Locality and checkability in wait-free computing

@article{Fraigniaud2013LocalityAC,
  title={Locality and checkability in wait-free computing},
  author={Pierre Fraigniaud and Sergio Rajsbaum and Corentin Travers},
  journal={Distributed Computing},
  year={2013},
  volume={26},
  pages={223-242}
}
This paper studies notions of locality that are inherent to the specification of distributed tasks by identifying fundamental relationships between the various scales of computation, from the individual process to the whole system. A locality property called projection-closed is identified. This property completely characterizes tasks that are wait-free checkable, where a task $$T =(\mathcal{I },\mathcal{O },\varDelta )$$T=(I,O,Δ) is said to be checkable if there exists a distributed algorithm… 

Space-Time Tradeoffs for Distributed Verification

The notion of a "t-PLS" is introduced, which allows the verification procedure to run for super-constant time, and an optimal tradeoff for testing that a network is acyclic (cycle free).

A hierarchy of local decision

It is shown that, by using distributed decision mechanisms based on the interaction between a prover and a disprover, the size of the certificates distributed to the nodes for certifying a given network property can be drastically reduced.

Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

In non-deterministic distributed decision each process is given an input value, and the processes should collectively decide whether their set of input values is a valid state of the system w.r.t. to some specification.

Announcement : Space-Time Tradeoffs for Distributed Verification

This paper constructs a universal t-PLS and proves that it uses the same amount of total communication as a known one-round universal PLS, and t factor smaller labels, and describes a recursive O(log∗ n) space verifier for acyclicity which does not assume previous knowledge of the run-time t.

Brief Announcement: Space-Time Tradeoffs for Distributed Verification

This paper constructs a universal t-PLS and proves that it uses the same amount of total communication as a known one-round universal PLS, and t factor smaller labels, and describes a recursive O(log* n) space verifier for acyclicity which does not assume previous knowledge of the run-time t.

Local Decision and Verification with Bounded-Size Outputs

This paper provides separation results between distributed decision and verification classes, and the size of the certificates enabling to verify distributed languages is analyzed.

What can be decided locally without identifiers?

The conjecture that identifiers are not needed in any decision problem is disproved, and it is shown that under all other combinations there are properties that can be decided locally if and only if identifiers are present.

Distributed Decision Problems: Concurrent Specifications Beyond Binary Relations

It is argued here that there is no need to go all the way to non-terminating interaction, to appreciate how different distributed computation is from sequential computation.

Distributed Testing of Excluded Subgraphs

It is shown that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too, and it is proved that both DFS and BFS testers fail to test \(K_k\)-freeness and \(C_k\) in a Constant number of Rounds for \(k\ge 5\).

References

SHOWING 1-10 OF 61 REFERENCES

Local Distributed Decision

It turns out that it is the combination of randomization with non-determinism that enables to decide all languages in constant time, and this helps to establish some structural results inspired by classical complexity theory.

The decidability of distributed decision tasks (extended abstract)

This paper gives the first necessary and sufficient conditions for task decidability in a range of different models and resilience levels and proves undecidability by exploiting classical decidabilit y results from algebraic topology.

Fast and compact self-stabilizing verification, computation, and fault detection of an MST

It is shown that optimizing the memory size carries at most a small cost in terms of time, in the context of minimum spanning tree (MST), and presents algorithms that are both time and space efficient for both constructing an MST and for verifying it.

Toward more localized local algorithms: removing assumptions concerning global knowledge

This paper provides a method for transforming a non-uniform local algorithm into a uniform one and introduces a new distributed tool called pruning algorithms, which it believes may be of independent interest.

Proof labeling schemes

The approach separates the configuration design from the verification, which allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.

Locally checkable proofs

It is shown that the proof complexities form a natural hierarchy of complexity classes: for many classical graph problems, the proof complexity is either 0, (1), (log n), or poly(n) bits per node.

A modular approach to shared-memory consensus, with applications to the probabilistic-write model

  • J. Aspnes
  • Computer Science
    Distributed Computing
  • 2011
It is shown that consensus can be solved by an alternating sequence of adopt-commit objects, and a randomized conciliator for any number of values in the probabilistic-write model with n processes that guarantees agreement with constant probability is given.

Locality in Distributed Graph Algorithms

  • N. Linial
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1992
This model focuses on the issue of locality in distributed processing, namely, to what extent a global solution to a computational problem can be obtained from locally available data.

Wait-free synchronization

A hierarchy of objects is derived such that no object at one level has a wait-free implementation in terms of objects at lower levels, and it is shown that atomic read/write registers, which have been the focus of much recent attention, are at the bottom of the hierarchy.

The BG distributed simulation algorithm

A shared memory algorithm that allows a set of f+1 processes to wait-free “simulate” a larger system of n processes, that may also exhibit up to f stopping failures, satisfies the requirements of a fault-tolerant distributed simulation.
...