpolation
-
Mundici, D. (1982), Complexity of Craig's interpolation, Fund. Inform. 5, 261-278.
-
(1982)
Fund. Inform.
, vol.5
, pp. 261-278
-
-
Mundici, D.1
-
18
-
-
0039271838
-
A lower bound for the complexity of Craig's interpolants in sentential logic
-
Mundici, D. (1983), A lower bound for the complexity of Craig's interpolants in sentential logic, Arch. Math. Logik 23, 27-36.
-
(1983)
Arch. Math. Logik
, vol.23
, pp. 27-36
-
-
Mundici, D.1
-
19
-
-
0039271822
-
Tautologies with a unique Craig interpolant, uniform vs. non-uniform complexity
-
Mundici, D. (1984), Tautologies with a unique Craig interpolant, uniform vs. non-uniform complexity, Ann. Pure Appl. Logic 27, 265-273.
-
(1984)
Ann. Pure Appl. Logic
, vol.27
, pp. 265-273
-
-
Mundici, D.1
-
20
-
-
77957678251
-
NP and Craig's interpolation theorem
-
North-Holland, Amsterdam
-
Mundici, D. (1984), NP and Craig's interpolation theorem, "Proc. Logic Colloquium 1982," pp. 345-358, North-Holland, Amsterdam.
-
(1984)
Proc. Logic Colloquium 1982
, pp. 345-358
-
-
Mundici, D.1
-
22
-
-
0001091728
-
Counting problems in bounded arithmetic
-
"Methods in Mathematical Logic," Springer-Verlag, Berlin/New York
-
Paris, J., and Wilkie, A. (1985), Counting problems in bounded arithmetic, in "Methods in Mathematical Logic," Lecture Notes in Mathematics, Vol. 1130, pp. 317-340, Springer-Verlag, Berlin/New York.
-
(1985)
Lecture Notes in Mathematics
, vol.1130
, pp. 317-340
-
-
Paris, J.1
Wilkie, A.2
-
23
-
-
0000589911
-
Probability of the pigeonhole principle and the existence of infinitely many primes
-
Paris, J. B., Wilkie, A. J., and Woods, A. R. (1988), Probability of the pigeonhole principle and the existence of infinitely many primes, J. Symbolic Logic 53, 1235-1244.
-
(1988)
J. Symbolic Logic
, vol.53
, pp. 1235-1244
-
-
Paris, J.B.1
Wilkie, A.J.2
Woods, A.R.3
-
24
-
-
0011521703
-
Every prime has a succinct certificate
-
Pratt, V. R. (1975), Every prime has a succinct certificate, SIAM J. Comput. 4, 214-220.
-
(1975)
SIAM J. Comput.
, vol.4
, pp. 214-220
-
-
Pratt, V.R.1
-
25
-
-
0031504901
-
Lower bounds for resolution and cutting planes proofs and monotone computations
-
Pudlák, P. (1997), Lower bounds for resolution and cutting planes proofs and monotone computations, J. Symbolic Logic 62(3), 981-998.
-
(1997)
J. Symbolic Logic
, vol.62
, Issue.3
, pp. 981-998
-
-
Pudlák, P.1
-
27
-
-
0000817789
-
Unprovability of lower bounds on the circuit size in certain fragments of bounded arithmetic
-
Razborov, A. A. (1995), Unprovability of lower bounds on the circuit size in certain fragments of bounded arithmetic, Izv. Ross. Akad. Nauk 59(1), 201-224.
-
(1995)
Izv. Ross. Akad. Nauk
, vol.59
, Issue.1
, pp. 201-224
-
-
Razborov, A.A.1
-
28
-
-
0037775875
-
-
Basic Research in Computer Science Center, RS-94-36, Aarhus, preprint
-
Razborov, A. A. (1994), On provably disjoint NP-pairs, Basic Research in Computer Science Center, RS-94-36, Aarhus, preprint.
-
(1994)
On Provably Disjoint NP-pairs
-
-
Razborov, A.A.1
-
29
-
-
0017930809
-
A method of obtaining digital signatures and public-key cryptosystems
-
Rivest, M., Shamir, A., and Adleman, L. (1978), A method of obtaining digital signatures and public-key cryptosystems. ACM Comm. 21, 120-126.
-
(1978)
ACM Comm.
, vol.21
, pp. 120-126
-
-
Rivest, M.1
Shamir, A.2
Adleman, L.3
-
30
-
-
0001588405
-
RSUV isomorphism
-
Clote and Krajíček, Eds., Oxford Univ. Press, Oxford
-
Takeuti, G. (1992), RSUV isomorphism, in "Arithmetic, Proof Theory and Computational Complexity" (Clote and Krajíček, Eds.), pp. 364-386, Oxford Univ. Press, Oxford.
-
(1992)
Arithmetic, Proof Theory and Computational Complexity
, pp. 364-386
-
-
Takeuti, G.1
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