## On Distributed Verification (2006)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Korman06ondistributed,

author = {Amos Korman and Shay Kutten},

title = {On Distributed Verification},

year = {2006}

}

### OpenURL

### Abstract

This paper describes the invited talk given at the 8th International

### Citations

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Citation Context ...state is not a trivial task even in a non- self stabilizing network, since in an asynchronous network local states are collected in different times, and may thus not be parts of the same global state =-=[11]-=-.) In terms of complexity, note, first, that the time complexity of the verification task above was linear in the number of nodes. Clearly, the communication cost for the above approach may be large. ... |

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Citation Context ...r, Dijkstra’s solution involves changes in the states of all the processors, as well as time that is long enough for all of them to be involved in the computation. (Moreover, a causal chain of events =-=[18]-=- of length Ω(n), where n is the number of the processors, may result.) A part of the elegance in Dijkstra’s algorithms was that they never really detected an illegal state. Instead, when the network w... |

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Citation Context .... This is different than what is assumed e.g. in [31]. We note that the following lemma also demonstrates a connection between the notion of proof labeling scheme and that of communication complexity =-=[43]-=-. Lemma 2. [40] The proof size of F all S and fAgreement is Θ(m). Proof. We first describe a trivial proof labeling scheme π = 〈M, D〉 of the desired size m. GivenGs such that fAgreement(Gs) = 1, for e... |

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Citation Context ...e number os nodes) but they too suggested, at least implicitly, the distributed verification of cycle freedom described in Section 3, see the work by Dolev, Israeli, and Moran, and by Arora and Gouda =-=[13, 4]-=-. The notion of local checking was presented in [9]. It bears similarities to the notion of local detection. Instead of a local predicate involving a node and all its neighbors, the local predicates i... |

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Citation Context ...of the graph. This MST verification problem was introduced by Tarjan in the sequential model. A linear time algorithm for computing an MST is known only in certain cases, or by a randomized algorithm =-=[35,37]-=-. On the other hand, the sequential verification algorithm of [34] is (edge) linear. In the context of distributed tasks, other measures of complexity are used, e.g., communication complexity. Still, ... |

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Citation Context ...family with a smaller proof size. The following example concerns the representation of various spanning trees in the system. The upper bound employs structures and ideas used in many papers including =-=[3, 5, 31, 14, 4,40]-=-. The lower bound is taken from [40]. A lower bound in the different model of silent stabilization for one of the tasks below was presented in [32]. Consider five different problems, obtained by assig... |

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Citation Context ...predicate involving a node and all its neighbors, the local predicates in [9] are defined over the two endpoints of one edge. This has a potential of simplifying algorithms using these predicates. In =-=[7]-=-, Awerbuch, Patt-Shamir, and Varghese extended the methodology of local detection and global correction to local detection and local correction. The methodology is applied in [7] to develop self-stabi... |

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Citation Context ...of the graph. This MST verification problem was introduced by Tarjan in the sequential model. A linear time algorithm for computing an MST is known only in certain cases, or by a randomized algorithm =-=[35,37]-=-. On the other hand, the sequential verification algorithm of [34] is (edge) linear. In the context of distributed tasks, other measures of complexity are used, e.g., communication complexity. Still, ... |

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Citation Context ...oduction This paper addresses the problem of locally verifying global properties. This task complements the task of locally computing global functions. Since many functions cannot be computed locally =-=[29, 42, 41]-=-, local verification may prove more useful than local computing - one can compute globally and verify locally. In terms of sequential time, there exists evidence that verification is sometimes easier ... |

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Citation Context ...family with a smaller proof size. The following example concerns the representation of various spanning trees in the system. The upper bound employs structures and ideas used in many papers including =-=[3, 5, 31, 14, 4,40]-=-. The lower bound is taken from [40]. A lower bound in the different model of silent stabilization for one of the tasks below was presented in [32]. Consider five different problems, obtained by assig... |

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Citation Context ...en stronger than in a sequential one. A common application of local distributed verification is in the context of self stabilization. See, for example, the local detection [31], or the local checking =-=[9]-=-, or the silent stabilization [32]. Self stabilization deals with algorithms that must cope with faults that are rather sever, though of a type that does occur in reality [27, 28]. The faults may caus... |

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Citation Context ...family with a smaller proof size. The following example concerns the representation of various spanning trees in the system. The upper bound employs structures and ideas used in many papers including =-=[3, 5, 31, 14, 4,40]-=-. The lower bound is taken from [40]. A lower bound in the different model of silent stabilization for one of the tasks below was presented in [32]. Consider five different problems, obtained by assig... |

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Citation Context ...e are communicated to larger distances. A specific subset of problems allows for a specific kind of self stabilization called silent stabilization. These are studied in Dolev, Gouda, and Schneider in =-=[32]-=-. Informally, when silent stabilization is obtained, the only activity a processor can be involved in is collecting the state information of its neighbors that appear in its local predicates, and comp... |

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Citation Context ...in the sequential model. A linear time algorithm for computing an MST is known only in certain cases, or by a randomized algorithm [35,37]. On the other hand, the sequential verification algorithm of =-=[34]-=- is (edge) linear. In the context of distributed tasks, other measures of complexity are used, e.g., communication complexity. Still, one can ask a similar natural question. Given S. Chaudhuri et al. ... |

53 |
A belated proof of self-stabilization
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Citation Context ...ibuted verification, in addition to its theoretical interest, can be very useful for the design of such algorithms. The notion of self stabilization was suggested by Dijkstra in 1974 ( [10], see also =-=[12]-=-). Dijkstra’s paper later won the ACM-PODC influential paper award, that shortly after that became the Dijkstra Prize in Distributed Computing awarded by the ACM (the Association for Computing Machine... |

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Citation Context ...overy step). A distributedsOn Distributed Verification 111 reset protocol restarts the base algorithm from a predetermined initial state. It was observed by Awerbuch, Patt-Shamir, Varghese, and Dolev =-=[8]-=- that it is not trivial to show that a general self stabilizing reset algorithm together with local detection can perform the transformation of any algorithm to a self stabilizing one correctly. Howev... |

40 | Self-stabilization over unreliable communication media
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Citation Context ...hm L and a vertex vs ∈ Gs, letN ′ L (v) beasetofn(v) fields, one per neighbor. Each field e =(v, u) inN ′ L (v), corresponding to edge e ∈ N(v), contains the following. (1) The port number of e in v; =-=(2)-=- the weight of e (if G is unweighted we regard each edge as having weight 1); (3) L(u). Let NL(v) =〈(sv,L(v)),N ′ L (v)〉. Informally, N ′ L (v) contains the labels given to all of v’s neighbors along ... |

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Citation Context ... with neighboring nodes. In the construction, h is the hight of the hypertree and μ is the weight of the weight of some edges that are crucial for the MST. That proof follows the general structure of =-=[39]-=- in the sense that labels for some (h − 1,μ 2 )-hypertree H ′ are computed using the labels for some (h, μ)-hypertree H. However, the specifics are more complex and require some new tricks. For exampl... |

31 | Fast and lean self-stabilizing asynchronous protocol
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Citation Context ... and network reset. As described above, the verification step using the method of [16] consumes Ω(n) time, while the verification using e.g. the approach of [31] takes O(1) time. Methods suggested in =-=[20,15,6,21,19]-=- to detect cycles sacrificed some time efficiency in order to reduce the total sizes of variables used in the local predicates compared to that of [31]. This suggests the existence of a size- time tra... |

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Citation Context ...e will be given by the ACM and EATCS (the European Association for Theoretical Computer Science). It took some years until the importance of that paper became evident, as highlighted first by Lamport =-=[17]-=-. However, since then, a lot of attention has been invested in self stabilization, and this sub-area now even has its own conference (SSS). In the above mentioned paper, Dijkstra studied the example o... |

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Citation Context ... and network reset. As described above, the verification step using the method of [16] consumes Ω(n) time, while the verification using e.g. the approach of [31] takes O(1) time. Methods suggested in =-=[20,15,6,21,19]-=- to detect cycles sacrificed some time efficiency in order to reduce the total sizes of variables used in the local predicates compared to that of [31]. This suggests the existence of a size- time tra... |

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Citation Context ...buted setting seems to be even stronger than in a sequential one. A common application of local distributed verification is in the context of self stabilization. See, for example, the local detection =-=[31]-=-, or the local checking [9], or the silent stabilization [32]. Self stabilization deals with algorithms that must cope with faults that are rather sever, though of a type that does occur in reality [2... |

22 |
Non-Exploratory Self-Stabilization for Constant-Space Symmetry-Breaking
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Citation Context ... and network reset. As described above, the verification step using the method of [16] consumes Ω(n) time, while the verification using e.g. the approach of [31] takes O(1) time. Methods suggested in =-=[20,15,6,21,19]-=- to detect cycles sacrificed some time efficiency in order to reduce the total sizes of variables used in the local predicates compared to that of [31]. This suggests the existence of a size- time tra... |

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Crash failures can drive protocols to arbitrary states
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Citation Context ...1], or the local checking [9], or the silent stabilization [32]. Self stabilization deals with algorithms that must cope with faults that are rather sever, though of a type that does occur in reality =-=[27, 28]-=-. The faults may cause the states of different nodes to be inconsistent with each other. For example, the collection of pointed edges may not be a tree, or may not be an MST. Self stabilizing algorith... |

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Citation Context ...dicting the fact that the pointed edges in G3 do not form a tree. ⊓⊔ In order to deal with verification tasks such as verifying spanning trees, the concept of proof labeling schemes was introduced in =-=[40]-=-. The formal definitions are given in Section 2. Informally, it is assumed that the state of every node has already been computed by some algorithm (in the above example, the state may consist of a po... |

19 | Distributed verification of minimum spanning trees
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Citation Context ...n the spirit of the proof of lemma 2 was then used in [40] to increase this lower bound to Ω(log n +logW )whereW is the maximum weight of an edge in the graph. This lower bound was later increased in =-=[38]-=- to Ω((log n log W )). The proof of the lower bound in [38] is quiet involved. It uses a new combinatorial structure termed (h, μ)-hypertrees that is a combination between (h, μ)-trees and a hypercube... |

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Citation Context ...for designing self stabilizing algorithms directly for several tasks such as shortest paths, topology update, leader election, and computing the maximum flow. Beauquier, Delaet, Dolev, and Tixeuil(in =-=[33]-=-) assumed that only the part of the state meant to be visible to the outside can be read by other nodes. (The output is the part that appears in the specification of the task to be performed.) It was ... |

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a continuation extension for
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Citation Context ...legal state, and then stayed in the set of legal states. This was also a characteristic of many later algorithms. While elegant, this approach makes the design of algorithms difficult. Katz and Perry =-=[16]-=- suggested a method of partitioning the design of self stabilizing algorithms: 1. Design an algorithm- the base algorithm, that is not necessarily self stabilizing (this implies a definition of the le... |

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Citation Context ...1], or the local checking [9], or the silent stabilization [32]. Self stabilization deals with algorithms that must cope with faults that are rather sever, though of a type that does occur in reality =-=[27, 28]-=-. The faults may cause the states of different nodes to be inconsistent with each other. For example, the collection of pointed edges may not be a tree, or may not be an MST. Self stabilizing algorith... |

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Citation Context ...oduction This paper addresses the problem of locally verifying global properties. This task complements the task of locally computing global functions. Since many functions cannot be computed locally =-=[29, 42, 41]-=-, local verification may prove more useful than local computing - one can compute globally and verify locally. In terms of sequential time, there exists evidence that verification is sometimes easier ... |

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