Tradeoffs between Nondeterminism and Complexity for Communication Protocols and Branching Programs
One of the few major open problems concerning nondeterministic communication complexity is to prove an asymptotically exact tradeoff between complexity and the number of available advice bits. This problem is solved here for the case of one-way communication.
Multipartition protocols are introduced as a new type of communication protocols using a restricted form of non-obliviousness. In order to be able to study methods for proving lower bounds on multilective and/or non-oblivious computation, these protocols are allowed to either deterministically or nondeterministically choose between different partitions of the input. Here, the first results showing the potential increase of the computational power by non-obliviousness as well as boundaries on this power are derived.
The above results (and others) are applied to obtain several new exponential lower bounds for different types of oblivious branching programs, which also yields new insights into the power of nondeterminism and randomness for the considered models. The proofs rely on a general technique described here which allows to prove explicit lower bounds on the size of oblivious branching programs in an easy and transparent way.
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- 1.H. Abelson. Lower bounds on information transfer in distributed computations. In Proc. of 19th IEEE Symp. on Foundations of Computer Science (FOCS), 151–158, 1978.Google Scholar
- 2.F. Ablayev. Randomization and nondeterminism are incomparable for polynomial ordered binary decision diagrams. In Proc. of 24th Int. Coll. on Automata, Languages, and Programming (ICALP), LNCS 1256, 195–202. Springer, 1997.Google Scholar
- 3.F. Ablayev and M. Karpinski. On the power of randomized branching programs. In Proc. of 23rd Int. Coll. on Automata, Languages, and Programming (ICALP), LNCS 1099, 348–356. Springer, 1996.Google Scholar
- 6.B. Bollig and I. Wegener. Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. Theory of Computing Systems, 32:487–503, 1999. (Earlier version in Proc. of 22nd Int. Symp. on Mathematical Foundations of Computer Science (MFCS), LNCS 1295, 159–168. Springer, 1997.)zbMATHCrossRefMathSciNetGoogle Scholar
- 9.P. Ďuriš, Z. Galil, and G. Schnitger. Lower bounds on communication complexity. In Proc. of 16th Ann. ACM Symp. on Theory of Computing (STOC), 81–91, 1984.Google Scholar
- 10.P. Ďuriš, J. Hromkovič, J. D. P. Rolim, and G. Schnitger. Las Vegas versus determinism for one-way communication complexity, finite automata, and polynomial-time computations. In Proc. of 14th Ann. Symp. on Theoretical Aspects of Computer Science (STACS), LNCS 1200, 117–128. Springer, 1997. To appear in Information and Computation.Google Scholar
- 13.J. Hromkovič. Communication Complexity and Parallel Computing. EATCS Texts in Theoretical Computer Science. Springer, Berlin, 1997.Google Scholar
- 14.J. Hromkovič and G. Schnitger. Nondeterministic communication with a limited number of advice bits. In Proc. of 28th Ann. ACM Symp. on Theory of Computing (STOC), 551–560, 1996.Google Scholar
- 16.J. Jain, J. Bitner, J. A. Abraham, and D. S. Fussell. Functional partitioning for verification and related problems. In T. Knight and J. Savage, editors, Advanced Research in VLSI and Parallel Systems: Proceedings of the 1992 Brown/MIT Conference, 210–226, 1992.Google Scholar
- 22.K. Mehlhorn and E. Schmidt. Las-Vegas is better than determinism in VLSI and distributed computing. In Proc. of 14th Ann. ACM Symp. on Theory of Computing (STOC), 330–337, 1982.Google Scholar
- 24.M. Sauerhoff. Complexity Theoretical Results for Randomized Branching Programs. PhD thesis, Univ. of Dortmund. Shaker, 1999.Google Scholar
- 25.M. Sauerhoff. On the size of randomized OBDDs and read-once branching programs for k-stable functions. In Proc. of 16th Ann. Symp. on Theoretical Aspects of Computer Science (STACS), LNCS 1563, 488–499. Springer, 1999.Google Scholar
- 26.M. Sauerhoff. Computing with restricted nondeterminism: The dependence of the OBDD size on the number of nondeterministic variables. To appear in Proc. of FST & TCS.Google Scholar
- 27.I. Wegener. The Complexity of Boolean Functions. Wiley-Teubner, 1987.Google Scholar
- 28.I. Wegener. Branching Programs and Binary Decision Diagrams—Theory and Applications. Monographs on Discrete and Applied Mathematics. SIAM, 1999. To appear.Google Scholar
- 29.A. C. Yao. Some complexity questions related to distributive computing. In Proc. of 11th Ann. ACM Symp. on Theory of Computing (STOC), 209–213, 1979.Google Scholar