97 research outputs found
Simple and Efficient Local Codes for Distributed Stable Network Construction
In this work, we study protocols so that populations of distributed processes
can construct networks. In order to highlight the basic principles of
distributed network construction we keep the model minimal in all respects. In
particular, we assume finite-state processes that all begin from the same
initial state and all execute the same protocol (i.e. the system is
homogeneous). Moreover, we assume pairwise interactions between the processes
that are scheduled by an adversary. The only constraint on the adversary
scheduler is that it must be fair. In order to allow processes to construct
networks, we let them activate and deactivate their pairwise connections. When
two processes interact, the protocol takes as input the states of the processes
and the state of the their connection and updates all of them. Initially all
connections are inactive and the goal is for the processes, after interacting
and activating/deactivating connections for a while, to end up with a desired
stable network. We give protocols (optimal in some cases) and lower bounds for
several basic network construction problems such as spanning line, spanning
ring, spanning star, and regular network. We provide proofs of correctness for
all of our protocols and analyze the expected time to convergence of most of
them under a uniform random scheduler that selects the next pair of interacting
processes uniformly at random from all such pairs. Finally, we prove several
universality results by presenting generic protocols that are capable of
simulating a Turing Machine (TM) and exploiting it in order to construct a
large class of networks.Comment: 43 pages, 7 figure
Self-Assembly of Infinite Structures
We review some recent results related to the self-assembly of infinite
structures in the Tile Assembly Model. These results include impossibility
results, as well as novel tile assembly systems in which shapes and patterns
that represent various notions of computation self-assemble. Several open
questions are also presented and motivated
Simple and efficient local codes for distributed stable network construction
In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction, we keep the model minimal in all respects. In particular, we assume finite-state processes that all begin from the same initial state and all execute the same protocol. Moreover, we assume pairwise interactions between the processes that are scheduled by a fair adversary. In order to allow processes to construct networks, we let them activate and deactivate their pairwise connections. When two processes interact, the protocol takes as input the states of the processes and the state of their connection and updates all of them. Initially all connections are inactive and the goal is for the processes, after interacting and activating/deactivating connections for a while, to end up with a desired stable network. We give protocols (optimal in some cases) and lower bounds for several basic network construction problems such as spanning line, spanning ring, spanning star, and regular network. The expected time to convergence of our protocols is analyzed under a uniform random scheduler. Finally, we prove several universality results by presenting generic protocols that are capable of simulating a Turing Machine (TM) and exploiting it in order to construct a large class of networks. We additionally show how to partition the population into k supernodes, each being a line of logk nodes, for the largest such k. This amount of local memory is sufficient for the supernodes to obtain unique names and exploit their names and their memory to realize nontrivial constructions
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