Meanders and their applications in lower bounds arguments
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Relations between communication complexity classes
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Monotone circuits for matching require linear depth
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Relativized counting classes: relations among thresholds, parity, and mods
Journal of Computer and System Sciences
Complexity classes defined by counting quantifiers
Journal of the ACM (JACM)
On oblivious branching programs of linear length
Information and Computation
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
Non-deterministic communication complexity with few witnesses
Journal of Computer and System Sciences
Geometric arguments yield better bounds for threshold circuits and distributed computing
Theoretical Computer Science
Communication complexity
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Complete Classifications for the Communication Complexity of Regular Languages
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Information Processing Letters
Information Processing Letters
On Toda's Theorem in Structural Communication Complexity
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Information Processing Letters
On covering and rank problems for boolean matrices and their applications
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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We develop upper and lower bound arguments for counting acceptance modes of communication protocols. A number of separation results for counting communication complexity classes is established. This extends the investigation of the complexity of communication between two processors in terms of complexity classes initiated by Babai et al. (Proceedings of the 27th IEEE FOCS, 1986, pp. 337-347) and continued in several papers (e.g., J. Comput. System Sci. 41 (1990) 402; 49 (1994) 247; Proceedings of the 36th IEEE FOCS, 1995, pp. 6-15). In particular, it will be shown that for all pairs of distinct primes p and q the communication complexity classes MODpPcc and MODqPcc are incomparable with regard to inclusion. The same is true for PPcc and MODmPcc, for any number m≥2. Moreover, non-determinism and modularity are incomparable to a large extend. On the other hand, if m=p1l1'...' prlr is the prime decomposition of m≥ 2, then the complexity classes MODmPcc and MODρ(m)Pcc coincide, where ρ(m)=p1'...'pr. The results are obtained by characterizing the modular and probabilistic communication complexity in terms of the minimum rank of matrices ranging over certain equivalence classes. Methods from algebra and analytic geometry are used. This paper is the completely revised and strongly extended version of the conference paper Damm et al. (Proc. 9th Ann. STACS, pp. 281-291) where a subset of the results was presented.