Michael Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM Journal on Computing, 29(5):1449--1483, March 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....always decide on at most k different values. In an asynchronous read write shared memory system of n processes where at most f can crash, k set agreement protocols have been designed for f k [10] It has then been shown that the k set agreement problem cannot be solved in systems in which f k ([6, 18, 27] for f = n Gamma 1 and [7] extends it to arbitrary f ) Thus, the degree of achievable agreement in an asynchronous system is related to the number of faults tolerated. In this paper we present condition based k set agreement protocols that work even if f k. We also identify conditions for which ....

Saks M. and Zaharoglou F., Wait-Free k-Set Agreement is Impossible: the Topology of Public Knowledge. Proc. 25th ACM Symposium on Theory of Computation, California (USA), pp. 101-110, 1993.

....to the k set agreement problem enables conversion of an arbitrary k fault tolerant n process solution for the k set agreement problem into a wait free k 1 process solution for the same problem. Since the k 1 process k set agreement problem has been shown to have no wait free solution [5, 18, 26], this transformation implies that there is no k fault tolerant solution to the n process k set agreement problem, for any n. More generally, the algorithm satis es the requirements of a fault tolerant distributed simulation. The distributed simulation implements a notion of fault tolerant ....

....into a waitfree k 1 process solution for the same problem. A wait free algorithm is one in which any non failing process terminates, regardless of the failure of any number of the other processes. Since the k 1 process k set agreement problem has been shown to have no wait free solution [5, 18, 26], this transformation implies that there is no k fault tolerant solution to the n process k set agreement problem, for any n. As another application, we show how the BG simulation algorithm can be used to obtain results of [12, 16] about the computability of some decision problems. Other ....

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M. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: The topology of public knowledge, In Proceedings of the

....are being used more and more as coordination devices, making standard (Turing) notions of computability and complexity insufficient for evaluating their behaviour in our mostly asynchronous world. In the last few years, techniques of modeling and analysis based on classical algebraic topology [8, 12, 15, 18, 22, 21, 23, 24, 25, 26, 35] in conjunction with distributed simulation methods [12, 11, 10, 30] have brought about significant progress in our understanding of computability problems in an asynchronous distributed setting. We feel the time is ripe to extend these techniques to address asynchronous complexity. This paper ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is im- possible: The topology of public knowledge. In Proceedings of the 1993.

....is a run of B in which some process performs d c s( operations on csk. The proof uses the following claim: Claim 3 Given an algorithm B with parameter d as above, then there is a (k Gamma 1) set consensus algorithm, B , for b d 1 c processes, that uses only atomic registers. From [3, 10, 19] we know that the l set consensus problem cannot be solved with atomic registers for l n. Hence, by the claim (k Gamma 1) b d 1 c, or d log k Gamma1 (b d 1 c) log k Gamma1 ( log k Gamma1 (n) Gamma log k Gamma1 2(d 1) Thus d = Omega Gamma181 k Gamma1 (n) because, lim ....

....records the 10 sequence of values it believes the csk had. Each emulated write to an atomic register by a virtual process is tagged by the value of the history of the corresponding emulator at the time of the write. Proof: The reduction actually emulates a full information version of algorithm B [3, 8, 10, 19]. Every atomic register A is replaced by a list that holds all the values that have ever been written to the register (single writer ) Each value written is tagged with the history of the writing emulator and is appended to the register. As old histories of an emulator are always a prefix of its ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proc. 25th ACM Symp. on Theory of Computing, May 1993.

....As we did in [1] we employ the reduction by emulation idea. That is, assume by way of contradiction that there is such a LE algorithm, A. We show how to use A to construct an l set consensus algorithm, B, among m l processes that uses only read write registers. Such an algorithm is impossible by [4, 11, 21]. In this paper we present a new emulation for the reduction which is much more sophisticated and involved than the one we have in [1] Claim 1 If there is a LE algorithm A among ) processes using one compare swap (k) and any number of atomic registers, then there is a (k Gamma 1) set ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proc. 25th ACM Symp. on Theory of Computing, May 1993.

....our setting from Alice and Bob to k parties, and the difference is that now the keys are given as outcomes of a random variable, rather than being pre set. In this abstract we concentrate on the two party case, without faulty parties. Like the methods for distributed consensus lower bounds in [5, 3, 25, 10, 11], our lower bounds use a form of Sperner s Lemma, but with the difference that the nodes in the simplicial complex used are labeled by random variables, rather than by processor IDs and features of local communication graphs (see [5] or views in [3] Our work also differs from that of Maurer ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proc. 25th STOC, pages 101--110, 1993.

....(as well as in the present work) is of combinatorial nature. Despite the added power of randomization, the characterizations and their proofs are fairly simple and yield e#ective procedures for testing solvability. This stands in sharp contrast to the recent works on deterministic solvability [8, 18, 27], which develop a methodology for characterizing decision tasks that are t resilient with respect to deterministic protocols (without built in consensus) These works are fairly complicated, use topological tools, and do not seem to yield e#ective characterization procedures. To the best of our ....

M. Saks and F. Zaharoglou, Wait-Free k-set Agreement is Impossible: The Topology of Public Knowledge, in Proceedings of 25th Symposium on the Theory of Computing, 1993, pp. 111--120.

....achieved, a contradiction. Observe the similarity between the mapping used in this proof and covering maps in topology. Indeed, further fascinating connections between topology and the impossibility of various tasks in asynchronous distributed computation have been recently discovered, see [BoG] [SZ] and [HS] The last remark of this subsection is that the assumed synchronization among processors is crucial for establishing BA. Fischer, Lynch and Patterson [FLP] showed that if message passing is completely asynchronous then consensus cannot be achieved even in the presence of a single bad ....

M. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: The topology of public knowledge, Proc. 25th ACM Symp. on Theory of Computing (1993) 101 - 110.

.... of a t resilient implementation of an n ported t set consensus object from the impossibility of a wait free implementation of a (t 1) ported t set consensus object, when implementations are restricted to use only registers [BG93a] The wait free impossibility result is proved independently in [BG93a, HS93, SZ93]. Our equivalence theorem di ers from Borowsky and Gafni s result in fundamental ways. First, our result concerns t resilient implementations of consensus, while theirs concerns t resilient implementations of t set consensus. The second, and more signi cant, di erence is that our result applies ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 25th ACM Symposium on Theory of Computing, pages 101-110, 1993. 27

.... this area, in particular, the book on distributed algorithms [46] other articles by Herlihy et al. 37] 38] 39] some slightly different methods, but still geometric in nature, in [2] 5] 6] 11] 22] which originated this field of research, starting with graph theoretical arguments) [51]. Also some ideas about classifying data structures according to what protocols they manage to solve are described in [42] 43] 53] This should be related to problem (CS2) Some links with directed homotopy have been hinted by one of the co authors [29] 30] 31] In concurrent databases, we ....

M. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: The topology of public knowledge, Proc. of the 25th STOC, ACM Press, 1993.

....from topology can be used to analyze concurrent systems has received a considerable amount of attention. In the past few years, researchers have developed powerful new tools based on classical algebraic topology for analyzing tasks in asynchronous models [AR96, BG93, GK99, HR94, HR95, HS99, SZ93] The principal innovation of these papers is to model computations as simplicial complexes (rather than graphs) and to derive connections between computations and the topological properties of these complexes. Our paper extends this topological approach in several new ways: it is the first to ....

Michael Saks and Fotis Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 25th ACM Symposium on Theory of Computing, pages 101--110, May 1993. SIAM Journal on Computing, to appear.

....of graph techniques. It was then a rather shared belief that one would have to use more powerful techniques in that case. The conjecture [Cha90] that the k set agreement problem cannot be solved in certain asynchronous systems was finally proven in three different papers independently, BG93] [SZ93] and [HS93] The renaming task, first proposed in [ABND 90] was finally solved in [HS93] There is a wait free protocol for the renaming task in certain asynchronous 8.2. RESULTS IN PROTOCOLS FOR DISTRIBUTED SYSTEMS 241 systems if the output name space is sufficiently large. It was already ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proc. of the 25th STOC. ACM Press, 1993.

....our knowledge, for other values of t it is not yet even known if the t solvability problem is decidable. An important progress in understanding the solvability problem was achieved recently by few pioneering papers, which study topological structures related to fault tolerant computations [BG93, SZ93, HS93, HS94] This approach provides a new insight to the problem, which was demonstrated by settling two open problems, concerning the t solvability of specific important tasks: BG93, HS93, SZ93] give tight bounds on the number of faults under which the set consensus problem [Cha90] can be ....

.... pioneering papers, which study topological structures related to fault tolerant computations [BG93, SZ93, HS93, HS94] This approach provides a new insight to the problem, which was demonstrated by settling two open problems, concerning the t solvability of specific important tasks: BG93, HS93, SZ93] give tight bounds on the number of faults under which the set consensus problem [Cha90] can be solved ( HS93, SZ93] consider the case t = n Gamma 1, while [BG93] generalizes the result for every t) HS93] see also [Her94b] provide a tight lower bound on solutions to the renaming problem ....

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M. Saks and F. Zaharoglou. Wait-free k- set agreement is impossible: The topology of public knowledge. In Proc. 25th ACM Symp. on Theory of Computing, May 1993.

....Um of sets. It follows that A r (S m ) A r Gamma1 (A 1 (S m ) is (m Gamma (n Gamma f) Gamma 1) connected. It follows that the asynchronous protocol complex is (f Gamma 1) connected (when m = n) and thus we can prove the impossibility of asynchronous k set agreement [BG93, HS93, SZ93] Theorem 17: If I the set of input values, and I = S n ; I) the input complex, then A r (I) is (f Gamma 1) connected for any r 0. Proof: For each input simplex S m , A r (S m ) is (m Gamma (n Gamma f) Gamma 1) connected (Lemma 16) so A r ( S m ; I) is also (m Gamma (n ....

Michael Saks and Fotis Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 25th ACM Symposium on Theory of Computing, May 1993. 31

.... used to give proofs of the impossibility of solution of Chaudhuri s set consensus task [Ch] and Attiya et al. s renaming task [At ] 1 Such proofs can be found in [HS1, HS3] although it should be noted that independent proofs of the impossibility of solution of the set consensus task appear in [BG2, SZ]. Arguments of this kind tend to focus on a single input configuration that is challenging for the task (such as a configuration of distinct inputs in the case of set consensus) and show that there is a topological obstruction to arranging on that simplex despite the refinement of the subdivision ....

....many useful and encouraging discussions during the research and writing of this paper. 2. Preliminaries 2.1 Model of computation. The model of computation for the present work is the asynchronous read write shared memory model that has been common in recent studies of wait free decision tasks [BG3, GK, HS2, HS3, SZ]. We assume a system of n 1 processes, p 0 ; pn . These processes run asynchronously, which means that no assumption is made about their relative speeds. The processes may therefore experience arbitrary delays relative to one another. Each process is assumed to have private memory that can ....

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M. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: The topology of public knowledge, Proceedings of the 25th ACM Symposium on the Theory of Computing, 1993, pp. 101--110.

....Point Theorem. Chaudhuri s conjecture was proved for shared memory systems with read write registers in [BG2] and [HS1] both using Sperner s Lemma. A somewhat weaker result, impossibility of wait free k set consensus for read write shared memory systems of size greater than k, was proved in [SZ] using Brouwer s Fixed Point Theorem. An additional contribution of [BG2] was a simulation technique whereby the question of k resilient computability in a system of size greater than k can, for certain decision tasks, be reduced to the question of wait free computability in a system of size k 1 ....

....n 0 , then any wait free solution of (m 1; k) consensus for n 1 processes implements a wait free solution of (m 1; k) consensus for n 0 1 processes. Thus, we focus attention on the critical case k = m = n. When n = 1, the task reduces to consensus, so we also assume n 2. It is known [SZ, BG2, HS1] that the (n 1; n) consensus task does not admit wait free solution. At present, we do not have a proof that this impossibility is detected by our algorithmic test for all n 2. Nevertheless, there seems to be good evidence that obstructions exist. We sketch a way to study the homology map ff ....

M. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: The topology of public knowledge, Proceedings of the 25th ACM Symposium on the Theory of Computing , 1993, 101--111.

....unresolved. Chor and Moscovici [16] later provided a graph theoretic characterization of tasks solvable in a system where the n 1 processes can solve (n 1) process consensus (either deterministically or randomized) In 1993, three research teams Borowsky and Gafni [10] Saks and Zaharoglou [39], and the current authors [30] independently derived lower bounds for the k set agreement problem of Chaudhuri. The proof of Borowsky and Gafni [10] is based on a powerful simulation method that allows N process protocols to be executed by fewer processes in a resilient way. Both Saks and ....

....the current authors [30] independently derived lower bounds for the k set agreement problem of Chaudhuri. The proof of Borowsky and Gafni [10] is based on a powerful simulation method that allows N process protocols to be executed by fewer processes in a resilient way. Both Saks and Zaharoglou [39] and the current authors [30] apply notions and techniques from mainstream combinatorial topology. Saks and Zaharoglou introduce an innovative and elegant formal model in which processors collective knowledge of the unfolding computation is treated as a topological space. They then apply a ....

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M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 1993 ACM Symposium on Theory of Computing, May 1993.

....algorithms. Immediate snapshots [19] are an extension of atomic snapshots, in which process p i can not obtain a view which is strictly between an update performed by another process p j and the following view p j obtains; they were used for renaming [19] and to study wait free solvable tasks [15, 18, 32]. In the M renaming problem [11] each process starts with a distinct name in some range and is required to choose a distinct name in a smaller range of size M . In the more general long lived M renaming problem [30] processes repeatedly acquire and release names in the smaller range. We ....

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 25th ACM Symposium on Theory of Computing, pages 101--110, 1993. Accepted to SIAM Journal on Computing. 24

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Michael Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM Journal on Computing, 29(5):1449--1483, March 2000.

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M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. Comput., 29(5):1449--1483, 2000.

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M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 25th ACM Symposium on Theory of Computing (STOC), pages 101--110, May 1993.

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Michael Saks and Fotis Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 1993 ACM Symposium on Theory of Computing, May 1993.

No context found.

M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proceedings of the 1993.

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M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. Comput., 29(5):1449--1483, Mar. 2000.

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Michael Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM Journal on Computing, 29(5), pages 1449--1483, March 2000.

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