On the computational power of self-stabilizing systems

AbstractThe computational power of self-stabilizing distributed systems is examined. Assuming availability of any number of processors, each with (small) constant size memory we show that any computable problem can be realized in a self-stabilizing fashion.The result is derived by presenting a distributed system which tolerates transient faults and simulates the execution of a Turing machine. The total amount of memory required by the distributed system is equal to the memory used by the Turing machine (up to a constant factor)

Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits

This paper considers the basic $\mathcal{PULL}$ model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of $n$ agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let all agents converge their output bits on the most frequent input bit of the sources (the majority bit). Note that the particular case of a single source agent corresponds to the classical problem of Broadcast. We concentrate on the severe fault-tolerant context of self-stabilization, in which a correct configuration must be reached eventually, despite all agents starting the execution with arbitrary initial states. We first design a general compiler which can essentially transform any self-stabilizing algorithm with a certain property that uses $\ell$-bits messages to one that uses only $\log \ell$-bits messages, while paying only a small penalty in the running time. By applying this compiler recursively we then obtain a self-stabilizing Clock Synchronization protocol, in which agents synchronize their clocks modulo some given integer $T$, within $\tilde O(\log n\log T)$ rounds w.h.p., and using messages that contain $3$ bits only. We then employ the new Clock Synchronization tool to obtain a self-stabilizing Majority Bit Dissemination protocol which converges in $\tilde O(\log n)$ time, w.h.p., on every initial configuration, provided that the ratio of sources supporting the minority opinion is bounded away from half. Moreover, this protocol also uses only 3 bits per interaction.Comment: 28 pages, 4 figure

Evaluating Asymmetric Multicore Systems-on-Chip using Iso-Metrics

The end of Dennard scaling has pushed power consumption into a first order concern for current systems, on par with performance. As a result, near-threshold voltage computing (NTVC) has been proposed as a potential means to tackle the limited cooling capacity of CMOS technology. Hardware operating in NTV consumes significantly less power, at the cost of lower frequency, and thus reduced performance, as well as increased error rates. In this paper, we investigate if a low-power systems-on-chip, consisting of ARM's asymmetric big.LITTLE technology, can be an alternative to conventional high performance multicore processors in terms of power/energy in an unreliable scenario. For our study, we use the Conjugate Gradient solver, an algorithm representative of the computations performed by a large range of scientific and engineering codes.Comment: Presented at HiPEAC EEHCO '15, 6 page