George Varghese, Self-stabilization by local checking and correction, PhD thesis, MIT, 1993, Published as Technical Report MIT/LCS/TR-583.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... On linear chain and ring networks, the PIF scheme is solved by the TC algorithms (refer to Section 2) Although few papers discuss the problem of PIF in the area of self stabilization, self stabilizing PIF algorithms are proposed to solve a wide class of problems, e.g. leader election [DIM97, Var93] snapshot [Var94] global reset [AKY90, AG94, AKM 93, APSV91, Var94] synchronization [ABDT98, AKM 93, AV91] Except in [CDPV01b, Var94] all self stabilizing PIF algorithms in the current literature work on oriented spanning trees. So, to design a reset or snapshot protocol using these ....

....literature work on oriented spanning trees. So, to design a reset or snapshot protocol using these self stabilizing PIF algorithms, the PIF algorithms must be modi ed such that every processor sends messages to all its outgoing links, including the links which are not in the spanning tree [Var93] 3.1 Optimality of the PIF Scheme in Tree Networks As for the DFTC algorithms for trees presented above, all the algorithms presented in this subsection use the cleaner [Vil98] The rst self stabilizing PIF algorithm for un oriented tree networks is presented in [BDPV99b] providing the same ....

G Varghese. Self-stabilization by local checking and correction (Ph.D. thesis). Technical Report MIT/LCS/TR-583, MIT, 1993.

....reset procedure. The stabilization time of that protocol is O(n ) where n is the actual number of nodes in the system. In [DIM91] a randomized spanning tree protocol is implicitly given. That protocol stabilizes in expected time O(d log n) where d is the actual diameter of the network. In [APV91, Var92] a general self stabilizing reset protocol is presented, whose stabilization time is O(n) In [AV91] a self stabilizing synchronizer is presented. This protocol stabilizes in time linear in a pre specified bound on the diameter of the network. Our Results. The contribution of our paper is ....

....For each node v 2 V , we denote by N (v) its neighborhood, i.e. the set of nodes adjacent to v. In this abstract we assume the model of unit capacity data links, in which there is at most one outstanding message in transit on every channel at any given time. This model was defined and justified [APV91, Var92] as a realistic model for any message passing system with some bound on the capacity of the channels. The message delivery time can be arbitrary, but for the purpose of time analysis we assume that each message is delivered in one time unit. We use the method of local detection [AKY90, APV91, ....

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George Varghese. Self-Stabilization by Local Checking and Correction. PhD thesis, MIT Lab. for Computer Science, 1992.

....of Awerbuch [5] However, the algorithms in [5] are not self stabilizing. One approach to designing a self stabilizing synchronizer is to combine the protocol of [5] with any self stabilizing reset protocol [4,1,7] Self stabilizing synchronizers were proposed in [16,28,2] for tree networks, and [27,6,8] for general networks. PIFbased self stabilizing synchronizers were proposed in [10,11,21] for tree networks, and [13,28] for general graphs. The algorithms in [10,11,13] are snap stabilizing. In [17] Gouda and Haddix proposed a self stabilizing neighborhood synchronizer (which they referred to ....

G. Varghese. Self-stabilization by local checking and correction (Ph.D. thesis). Technical Report MIT/LCS/TR-583, MIT, 1993.

....s il n y a pas. 5.2.3 La propagation d information avec retour Le probl eme du PIF est equivalent au probl eme de la TC sur l anneau et sur la cha ne. De nombreux protocoles auto stabilisants de PIF ont et e apport es dans la r esolution de probl emes, comme l election de leader [DIM97b, Var93] la r e initialisation [AKY90, AG94, AKM 93] et la synchronisation [ABDT98, AKM 93, AV91] du syst eme. Tous ces travaux supposent la construction ou l existence d un arbre couvrant du r eseau. Dans le cas d un protocole de PIF seulement auto stabilisant, en fonction de l etat initial, une ....

G. Varghese. Self-stabilization by local checking and correction (Ph.D. thesis). Technical Report MIT/LCS/TR-583, MIT, 1993.

....petit laria.u picardie.fr. 1 Related Work. On linear chain networks, the self stabilizing PIF problem is solved by the self stabilizing TC algorithms [BGW89, BP89, Gho93, GH96, Vil99] Self stabilizing PIF algorithms for tree and arbitrary networks have been proposed in [BDPV99b, DIM97, Kru79, Var93] Self stabilizing PIF protocols have also been used in the area of synchronizers [ABDT98, AKM 93, AV91] Snap stabilizing PIF protocols for tree networks were proposed in [BDPV99c, BDPV99a] Except the algorithms in [Gho93, Vil99] all TC algorithms for linear chains work on an oriented ....

G Varghese. Self-stabilization by local checking and correction (Ph.D. thesis). Technical Report MIT/LCS/TR-583, MIT, 1993.

....arbitrary transient faults. A self stabilizing system, regardless of the initial states of the processors and initial messages in the links, is guaranteed to converge to the intended behavior in finite time. Related Work. PIF algorithms have been proposed in the area of self stabilization [7, 8, 9, 16, 18, 20, 21]. The self stabilizing PIF protocols have also been used in the area of self stabilizing synchronizers [2, 4, 6] The most general method to repair the system is to reset the entire system after a transient fault is detected. Reset protocols are also PIF based algorithms. Several reset protocols ....

....and Perry used the self stabilizing snapshot algorithm in designing a protocol that transforms non selfstabilizing to self stabilizing algorithms. In [14] the PIF scheme has been used to provide a distinct identifier to each (anonymous) processor of a uniform system (naming problem) Except in [20], all self stabilizing PIF algorithms in the current literature work on a rooted tree. These protocols assume an underlying self stabilizing rooted spanning tree construction algorithm, 1, 3, 4, 12, 15] So, to design a reset or snapshot protocol using these self stabilizing PIF algorithms, the ....

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G. Varghese. Self-stabilization by local checking and correction (Ph.D. thesis). Technical Report MIT/LCS/TR-583, MIT, 1993.

....if the system is properly initialized then the invariant is always satisfied and if the system is placed in an arbitrary state then continued execution of the system eventually reaches a state from where the invariant is always satisfied. Likewise, the generic methods for designing stabilization [1,3,12,18] also assume implementation specific details as input: 3, 12] assume the availability of the implementation invariant, 1] relies on the knowledge of the 0 Email: fanish,demirbasg cis.ohio state.edu, sandeep cse.msu.edu; Tel: 1 614 292 1836 ; Fax: 1 614 292 2911 ; Web: ....

....anish, demirbasg, http: www.cse.msu.edu sandeep ; This work was partially sponsored by NSA Grant MDA904 96 1 0111, NSF Grant NSF CCR 9972368, an Ameritech Faculty Fellowship, and grants from Microsoft Research and Michigan State University. implementation actions, and [18] takes as input a locally checkable consistency predicate derived from implementation. The apparently intimate connection between stabilization and the details of implementation has raised the following serious concerns: 1) Stabilization is not feasible for many applications whose ....

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G. Varghese. Self-stabilization by local checking and correction. PhD thesis, MIT/LCS/TR-583, 1993.

....period of time then the system converges into a consistent global state and can solve the task. A transient fault is a fault that causes the state of a process (its local state, programm counter and its shared variables) to change arbitrarily. More about self stabilization can be found in e.g. [7, 2, 9, 5, 4, 22]. So, if we want to sum it all up, the ideal clock synchronization algorithm that is highly resilient to failures must have the following characteristics: i) it must tolerate any number of processors napping faults like the authenticated Byzantine model but guarantees that the nonfaulty ....

G. Varghese. Self-Stabilization by Local Checking and Correction. Ph.D. Thesis, MIT Laboratory for Computer Science, 1992.

....if they fail. They do, however, allow channels to fail and the messages sent on those channels to be lost. Their program is not stabilizing tolerant. While little work has been done on bounded memory masking tolerant resets, bounded memory stabilizing tolerant resets have received more attention [2, 6, 7, 8, 9, 10, 11]. All of these programs are stabilizing tolerant to fail stops and repairs, but they are not masking tolerant to them. Specifically, in the presence of fail stops and repairs, they allow premature completion of distributed resets. Masuzawa has presented a reset program [12] that tolerates two ....

....may be determined dynamically, say by a checkpointing program. In our program, in stable states, the processes form a rooted tree and all reset operations are performed on this underlying tree. An alternative approach would be to construct the tree dynamically in every reset operation, as in [7, 6]. Analogous to their reset program, there exists a reset program that is masking tolerant to fail stop and repair faults and stabilizing tolerant to transient faults and that does not use an underlying tree. Finally, we reiterate that our assumption that the distributed reset request be initiated ....

G. Varghese. Self-stabilization by local checking and correction. PhD thesis, MIT/LCS/TR-583, 1993.

....Previous Work. Gouda and Multari [1] present an indepth study of stabilization in networks protocols, although the protocols they consider are not explicitly timing based. In fact, we have found only a few stabilizing protocols in the literature that are explicitly timing based. Varghese [2] discusses how propagation of information with feedback may be achieved in a stabilizing fashion using timing based actions on a tree network. He also refers to timing based stabilizing solutions for maintaining spanning trees (due to Perlman) data links and virtual circuits (due to Spinelli) ....

G. Varghese. Self-stabilization by local checking and correction Ph.D. Dissertation, 1992. Massachusetts Institute of Technology.

....have been studied extensively. Gallagher et al. [6] have presented an elegant solution but their solution is faultintolerant, i.e. their solution does not solve the spanning tree reconfiguration problem. More recently, stabilizing algorithms for spanning tree reconfiguration have been presented [2, 5, 7] that tolerate failures as well as repairs of both nodes and edges, but these programs are significantly more complex than RST, since they allow for the formation of transient cycles in the graph of the parent variables. Moreover, in the average case, these programs converge much slower than RST. ....

G. Varghese, "Self-stabilization by local checking and correction", Ph.D. Dissertation, Massachusetts Institute of Technology (1992).

....network edge, where n is the number of processors. 1. 3 Self stabilizing reset A general methodology for making protocols self stabilizing is to design a self stabilizing reset protocol which in case when something goes wrong can restart a system from a good initial state (see, for example, [AG90, KP90, APV91, Var 92]. Informally, the challenge (and the main technical difficulty) of designing a self stabilizing reset protocol is to ensure that even if something goes wrong during the execution of the reset protocol itself, this condition will be detected and corrected. Once this is accomplished, it is ....

....reset if it detects an error. Finally, self stabilizing reset and self stabilizing spanning tree protocols can be used as a general compiler which turn network protocols which work only in static networks and only with proper initialization into ones robust against both memory and link failures [KP90, APV91, AV91, Var 92]. We show how all of this can be done using only very small memory per processor. Our main technical contribution is a memory efficient and selfstabilizing reset protocol: 3 MAIN THEOREM: There exists a deterministic self stabilizing reset protocol for arbitrarytopology asynchronous uniform ....

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G. Varghese, Self-Stabilization by Local Checking and Correction, MIT LCS Ph.D. Thesis, 1992. 15

....a 1990 comment by Lamport and Lynch [4] that a solution for the distributed reset problem using a finite number of identifiers would be quite useful, but we know of no such algorithm . A few bounded space stabilizing solutions have been discovered since then by Arora and Gouda [2] and Varghese [5]. For the case of masking fault tolerant distributed resets, Afek and Gafni [6] have shown a masking fault tolerant solution with bounded sequence numbers, under the assumption that nodes may not fail but channels may fail and, thus, messages sent on these channels may be lost. As of this ....

....state need not be fixed apriori; it may be determined dynamically by, say, a checkpointing program. We note that although our reset program uses a tree that spans the up processes in the system, the use of a tree is not necessary. Analogous to the stabilizing reset program due to Varghese [5], there exists a reset program that is masking tolerant to fail stop and repair faults and stabilizing tolerant to transient faults, and does not use an underlying tree. Finally, in our reset program, the assumption that the distributed reset request is initiated only at the root process is not ....

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G. Varghese. Self-stabilization by local checking and correction. PhD thesis, MIT/LCS/TR-583, 1993.

....reset procedure. The stabilization time of that protocol is O(n 2 ) where n is the actual number of nodes in the system. In [DIM91] a randomized spanning tree protocol is implicitly given. That protocol stabilizes in expected time O(d log n) where d is the actual diameter of the network. In [APV91, Var92] a general self stabilizing reset protocol is presented, whose stabilization time is O(n) In [AV91] a self stabilizing synchronizer is presented. This protocol stabilizes in time linear in a pre specified bound on the diameter of the network. It is worth mentioning the important work of ....

....(G) max u;v2V fdist(u; v)g. For each node v 2 V , we denote N (v) fu : dist(u; v) 1g. In this abstract we assume the model of unit capacity data links, in which there is at most one outstanding message in transit on every channel at any given time. This model was defined and justified [APV91, Var92] as a realistic model for any message passing system with some bound on the capacity of the channels. The message delivery time can be arbitrary, but for the purpose of time analysis we assume that each message is delivered in one time unit. We use the method of local detection [AKY90, APV91, ....

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George Varghese. Self-Stabilization by Local Checking and Correction. PhD thesis, MIT Lab. for Computer Science, 1992.

....a good state by having each node periodically check and correct the state of the links to each of its neighbors. The idea of using local checking arises naturally from the solutions considered in this paper. Since then, we have generalized this method and applied it to a number of other problems [APV91, Var92]. The only previously known general technique [KP90] for self stabilization was based on global checking and correction in which a single leader node periodically checks the state of the entire network. Global checking and correction is typically more general but less efficient than local ....

....known general technique [KP90] for self stabilization was based on global checking and correction in which a single leader node periodically checks the state of the entire network. Global checking and correction is typically more general but less efficient than local checking and correction [Var92]. Interestingly enough, the end to end problem is one problem where global correction is inapplicable while local correction is applicable For example, if the method of [KP90] is applied to a fail stop network, the global check may may never terminate. Although local checking may also not ....

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George Varghese. Self-stabilization by local checking and correction. Ph.D. thesis, to appear as a LCS Technical Report, 1992.

..... Hence, by Lemma 6.7, the x values of all processes are identical. It follows that when 0 executes for the first time after state s, corr pred is true. 7 Discussion Related work. Since Dijkstra presented the selfstabilizing token ring program in 1974, it has been proved using various techniques [1, 6, 10, 13, 15]. Of these, the proofs by Qadeer and Shankar [13] and Merz [10] have been verified by a theorem prover. Merz constructs a complicated variant function consisting of the enabled processes, the distance between the x value of the process 0 and the missing value, etc. and shows that it decreases ....

....However, these reduced interactions come at a very high cost; the creativity required to find this variant function. Also, that proof is hard to comprehend since it does not match with the intuitive understanding of the token ring program. Qadeer and Shankar closely follow the proof by Varghese [15], and their proof is simpler than that by Merz. However, since they try to prove the properties of the entire program, some of their proofs are more complex than they need to be. For example, they prove that each process eventually gets the token using the following variant: p(j) sumfk : k has a ....

G. Varghese. Self-stabilization by local checking and correction.

....state to a legitimate global state in a bounded amount of time with no external intervention. Throughout this paper, we will use this definition of a self stabilizing algorithm. Another way of defining a self stabilizing distributed algorithm is in terms of behavior sequences, as discussed in [18]. In the distributed paradigm, self stabilization is gaining increasing attention because it provides a formal and unified view of fault tolerance [17] A number of recent papers have developed self stabilizing algorithms for a variety of problems [1, 3, 10, 11, 14, 15] It is easy to see that if ....

G. Varghese. Self-Stabilization by local checking and correction. PhD thesis, M.I.T, 1992.

....control subsystem. The first step, detection, can be thought of as an online process that gives indication of malfunctioning. Real time detection mechanisms are usually implemented within the network protocols and devices. For example, protocol errors can be detected by finite state machines [1] [3]. The second step, consists of fault localization and identification. Fault localization is typically achieved through algorithms that compute a possible set of faults while fault identification is done by testing the hypothetical faulty component(s) The last step, repair is achieved by taking ....

G. Varghese, Self-Stabilization by Local Checking and Correction. PhD thesis, Massachusetts Institute of Technology, Cambridge, Mass., Oct. 1992.

....set of behaviors) An IOA A stabilizes to the behaviors in P if for every behavior fi of A there is a suffix of fi that is in P . Similarly, we can specify that A stabilizes to the behaviors of some other automaton B in the same way. The behavior stabilization definition used in this section and [Var92b] is a special case of a definition suggested by Nancy Lynch. Finally, we have a simple lemma that ties together the execution and behavior stabilization definitions. It states that execution stabilization implies behavior stabilization. 13 In fact, the only method we know to prove a behavior ....

....that this way of understanding his example is clearer and illustrates a general method. The general method of local checking and correction was first introduced in [APV91b] 4. 3 Dijkstra s first example as Counter Flushing The counter flushing paradigm described in this section is taken from [Var92b]. Dijkstra s first example is modelled by the automaton D2 shown in Figure 10. As in the previous example, the nodes (once again numbered from 0 to n Gamma 1) are arranged such that node 1 has node 0 and node 2 as its neighbors and so on. However, in this case we also assume that Process 0 and n ....

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George Varghese. Self-stabilization by local checking and correction. Ph.D. thesis, to appear as a LCS Technical Report, 1992. 67

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George Varghese, Self-stabilization by local checking and correction, PhD thesis, MIT, 1993, Published as Technical Report MIT/LCS/TR-583.

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G. Varghese. Self-Stabilization by Local Checking and Corrections. PhD thesis, MIT, 1992. 9

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George Varghese, Self-stabilization by local checking and correction, PhD thesis, MIT, 1993, Published as Technical Report MIT/LCS/TR-583.

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G Varghese. Self-stabilization by local checking and correction (Ph.D. thesis). Technical Report MIT/LCS/TR-583, MIT, 1993. 14

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G. Varghese, "Self-Stabilization by local checking and correction", Ph.D. thesis, 1992.

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George Varghese. Self-Stabilization by Local Checking and Correction. PhD thesis, MIT Lab. for Computer Science, 1992. 117

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