Upper and lower bounds for certain GRAPH-ACCESSIBILITY-PROBLEMs on bounded alternating ω-BRANCHING PROGRAMs
In the following we investigate the computational complexity of various ω-GRAPH ACCESSIBILITY PROBLEMs on the most general restricted type of ω-branching programs for for which, up to now, exponential lower bounds on the size can be proved. By means of exponential lower bounds on various ranks of certain communication matrices we prove that ωGRAPH ACCESSIBILITY PROBLEMs can not be computed by bounded alternating ω-branching programs within polynomial size In contrast, ω-GRAPH ACCESSIBILITY PROBLEMs restricted to monotone graphs can by computed by such devices.
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- [AM86]N. Alon, W. Maass: Meanders, Ramsey theory and lower bounds, Proc. 27th ACM STOC, 1986, 30–39.Google Scholar
- [DKMW90]C. Damm, M. Krause, Ch. Meinel, S. Waack: Separating Restricted MOD p-Branching Program Classes, Informatik-Preprint 3; Humboldt-Universität Berlin, 1990.Google Scholar
- [Imm87]N. Immerman: Languages that Capture Complexity Classes, SIAM J. Comput., Vol. 16, No. 4, 1987, 760–778.Google Scholar
- [HMT88]A. Hajnal, W. Maass, G. Turan: On the Communication Complexity of Graph Problems. Proc. 20th STOC (1988) 186–191.Google Scholar
- [KMW89]M. Krause, Ch. Meinel, S. Waack: Separating Complexity Classes Related to Certain Input Oblivious Logarithmic Space Bounded Turing Machines, Proc. 4th IEEE Structure in Complexity Theory, 1989, 240–259.Google Scholar
- [KW89]M. Krause, S. Waack: On Oblivious Branching Programs of Linear Length, Proc. FCT'89, LNCS 380, 287–296.Google Scholar
- [Lov89]L. Lovasz: Communication Complexity: A Survey. Technical Report CS-TR-204-89, Princeton University.Google Scholar
- [Mei86]Ch. Meinel: P-Projection Reducibility and the Complexity Classes L(nonuniform) and NL(nonuniform), Proc. MFCS'86, LNCS 233, 527–535.Google Scholar
- [Mei88]Ch. Meinel: Polynomial Size Ω-branching Programs and their Computational Power, Proc. STACS'88, LNCS 294, 81–90.Google Scholar
- [Mei89]Ch. Meinel: Modified Branching Programs and Their Computational Power, LNCS 370, Springer Verlag, 1989.Google Scholar
- [MW91]Ch. Meinel, S. Waack: Upper and Lower Bounds for Certain Graph-Accessibility-Problems on Bounded Alternating Branching Programs. Preprint No. 276/1991, TU Berlin, FB Mathematik, 1991.Google Scholar
- [PŽ83]P. Pudlak, S. Žak: Space Complexity of Computations, Techn. Report Univ. of Prague, 1983.Google Scholar
- [Sav70]W. Savitch: Relationships Between Nonderterministic and Deterministic Tape Complexities, J. Comp. Sys. Sci., Vol. 4, No. 2, 1970, 177–192.Google Scholar