No abstract

We study walt-free computation using (read/write) shared memory under a range of assumptions on the arrival pattern of processes. We distinguish first between bounded and infinite arrival patterns, and further distinguish these models by restricting the number of arrivals minus departures, the concurrency. Under the condition that no process takes infinitely many steps without terminating, for any finite bound k > 0, we show that bounding concurrency reveals a strict hierarchy of computational models: a model in which concurrency is bounded by k + 1 is strictly weaker than the model in which concurrency is bounded by k, for all k > 1. A model in which concurrency is bounded in each run, but no bound holds for all runs, is shown to be weaker than a k-bounded model for any k. The unbounded model is shown to be weaker still--in this model, finite prefixes of runs have bounded concurrency, but runs are admitted for which no finite bound holds over all prefixes. Hence, as the concurrency grows, the set of solvable problems strictly shrinks. Nevertheless, on the positive side, we demonstrate that many interesting problems (collect, snapshot, renaming) are solvable even in the infinite arrival, unbounded concurrency model. This investigation illuminates relations between notions of wait-free solvability distinguished by arrival pattern, and notions of adaptive, one-shot, and long-lived solvability.

Abstract. Work to date on algorithms for message-passing systems has explored a wide variety of types of faults, but corresponding work on shared memory systems has usually assumed that only crash faults are possible. In this work, we explore situations in which processes accessing shared objects can fail arbitrarily (Byzantine faults).

Afek * Michael Merrittt qComputer Science Dept., Tel-Aviv Univ., Israel 69978, and AT&T Labs. Partial support provided by BSF grant 94-00297. t AT&T Labs, 180 Pwk Av., Florhm park, NJ 07932-0971. Partial support provided by BSF grant 94-00297. $The Open Univ., 16 Kiausner st., P.O, B. 39328, Tel-Aviv 61392, Israel, and AT&T Labs. $~SOF p=~el Softwme, I~r=l Permissionto make digitalfiord copiesof all or pwt of thismaicri;)iIbr personrd or ci,~room useis grantedwithout fee pmvidcdIIMI the cOpies are not madeor distributedfor profit or conrmcrcialodvruttage. the cofryright notice.the (itle of the publicationand it..dotezppmr. md noticeis given ttrd copyright is by permissionof the ACM. hw. 10 COPY Olll*~i~. to republish,to poston scwm or to redistribttte10 lists.requircw spccilic pemlissiontd/Or fee 1997 POD{" 97 Scmto Borbrm (.'.4 [ISA

The notion of an anonymous shared memory (recently introduced in PODC 2017) considers that processes use different names for the same memory location. As an example, a location name A used by a process p and a location name B = A used by another process q can correspond to the very same memory location X, and similarly for the names B used by p and A used by q which may (or may not) correspond to the same memory location Y = X. Hence, there is permanent disagreement on the location names among processes. In this context, the PODC paper presented -among other results-a symmetric deadlock-free mutual exclusion (mutex) algorithm for two processes and a necessary condition on the size m of the anonymous memory for the existence of a symmetric deadlock-free mutex algorithm in an n-process system. This condition states that m must be greater than 1 and belong to the set M (n) = {m : ∀ ℓ : 1 < ℓ ≤ n : gcd(ℓ, m) = 1} (symmetric means that, while each process has its own identity, process identities can only be compared with equality).The present paper answers several open problems related to symmetric deadlock-free mutual exclusion in an n-process system (n ≥ 2) where the processes communicate through m registers. It first presents two algorithms. The first considers that the registers are anonymous read/write atomic registers and works for any m greater than 1 and belonging to the set M (n). Hence, it shows that this condition on m is both necessary and sufficient. The second algorithm considers that the registers are anonymous read/modify/write atomic registers. It assumes that m ∈ M (n). These algorithms differ in their design principles and their costs (measured as the number of registers which must contain the identity of a process to allow it to enter the critical section). The paper also shows that the condition m ∈ M (n) is necessary for deadlock-free mutex on top of anonymous read/modify/write atomic registers. It follows that, when m > 1, m ∈ M (n) is a tight characterization of the size of the anonymous shared memory needed to solve deadlock-free mutex, be the anonymous registers read/write or read/modify/write.

No abstract

We consider concurrent systems in which there is an unknown upper bound on memory access time.Such a model is inherently different from asynchronous model where no such bound exists, and also from timing-baaed models where such a bound exists and is known a priori. The appeal of our model lies in the fact that whtie it abstracts from implementation details, it is a better approximation of real concurrent systems compared to the

Abstract. A mutual exclusion algorithm is presented that has four desired properties: (1) it satisfies FIFO fairness, (2) it satisfies localspinning, (3) it is adaptive, and (4) it uses finite number of bounded size atomic registers. No previously published algorithm satisfies all these properties. In fact, it is the first algorithm (using only atomic registers) which satisfies both FIFO and local-spinning, and it is the first bounded space algorithm which satisfies both FIFO and adaptivity. All the algorithms presented are based on Lamport's famous Bakery algorithm [27], which satisfies FIFO, but uses unbounded size registers (and does not satisfy local-spinning and is not adaptive). Using only one additional shared bit, we bound the amount of space required by the Bakery algorithm by coloring the tickets taken in the Bakery algorithm. The resulting Black-White Bakery algorithm preserves the simplicity and elegance of the original algorithm, satisfies FIFO and uses finite number of bounded size registers. Then, in a sequence of steps (which preserve simplicity and elegance) we modify the new algorithm so that it is also adaptive to point contention and satisfies local-spinning.