Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Tradeoffs between communication and space
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Monotone circuits for matching require linear depth
Journal of the ACM (JACM)
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The entropic limitations on VLSI computations(Extended Abstract)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh 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
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Tight Lower Bounds for the Distinct Elements Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Communication-space tradeoffs for unrestricted protocols
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
Communication Complexity with Synchronized Clocks
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Non-uniform ACC Circuit Lower Bounds
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Property Testing Lower Bounds via Communication Complexity
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
The cell probe complexity of dynamic range counting
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Streaming and communication complexity of clique approximation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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In the past thirty years, Communication Complexity has emerged as a foundational tool to proving lower bounds in many areas of computer science. Its power comes from its generality, but this generality comes at a price---no superlinear communication lower bound is possible, since a player may communicate his entire input. However, what if the players are limited in their ability to recall parts of their interaction? We introduce memory models for 2-party communication complexity. Our general model is as follows: two computationally unrestricted players, Alice and Bob, each have s(n) bits of memory. When a player receives a bit of communication, he "compresses" his state. This compression may be an arbitrary function of his current memory contents, his input, and the bit of communication just received; the only restriction is that the compression must return at most s(n) bits. We obtain memory hierarchy theorems (also comparing this general model with its restricted variants), and show super-linear lower bounds for some explicit (non-boolean) functions. Our main conceptual and technical contribution concerns the following variant. The communication is one-way, from Alice to Bob, where Bob controls two types of memory: (i) a large, oblivious memory, where updates are only a function of the received bit and the current memory content, and (ii) a smaller, non-oblivious/general memory, where updates can be a function of the input given to Bob. We exhibit natural protocols where this semi-obliviousness shows up. For this model we also introduce new techniques through which certain limitations of space-bounded computation are revealed. One of the main motivations of this work is in understanding the difference in the use of space when computing the following functions: Equality (EQ), Inner Product (IP), and connectivity in a directed graph (REACH). When viewed as communication problems, EQ can be decided using 0 non-oblivious bits (and log2 n oblivious bits), IP requires exactly 1 non-oblivious bit, whereas for REACH we obtain the same lower bound as for IP and conjecture that the actual bound is Omega(log2 n). In fact, proving that 1 non-oblivious bit is required becomes technically sophisticated, and the question even for 2 non-oblivious bits for any explicit boolean function remains open.