S. FORTUNE AND J. WYLLIE, Parallelism in Random Access Machines, in Proc. 10th ACM Symp. Theory of Computing, San Diego, CA., May 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....BSP and LogP. Finally, section 2.3 surveys the skeleton oriented languages and their cost models, especially BMF style programming. 2. 1 The PRAM Model The most influential early theoretical parallel computation model is the parallel random access machine (PRAM) introduced by Fortune and Wyllie [36], which has been used widely to assess the theoretical performance analysis of parallel algorithms. The PRAM consists of a shared memory and a number of processors each with local memory. The processors are controlled by a common clock and operate synchronously. In every cycle each processor may ....

S. Fortune and J. Wyllie. Parallelism in Random Access Machine. In Conference record of the Tenth Annual ACM Symposium on Theory of Computing, pages 114--118, San Diego, California, May 1978.

....found in a potential PRO library. Finally, we conclude the paper in Section 7 with some remarks. 2 Existing models and their limitations There exists a plethora of parallel computation models in the literature. On the theoretical end, we find the Parallel Random Access Machine (PRAM) model [8, 17] which in its simplest form posits a set of p processors, with global shared memory, executing the same program in lockstep. In this model, every processor can access any memory location at unit cost of time regardless of the memory location. This assumption is in obvious disagreement with the ....

....Lock step indicates that the processors are fully synchronized at each step (of a universal clock) without accounting for synchronization. Bulksynchrony indicates that there can be asynchronous operations between synchronization barriers. The row labeled memory shows how the model views 8 PRAM [8] QSM [13] BSP [22] LogP [5] CGM [4] PRO synch. lock step bulk synch. bulk synch. asynch. asynch. asynch. memory sh. sh. dist. dist. priv. priv. commun. SM SM MP MP MP SM MP SM parameters n p, g, n p, g, L, n p, g, l, o, n p, n p, n, Aseq granularity fine fine coarse fine coarse Grain(n) ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th ACM Symposium on Theory of Computing, pages 114--118, May 1978.

....of unbounded size and consisting of memory cells, each of which can store an arbitrary integer. Each processor can access any cell of the global memory cell in one step, and appropriate measures are taken to resolve (or forbid a priori) memory access conflicts. For more details on this model, see [21]. We use the abbreviation PSPACE to refer to the class of problems that can be decided by (multi tape) Turing machines using an amount of work space that is polynomial in the size of the input. PSPACE is a very fundamental and (with respect to variations of the machine model) very robust ....

....bound (for the Turing machine model) was generalized to PIMP: Theorem 4 Let P be a polynomial ideal membership problem over Q, and let s be the size of the input for P . Then there is a PRAM algorithm which solves P in parallel time using 2 processors. Using the Parallel Computation Thesis ([21]) and techniques from [47] one obtains Theorem 5 The polynomial ideal membership problem is solvable in sequential space exponential in the size of the problem instance. for the decision problem, and also, for the representation problem, 6 Theorem 6 Let f and g 1 ; g w be multivariate ....

[Article contains additional citation context not shown here]

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 114--118, New York, 1978. ACM, ACM Press.

....been shown to be P complete [11, 19] and it is therefore very unlikely that any substantial parallel speedup can be achieved. Our main result is an NC algorithm for the UET scheduling problem on interval orders and an arbitrary number of parallel processors. It runs in O(log of a CREW PRAM [6] whereas the previous algorithm of [19] requires the same time bound but n processors on the stronger CRCW PRAM model which allows concurrent writes in addition to concurrent reads of the same memory cell. Our result is important in two respects. First, it is one of very few cases where an ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 114--118, New York, 1978. ACM, ACM Press.

....data and the links along which data flow, forming a network having both structural and dynamic properties. The issue of communication is only recently beginning to receive attention in keeping with its importance in models of parallel computation. Most parallel models following the precedent of [6] start with the assumption of perfect communication, namely no delay and unlimited bandwidth. Algorithms based on such models may appear to be highly performant, but more realistic assumptions [4] about the underlying communication system reveal significant degradation of their behavior. In ....

S. Fortune and J. Wyllie, Parallelism in Random Access Machines, in Proceedings of the 10th Annual Symposium on Theory of Computing, San Diego, CA, 1978.

....found in a potential PRO library. Finally, we conclude the paper in Section 7 with some remarks. 2 Existing models and their limitations There exists a plethora of parallel computation models in the literature. On the theoretical end, we find the Parallel Random Access Machine (PRAM) model [8, 17] which in its simplest form posits a set of p processors, with global shared memory, executing the same program in lockstep. In this model, every processor can access any memory location at unit cost of time regardless of the memory location. This assumption is in obvious disagreement with the ....

....tabular format for comparison is inspired by a similar presentation in [13] where the Queuing Shared Memory (QSM) model is proposed. The columns of Table 1 are labeled with the names of the selected models in our comparison and some relevant features of a model are listed along the rows. 6 PRAM [8] QSM [13] BSP [22] LogP [5] CGM [4] PRO synch. lock step bulk synch. bulk synch. asynch. asynch. asynch. memory sh. sh. dist. dist. priv. priv. commun. SM SM MP MP MP SM MP SM parameters n p, g, n p, g, L, n p, g, l, o, n p, n p, A, n granularity fine fine coarse fine coarse Grain(n) speedup ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th ACM Symp. on Theory of Computing, pages 114--118, May 1978.

....found in a potential PRO library. Finally, we conclude the paper in Section 7 with some remarks. 2. Existing models and their limitations There exists a plethora of parallel computation models in the literature. On the theoretical end, we find the Parallel Random Access Machine (PRAM) model [8, 17] which in its simplest form posits a set of p processors, with global shared memory, executing the same program in lockstep. In this model, every processor can access any memory location at unit cost of time regardless of the memory location. This assumption is in obvious disagreement with the ....

....l and o are are taken into account in PRO, even though they are not explicitly used as parameters. Latency is taken into consideration since the length of a superstep is determined by the sum of the computational and communication cost. Communication overhead is hidden by the PRO PRAM [8] QSM [13] BSP [22] LogP [5] CGM [4] PRO synch. lock step bulk synch. bulk synch. asynch. asynch. asynch. memory sh. sh. dist. dist. priv. priv. commun. SM SM MP MP MP SM MP SM parameters n p, g, n p, g, L, n p, g, l, o, n p, n p, n, A seq granularity fine fine coarse fine coarse Grain(n) ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th ACM Symposium on Theory of Computing, pages 114--118, May 1978.

....input samples of size n. 3. An Efficient Parallel Algorithm Whereas the RAM model has been generally accepted as the most suitable model for developing and analyzing sequential algorithms, such a consensus has not yet been reached in the area of parallel computing. The PRAM model introduced in [6], is usually considered an acceptable compromise. A PRAM consists of a number of processors, each of which has its own local memory and can execute its local program, and all of which can communicate by exchanging data through a shared memory. Variants of the PRAM model differ in the constraints ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proc. 10th Ann. ACM Symp. Theory of Computing, pp. 114--118, New York, 1978, ACM Press.

....the problem of efficiently allocating sets of processors to the subproblems (nodes of the tree) becomes evident. Our goal in this paper is to solve this problem in a way causing minimal overhead in addition to the running time needed by the divide and conquer steps themselves. Unlike for PRAM s [FW78] which provide complete processor interconnection and hence simple processor allocation mechanisms (but see also [vG89] this problem is much more difficult on network architectures. Two major hurdles are (i) allocating appropriately sized subnetworks to subproblems and (ii) routing the ....

S. Fortune and J. Wyllie. Parallelism in random access machines. Proceedings of the 10th ACM Symposium on Theory of Computing, 114--118, 1978.

....of deciding whether a certain homogeneous linear system (of exponential size) has a non trivial solution. The latter is known to be solvable by a parallel algorithm using polynomial number of processors and running in time polylogarithmic in the size of the system. The Parallel Computation Thesis [FW78] then implies the existence of a sequential algorithm which uses space polylogarithmic in the size of the input (thus polynomial space for the system under study) 2 Notations and Some Fundamental Concepts 2.1 Polynomials and Ideals Let X = be a finite set of indeterminates. By k[X] we ....

....only when it is required. After it has been fed into the algorithm the storage will be freed again. As proved in [May89] the bookkeeping and recomputation overhead caused by this approach alters neither the parallel time O(log n) nor the space requirements. By the Parallel Computation Thesis ([FW78]) we can perform the same computation sequentially using no more space than the square of the time required by the parallel algorithm. In our case, since the order of the matrix F is bounded by , we obtain the following result: Proposition 2. Let I be an ideal in the polynomial ring Q[X] and ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 114--118, New York, 1978. ACM, ACM Press.

....the normal form of a polynomial into a system of linear equations, Kuhnle and Mayr exhibited in [KuMa96] an exponential space computation of Grobner bases. This, however, is based on very complex parallel computations like parallel rank computations of matrices, and the Parallel Computation Thesis [FW78]. In this paper, we make use of the close relationship between commutative semigroups and pure difference binomial ideals (for an investigation of the algebraic structure of general binomial ideals see [EiSt94] Based on the algorithm in [MM82] for the uniform word problem in commutative ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 114--118, New York, 1978. ACM, ACM Press.

....models has emerged, whose members attempt to abstract and formalize the salient features of vectorized and or parallel computation. We mention the following examples: i) vector machines (Pratt Stockmeyer [14] ii) MRAM s (Hartmanis Simon [10] iii) PLRAM s (Fortune Wyllie [8]) iv) k PRAM s (Savitch Stimson [17] v) alternating Turing machines (Chandra, Kozen Stockmeyer [2] vi) LPRAM S (Savitch [16] vii) Concurrent Read Exclusive Write PRAM s (CREW PRAM s, see e.g. Stockmeyer Vishkin [19] viii) SIMDAG s (Goldschlager [9] For definitions we ....

Fortune, S., and J. Wyllte, Parallelism in random access machines, Proc. 10 th ACM Sympos. Theory of Comput., San Diego, 1978, PP. 89-94.

....plus the time needed for d(P Gamma 1) Gamma 1 communication operations. The third constructs schedules of length at most 3 Gamma P 2 times the length of a minimum length schedule plus the duration of d(d Gamma 1) P Gamma 1) Gamma 1 communication operations. 1 Introduction The PRAM [10] is the most common model of parallel computation. A PRAM consists of a collection of processors that execute a parallel program in a synchronous manner; processors communicate by writing and reading in global memory. The PRAM model does not capture the complexity of communication in the execution ....

S. Fortune and J. Wyllie. Parallelism in Random Access Machines. In Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, pages 114--118, 1978.

....a constant factor. Arithmetic depth T1 (or parallel time) and work T 1 (or sequential time) are evaluated from G taking into account weights of nodes. T1 is a lower bound of the minimal time required by any schedule on an unbounded number of processors ignoring communications times (PRAM model [8]) T 1 is the number of operations required by a sequential execution of the algorithm. Since the best schedule may replicate some arithmetic nodes in order to minimize completion time, note that T 1 is also a lower bound on the number of operations performed by any schedule. Communication delay ....

....program on various machine models; time and space required by the execution on the machine (including the cost of the scheduling algorithm) are related to above abstract costs defined on the program itself that are independent from the machine. 3. 3 Scheduling on a PRAM The PRAM model [8, 12] allows to get rid off communication overheads. In order to be consistent with Athapascan 1, we consider a CRCW PRAM with cumulative concurrent write ones. We focus here on the time required to schedule tasks on such a machine. With no restriction, we assume that during execution, any task has ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proc. of the 10th ACM Symposium on Theory of Computing, pages 114--118, San Diego, CA, 1978. ACM Press.

....linear systems. The computational parallel cost of their algorithm is O (logz) with zo( processors, while the best deterministic algorithm for this problem takes O (log 2 )time on o( processors. In this paper we adopt as computational model the parallel raw, dom access macbible (PRAM, see [7]) in particular the results can be proved for the CREW PRAM model. In a cocurretread, e clusive write (CREW) PRAM, multiple processors are allowed to read from the same location of the shared memory at the same time, but only one processor can write to any location during a single step. This ....

S. Fortune and J. Wyllie. Parallelism in Random Access Machines. Proc. loth ACM 5'ymp. on Theory of Computing (3'TOC), pages 114 118, 1978.

....are keys to being able to integrate abstract solutions with realizable hardware and software systems. The efficiency and scalability of parallel algorithms have been the subject of research since the seventies. A model of parallel computation known as the Parallel Random Access Machine or PRAM [44] has attracted much attention, and many efficient and optimal algorithms have been designed for it (the surveys [40, 58] contain a wealth of information on the subject) The PRAM is a convenient abstraction that combines the power of parallelism with the simplicity of a RAM (Random Access ....

....we address the following issues: the reliability and synchronization of parallel processors that can be modeled by PRAMs, and the efficiency of computation on such processors. The model of parallel computation that serves as the basis for this work is the synchronous PRAM of Fortune and Wyllie [44], with concurrent reads and concurrent writes (CRCW) The convention for determining which processor or processors succeed, when concurrently writing to shared memory, is immaterial in our algorithms. We investigate fault prone PRAMs whose processors exhibit fail stop processor behavior, such as ....

[Article contains additional citation context not shown here]

S. Fortune and J. Wyllie, "Parallelism in Random Access Machines", Proc. the 10th ACM Symposium on Theory of Computing, pp. 114-118, 1978.

....recursions, reactiveness, in nite behaviours, empty loop body and a simple form of parallelism. It is the minimum language of this kind. A similar language Logic of Global Synchrony (or Logs for short [5] allowing multiple program variables has been successfully applied to speci cations of PRAM [11] and BSP [16] The following contributions are made in this paper: 1. Tarski s xpoint theorem is shown not to be directly applicable to language L , because the most appropriate denotation of the bottom of the partial order is the speci cation containing all nonterminating behaviours (see the ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th Annual ACM Symposium on Theory of Computing, pages 114-118, 1978.

....a little efficiency. We now consider some of the existing models and their merits. 2.2. 1 The Traditional PRAM and its Variants If there is one model of parallel computation which stands out from the rest as being reasonably widely accepted, it is the Parallel Random Access Machine (PRAM) [16]. The great advantages of this model stem from its simplicity it merely consists of a number of processes sharing a global random access memory, reading data from it, writing data to it and performing local computations. All processors perform one of these operations at a time in lock step ....

S. Fortune and J. Wyllie. "Parallelism in Random Access Machines". Proceedings of 10th Annual ACM Symposium on Theory of Computing, pages 114--118, 1978.

....and decompressing the images. It is certain that the user would greatly appreciate if the image were decompressed within a second or two, instead of 10 or 20 seconds if there are computing potential to do so. Parallel random access machine (PRAM) first proposed by Fortune and Wyllie in 1978 [Fortune78] is a general model for parallel computation. While building of shared memory has remained unfeasible, there has been a considerable effort to simulate an ideal shared memory machine like a PRAM with a physically distributed memory machine, which consists of processors and memory modules ....

....considerations of parallel processing such as communication between processors. One can simply assume that the communication does not cost anything. A computational model that embodies this assumption is the parallel random access machine (PRAM) first proposed by Fortune and Wyllie in 1978 [Fortune78] as a general model for parallel computation. Although the PRAM model is somewhat idealistic, a substantial number of efficient PRAM simulations have been designed that allow efficient implementation on real parallel architectures. Moreover, the PRAM may be viewed as a virtual parallel machine ....

S. Fortune and J. Wyllie (1978), Parallelism in Random Access Machines, of 10th ACM STOC (Association for Computing Machinery, New York): 114-118.

....5. 2 The BSP model The exploration of parallel computation within theoretical computer science has been led by the study of time, processor and space complexities of ideal parallel machines which communicate via a shared memory; this is known as the Parallel Random Access Machine (PRAM) Model [2]. The PRAM model assumes that an unbounded set of processors shares a global memory. In a single step, a processor can either read or write one data word from the global memory into its local address space, or perform some basic computational operation. The simplicity of the model has, over the ....

S. Fortune and J. Wyllie, Parallelism in random access machines, in: Proceedings of the 10-th Annual ACM Symposium on Theory of Computing (1978) 114-118.

.... [AA82] ffl RPCs, Client Server models [BN84, MW91] ffl Petri Nets [Rei85] ffl Alternating Turing Machines [CKS81, Ruz80] ffl Boolean circuits [CSV84, SV84] ffl Systolic Arrays [Kun82] ffl Associative Processors [Pot92, SKA92] ffl PRAM (several varieties: EREW, CREW, several kinds of CRCW) FW78, Gol82, SS79] ffl V RAM (data parallel) model [Ble90, HS86] Each model sprang from a different research community in response to completely different problems. As a result, these models are so far removed from each other that it is often difficult to translate research advances from one area to ....

S. Fortune and J. Wyllie. Parallelism in random access machines. In Symposium on Theory of Computing, pages 114--118, 1978.

....have attracted considerable attention from the research community. For an examination of models not discussed here, we refer the reader to [Akl97] LMR95] and [MMT95] 7 P P 0 1 . SHARED MEMORY P p 1 Figure 2.1: The PRAM model. 2.1. 1 PRAM The Parallel Random Access Machine (PRAM) [FW78] is the most widely used parallel computational model. The PRAM model consists of p sequential processors sharing a global memory as shown in Figure 2.1. During each time step or cycle, each processor executes a RAM instruction or accesses global memory. After each cycle, the processors implicitly ....

....synchronize to execute the next instruction. In the PRAM model, more than one processor can try to read from or write into the same memory location simultaneously. CRCW (Concurrent read, concurrent write) CREW (Concurrent read, exclusive write) and EREW (Exclusiveread, exclusive write) PRAMs [FW78] handle simultaneous access of several processors to the same location of global memory. The CRCW PRAM, the most powerful PRAM model, uses a protocol to resolve concurrent writes. Example protocols include arbitration (an arbitrary processor proceeds with the write operation) prioritization (the ....

S. Fortune and J. Wyllie. "Parallelism in Random Access Machines." In Proceedings of the 10th Annual Symposium on Theory of Computing, pp. 114--118, 1978.

....and programming models appear in Table 3.1. Before we describe the A ZPL performance model, we summarize some other parallel machine models. The PRAM (parallel random access machine) models a parallel machine with p serial processors that have unit time access to a single shared memory [FW78] This model ob1 CTA is an acronym for candidate type architecture. A type architecture and machine model are synonymous. 23 Table 3.1: Serial and parallel models. Serial Parallel Machine model von Neumann CTA Programming model Imperative procedural Phase Abstractions Language C, Fortran, ....

Steven Fortune and James Wyllie. Parallelism in random access machines. In Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, pages 114-- 8, 1978.

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S. FORTUNE AND J. WYLLIE, Parallelism in Random Access Machines, in Proc. 10th ACM Symp. Theory of Computing, San Diego, CA., May 1978.

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S. Fortune and J. Wyle. Parallelism in random access machines. Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, 1978, pages 114--118.

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S. Fortune and J. Willie. Parallelism in random access machines. In Proc. of 10th ACM Symposium on Theory of Computing, pages 114--118, 1978.

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S. Fortune and J. Willie. Parallelism in random access machines. In Proc. of 10th ACM Symposium on Theory of Computing, pages 114--118, 1978.

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Fortune S, Wyllie J. Parallelism in random access machines. Proceedings of the 10th STOC. ACM: New York, NY, 1977; 114--118.

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Steven Fortune and James Wyllie. Parallelism in random access machines. In Proc. 10th Annual ACM Symposium on Theory of Computing, pages 114--118, 1978.

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FORTUNE,S.AND WYLLIE, J. 1978. Parallelism in random access machines. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing. ACM Press, New York, NY 114-- 118.

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S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th Annual ACM Symposium on Theory of Computing, pages 114--118. ACM Press, 1978.

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S. Fortune and J. Wyllie, Parallelism in random access machines. Proc. 10th Annual ACM Symp. on Theory of Computing : 114--118, 1978.

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S. FORTUNE AND J. WYLLIE, Parallelism in Random Access Machines, in Proc. 10th ACM Symp. Theory of Computing, San Diego, CA., May 1978.

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S. Fortune and J. Wyllie. Parallelism in random access machines. Proc. 10th Annual ACM Symp. on Theory of COmputing, San Diego, California, 1978, 114-118. 13

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S. Fortune and J. Wyllie. Parallelism in random access machines. Proc. 10th Annual ACM Symp. on Theory of Computing, San Diego, California, 1978, 114-118.

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S. Fortune and J. Wyllie. Parallelism in random access machines. Proc. 10th ACM Symp. on Theory of Computing, 114-118(1978).

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S. Fortune and J. Wyllie. Parallelism in Random Access Machines. In Proceedings of the 10'th ACM Symposium on Theory of Computing (STOC), pages 114--118. ACM, NewYork, May 1978.

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S. Fortune and J. Wyllie, "Parallelism in random access machines, " in Proceedings of the ACM Symposium on the Theory of Computing ~Association for Computing Machinery, New York, 1978!, pp. 114--118.

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Fortune S, Wyllie J. Parallelism in random access machines. Proceedings of the 10th STOC. ACM: New York, NY, 1977; 114--118.

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S. Fortune and J. Wyllie. Parallelism in random access machines. In Proc. ACM Symp. on Theory of Computation, pages 114--118, 1978.

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S. Fortune and J. Wyllie. Parallelism in Random Access Machines. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, pages 114--118, 1978.

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S. Fortune and J. Wyllis. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing , pp. 114-118. ACM, ACM Press, New York, 1978.

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S. Fortune and J. Wyllie, "Parallelism in random access machines," Proc. 10th Annual ACM Symposium on Theory of Computing,1 978, pp.1.

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S. Fortune and J. Wyllie. Parallelism in random access machines. In Proc. of STOC, pages 114-118, 1978.

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S. Fortune and J. Wyllie, Parallelism in random access machines, in ACM Symp. on Theory of Computing, 1978, pp. 114--118. 13

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Stephen Fortune and James Wyllie. Parallelism in random access machines. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, pages 114--118. ACM Press, 1978.

No context found.

S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th Annual ACM Symposium on Theory of Computing, pages 114--118. ACM Press, 1978.

No context found.

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 114--118, New York, 1978. ACM, ACM Press.

No context found.

S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, pages 114--118, 1978.

No context found.

S. Fortune and J. Wyllie. Parallelism in Random Access Machines. In Tenth ACM Symposium on Theory of Computing, pages 114--118, San Diego, CA, 1978.

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