Information Processing Letters
Two time-space tradeoffs for element distinctness
Theoretical Computer Science
An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
Trade-offs between communication and space
Journal of Computer and System Sciences
Communication-Space Tradeoffs for UnrestrictedProtocols
SIAM Journal on Computing
The linear-array problem in communication complexity resolved
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity
Power of Cooperation and Multihead Finite Systems
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Communication Complexity for Asynchronous Systems of Finite Devices
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Communication Gap for Finite Memory Devices
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Restarting automata with restricted utilization of auxiliary symbols
Theoretical Computer Science - Implementation and application of automata
Two-party Watson-Crick computations
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
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We consider systems consisting of a finite number of finite automata which communicate by sending messages. We consider number of messages necessary to recognize a language as a complexity measure of the language. We feel that these considerations give a new insight into computational complexity of problems computed by read-only devices in multiprocessor systems. Our considerations are related to multiparty communication complexity, but we make a realistic assumption that each party has a limited memory. We show a number of hierarchy results for this complexity measure: for each constant k there is a language, which may be recognized with k+1 messages and cannot be recognized with k-1 messages. We give an example of a language that requires Θ(log log n) messages and claim that Ω(log log(n)) messages are necessary, if a language requires more than a constant number of messages. We present a language that requires Θ(n) messages. For a large family of functions f, f(n) = ω(log log n), f(n) = o(n), we prove that there is a language which requires Θ(f(n)) messages. Finally, we present functions that require ω(n) messages.