On the Bit Complexity of Iterated Memory
🤖 AI Summary
This work investigates the minimal memory capacity—measured in bits per IIS element—required to simulate full-information protocols in the Iterated Immediate Snapshot (IIS) model while preserving isomorphic equivalence. We establish the first bit-level complexity framework for iterative memory, integrating information theory, state complexity of deterministic finite automata, and bit-sensitive computational modeling to characterize tight trade-offs among time, space, and precision. We derive exact bit-complexity upper and lower bounds for fundamental iterative tasks—including consensus and snapshot read/write—demonstrating that their memory requirements grow exponentially with the number of iterations. Our core contribution lies in identifying information-theoretic bottlenecks inherent in state compression and reuse, thereby establishing fundamental bit-level computability boundaries for distributed iterative computation.
Application Category
Problem
Research questions and friction points this paper is trying to address.
Determine minimal memory capacity
Simulate full-information protocol rounds
Bit complexity per process requirement
Innovation
Methods, ideas, or system contributions that make the work stand out.
Minimal memory capacity simulation
Bit complexity per process
Iterated immediate snapshot model
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