메뉴 건너뛰기




Volumn 29, Issue 6, 2000, Pages 1939-1967

On interpolation and automatization for Frege systems

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; INTEGER PROGRAMMING; INTERPOLATION; POLYNOMIALS; THRESHOLD ELEMENTS; VECTORS;

EID: 0034478771     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539798353230     Document Type: Article
Times cited : (109)

References (32)
  • 1
    • 51249171493 scopus 로고
    • The monotone circuit complexity of boolean functions
    • N. ALON AND R. BOPPANA, The monotone circuit complexity of Boolean functions, Combinatorica, 7 (1987), pp. 1-22.
    • (1987) Combinatorica , vol.7 , pp. 1-22
    • Alon, N.1    Boppana, R.2
  • 2
    • 0342800635 scopus 로고    scopus 로고
    • Minimal propositional proof length is NP-hard to linearly approximate
    • to appear
    • A. ALEKNOVICH, S. Buss, S. MORAN, AND T. PITASSI, Minimal propositional proof length is NP-hard to linearly approximate, J. Symbolic Logic, to appear.
    • J. Symbolic Logic
    • Aleknovich, A.1    Buss, S.2    Moran, S.3    Pitassi, T.4
  • 3
    • 85031632127 scopus 로고    scopus 로고
    • Generalized Diffie-Hellman modulo a composite is not weaker than factoring
    • Record 97-14
    • E. BIHAM, D. BONEH, AND O. REINGOLD, Generalized Diffie-Hellman modulo a composite is not weaker than factoring, Theory of Cryptography Library, Record 97-14, available from http://theory.lcs.mit.edu/tcryptol/homepage.html.
    • Theory of Cryptography Library
    • Biham, E.1    Boneh, D.2    Reingold, O.3
  • 4
    • 0022811668 scopus 로고
    • Log depth circuits for division and related problems
    • P. BEAME, S. COOK, AND H. J. HOOVER, Log depth circuits for division and related problems, SIAM J. Comput., 15 (1986), pp. 994-1003.
    • (1986) SIAM J. Comput. , vol.15 , pp. 994-1003
    • Beame, P.1    Cook, S.2    Hoover, H.J.3
  • 6
    • 0039007501 scopus 로고
    • Lower bounds for cutting planes proofs with small coefficients
    • Las Vegas, NV
    • M. BONET, T. PITASSI, AND R. RAZ, Lower bounds for cutting planes proofs with small coefficients, in Proceedings ACM Symposium on the Theory of Computing, Las Vegas, NV, 1995, pp. 575-584. Also in J. Symbolic Logic, 62 (1997), pp. 708-728.
    • (1995) Proceedings ACM Symposium on the Theory of Computing , pp. 575-584
    • Bonet, M.1    Pitassi, T.2    Raz, R.3
  • 7
    • 0031481402 scopus 로고    scopus 로고
    • M. BONET, T. PITASSI, AND R. RAZ, Lower bounds for cutting planes proofs with small coefficients, in Proceedings ACM Symposium on the Theory of Computing, Las Vegas, NV, 1995, pp. 575-584. Also in J. Symbolic Logic, 62 (1997), pp. 708-728.
    • (1997) J. Symbolic Logic , vol.62 , pp. 708-728
  • 8
    • 44949274401 scopus 로고
    • The undecidability of k-provability
    • S. Buss, The undecidability of k-provability, Ann. Pure Appl. Logic, 53 (1991), pp. 75-102.
    • (1991) Ann. Pure Appl. Logic , vol.53 , pp. 75-102
    • Buss, S.1
  • 9
    • 0040355449 scopus 로고
    • On Godel's theorems on lengths of proofs II: Lower bounds for recognizing k symbol provability
    • P. Clote and J. Remmel, eds., Birkhäuser Boston, Cambridge, MA
    • S. Buss, On Godel's theorems on lengths of proofs II: Lower bounds for recognizing k symbol provability, in Feasible Mathematics II, P. Clote and J. Remmel, eds., Birkhäuser Boston, Cambridge, MA, 1995, pp. 57-90.
    • (1995) Feasible Mathematics , vol.2 , pp. 57-90
    • Buss, S.1
  • 10
    • 0030304213 scopus 로고    scopus 로고
    • Cutting planes, connectivity and threshold logic
    • S. Buss AND P. CLOTE, Cutting planes, connectivity and threshold logic, Arch. Math. Logic, 35 (1996), pp. 33-62.
    • (1996) Arch. Math. Logic , vol.35 , pp. 33-62
    • Buss, S.1    Clote, P.2
  • 11
    • 0032676863 scopus 로고    scopus 로고
    • An exponential lower bound for the size of monotone real circuits
    • S. COOK AND A. HAKEN, An exponential lower bound for the size of monotone real circuits, J. Comput. System Sci., 58 (1999), pp. 326-330.
    • (1999) J. Comput. System Sci. , vol.58 , pp. 326-330
    • Cook, S.1    Haken, A.2
  • 15
    • 0031478484 scopus 로고    scopus 로고
    • Interpolation theorems, lower bounds for proof systems and independence results for bounded arithmetic
    • J. KRAJÍČEK, Interpolation theorems, lower bounds for proof systems and independence results for bounded arithmetic, J. Symbolic Logic, 62 (1997), pp. 457-486.
    • (1997) J. Symbolic Logic , vol.62 , pp. 457-486
    • Krajíček, J.1
  • 16
    • 0009942942 scopus 로고
    • Lower bounds to the size of constant-depth propositional proofs
    • J. KRAJÍČEK, Lower bounds to the size of constant-depth propositional proofs, J. Symbolic Logic, 59 (1994), pp. 73-86.
    • (1994) J. Symbolic Logic , vol.59 , pp. 73-86
    • Krajíček, J.1
  • 17
    • 0040689280 scopus 로고    scopus 로고
    • Discretely ordered modules as a first-order extension of the cutting planes proof system
    • J. KRAJÍČEK, Discretely ordered modules as a first-order extension of the cutting planes proof system, J. Symbolic Logic, 63 (1998), pp. 1582-1596.
    • (1998) J. Symbolic Logic , vol.63 , pp. 1582-1596
    • Krajíček, J.1
  • 18
    • 84957700855 scopus 로고
    • 2 and EF
    • Logic and Computational Complexity, D. Leivant, ed., Springer-Verlag, New York
    • 2 and EF, in Logic and Computational Complexity, D. Leivant, ed., Lecture Notes in Comput. Sci. 960, Springer-Verlag, New York, 1995, pp. 210-220.
    • (1995) Lecture Notes in Comput. Sci. , vol.960 , pp. 210-220
    • Krajíček, J.1    Pudlak, P.2
  • 21
    • 0024139776 scopus 로고
    • A key distribution system equivalent to factoring
    • K. MCCURLEY, A key distribution system equivalent to factoring, J. Cryptology, 1 (1988), pp. 95-105.
    • (1988) J. Cryptology , vol.1 , pp. 95-105
    • McCurley, K.1
  • 22
    • 0343670930 scopus 로고
    • Complexity of Craig's interpolation
    • D. MUNDICI, Complexity of Craig's interpolation, Fund. Inform., 5 (1982), pp. 261-278.
    • (1982) Fund. Inform. , vol.5 , pp. 261-278
    • Mundici, D.1
  • 23
    • 0039271838 scopus 로고
    • A lower bound for the complexity of Craig's interpolants in sentential logic
    • D. MUNDICI, A lower bound for the complexity of Craig's interpolants in sentential logic, Arch. Math. Logik Grundlag, 23 (1983), pp. 27-36.
    • (1983) Arch. Math. Logik Grundlag , vol.23 , pp. 27-36
    • Mundici, D.1
  • 24
    • 0039271822 scopus 로고
    • Tautologies with a unique Craig interpolant, uniform vs. non-uniform complexity
    • D. MUNDICI, Tautologies with a unique Craig interpolant, uniform vs. non-uniform complexity, Ann. Pure Appl. Logic, 27 (1984), pp. 265-273.
    • (1984) Ann. Pure Appl. Logic , vol.27 , pp. 265-273
    • Mundici, D.1
  • 25
    • 0342800619 scopus 로고    scopus 로고
    • Personal Communication
    • M. NAOR, Personal Communication, 1996.
    • (1996)
    • Naor, M.1
  • 26
    • 0031504901 scopus 로고    scopus 로고
    • Lower bounds for resolution and cutting planes proofs and monotone computations
    • P. PUDLAK, Lower bounds for resolution and cutting planes proofs and monotone computations, J. Symbolic Logic, 62 (1997), pp. 981-998.
    • (1997) J. Symbolic Logic , vol.62 , pp. 981-998
    • Pudlak, P.1
  • 27
    • 0040468448 scopus 로고    scopus 로고
    • Algebraic models of computation and interpolation for algebraic proof systems
    • Proof Complexity and Feasible Arithmetic, S. Buss, ed., Springer-Verlag, New York
    • P. PUDLÁK AND J. SGALL, Algebraic models of computation and interpolation for algebraic proof systems, in Proof Complexity and Feasible Arithmetic, S. Buss, ed., Lecture Notes in Comput. Sci. 39, Springer-Verlag, New York, 1998, pp. 279-295.
    • (1998) Lecture Notes in Comput. Sci. , vol.39 , pp. 279-295
    • Pudlák, P.1    Sgall, J.2
  • 28
    • 0001802357 scopus 로고    scopus 로고
    • On the complexity of propositional calculus
    • Cambridge University Press, Cambridge, UK
    • P. PUDLAK, On the complexity of propositional calculus, in Logic Colloquium 97, Cambridge University Press, Cambridge, UK, 1999, pp. 197-218.
    • (1999) Logic Colloquium , vol.97 , pp. 197-218
    • Pudlak, P.1
  • 29
    • 0000492603 scopus 로고
    • Lower bounds for the monotone complexity of some Boolean functions
    • in Russian
    • A. RAZBOROV, Lower bounds for the monotone complexity of some Boolean functions, Dokl. Akad. Nauk. SSSR, 281 (1985), pp. 798-801 (in Russian). English translation in Soviet Mathematics Doklady, 31 (1985), pp. 354-357.
    • (1985) Dokl. Akad. Nauk. SSSR , vol.281 , pp. 798-801
    • Razborov, A.1
  • 30
    • 0000574714 scopus 로고
    • A. RAZBOROV, Lower bounds for the monotone complexity of some Boolean functions, Dokl. Akad. Nauk. SSSR, 281 (1985), pp. 798-801 (in Russian). English translation in Soviet Mathematics Doklady, 31 (1985), pp. 354-357.
    • (1985) Soviet Mathematics Doklady , vol.31 , pp. 354-357
  • 31
    • 0000817789 scopus 로고
    • Unprovability of lower bounds on the circuit size in certain fragments of bounded arithmetic
    • A. RAZBOROV, Unprovability of lower bounds on the circuit size in certain fragments of bounded arithmetic, Izv. Ross. Akad. Nauk. Ser. Mat., 59 (1995), pp. 201-224.
    • (1995) Izv. Ross. Akad. Nauk. Ser. Mat. , vol.59 , pp. 201-224
    • Razborov, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.