Lower bounds for monotone real circuit depth and formula size and tree-like cutting planes

Information Processing Letters

Volumn 67, Issue 1, 1998, Pages 37-41

  Johannsen, Jan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Communication complexity; Computational complexity; Cutting planes proof; Monotone circuit

Indexed keywords

COMPUTATIONAL COMPLEXITY; THEOREM PROVING; TREES (MATHEMATICS);

MONOTONE REAL CIRCUITS; TREE LIKE CUTTING PLANES;

DIGITAL CIRCUITS;

EID: 0032119717     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-0190(98)00079-9     Document Type: Article

References (11)

1. M.L. Bonet, T. Pitassi, R. Raz, Lower bounds for cutting planes proofs with small coefficients, J. Symbolic Logic 62 (1997) 708-728.
2. R.B. Boppana, M. Sipser, The complexity of finite functions, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, Vol. A, Elsevier, Amsterdam, 1990, Chapter 14, pp. 757-804.
3. P. Clote, A. Setzer, On PHP, st-connectivity and odd charged graphs, in: P. Beame, S.R. Buss (Eds.), Proof Complexity and Feasible Arithmetics, AMS DIMACS Series, Vol. 39, 1998, pp. 93-117.
4. W. Cook, C. Coullard, G. Turán, On the complexity of cutting plane proofs, Discrete Appl. Math. 18 (1987) 25-38.
5. R. Impagliazzo, T. Pitassi, A. Urquhart, Upper and lower bounds for tree-like cutting planes proofs, in: Proc. 9th LICS, 1994.
6. M. Karchmer, Communication Complexity: A New Approach to Circuit Depth, MIT Press, Cambridge, MA, 1989.
7. M. Karchmer, A. Wigderson, Monotone circuits for connectivity require super-logarithmic depth, in: Proc. 20th STOC, 1988, pp. 539-550.
8. J. Krajíček, Interpolation by a game, Math. Logic Quarterly, to appear.
9. J. Krajíček, Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic, J. Symbolic Logic 62 (1997) 457-486.
10. P. Pudlák, Lower bounds for resolution and cutting plane proofs and monotone computations, J. Symbolic Logic 62 (1997) 981-998.
11. A. Rosenbloom, Monotone real circuits are more powerful than monotone Boolean circuits, Inform. Process. Lett. 61 (1997) 161-164.