P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....writing the same value. If they are not, the program is not a CRCW PRAM program. This has the unfortunate effect that whether a program is a CRCW PRAM program or not becomes undecidable. The other two types of PRAM considered are the concurrent read owner write (CROW) PRAM, introduced by Dymond [7]. In this type of PRAM, each global memory cell is owned by a particular processor, and only that processor may write to it. A processor may read any global memory cell. We will assume for the sake of simplicity that there are as many processors as global memory cells, and that they are paired, ....

Dymond, and Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recognition. JACM: Journal of the ACM 47 (2000).

....if g belongs 9 to the accepting set. By assumption, this can be done in logspace and so by a polynomial number of processors working in logarithmic time and satisfying the OROW condition. The time used by the machine is O(log n) O(d(n) which is equal to O(d(n) 2 Results from [4] and [3] suggest that LOGDCFL could be more powerful than OROW(log n) Recall that Dymond and Ruzzo proved that LOGDCFL corresponds precisely to CROW(log n) Hence, if LOGDCFL is effectively equal to the class of languages recognized by uniform parenthesized programs over polynomial groupoids, then it ....

P.W. Dymond and W.L. Ruzzo, Parallel RAMs with Owned Global Memory and Deterministic Context-Free Languages Recognition, Proc. 13th International Colloquium on Automata, Languages and programming, 1986, pp.95-104.

....determine if g belongs to the accepting set. By assumption, this can be done in logspace and so by a polynomial number of processors working in logarithmic time and satisfying the OROW condition. The time used by the machine is O(log n) O(d(n) which is equal to O(d(n) 2 Results from [30] and [27] suggest that LOGDCFL could be more powerful than OROW PRAM(logn) Recall that Dymond and Ruzzo proved that LOGDCFL corresponds precisely to CROW PRAM(log n) Hence, if LOGDCFL is effectively equal to the class of languages recognized by L uniform parenthesized programs over polynomial ....

P.W. Dymond and W.L. Ruzzo, Parallel RAMs with Owned Global Memory and Deterministic Context-Free Languages Recognition, Proc. 13th International Colloquium on Automata, Languages and programming, 1986, pp.95-104.

....at most one processor can write to each memory cell at a given step. Many algorithms designed for CREW and EREW PRAMs avoid write conflicts by having each processor own one cell to which all its writes are performed. These restricted models are called the concurrent read owner write (CROW) PRAM [DR86] and the exclusive read owner write (EROW) PRAM [FW90] respectively. When concurrent writes are allowed, it is necessary to specify how conflicts are resolved. Three of the most frequently used concurrent read concurrent write (CRCW) PRAMs are considered here. A number of others are discussed ....

....times faster on an EREW PRAM than on a CROW PRAM. The tth Fibonacci number, F t , is defined by the recurrence F 0 = 0; F 1 = 1; and F t = F t Gamma1 F t Gamma2 ; for t 2 and satisfies the inequalities ( 1 p 5) 2) t Gamma2 F t ( 1 p 5) 2) t Gamma1 for t 0. EXERCISE 21.19 [CDR86] Prove that an EREW PRAM can compute the OR of n input bits using n processors and shared memory cells in t steps, provided F 2t 1 n. In the example above, there is at most one processor that writes into a particular memory cell at a particular time step on any input. This is not the case for ....

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P. Dymond and W.L. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recognition. In ICALP, pages 95--104, July 1986.

....simultaneous read accesses are still allowed. Finally there are EREW PRAMs that forbid both simultaneous read and write access. In addition to these classical models even more restrictive memory access mechanisms were considered: Dymond and Ruzzo introduced CROW PRAMs, a restriction of CREW PRAMs [DR86]. In CROW PRAMs each memory cell is mapped to one processor, its owner. Only this special processor is allowed to write into this memory cell. Analogously to this owner write PRAM, also a owner read restriction can be defined which leads to OROW PRAMs that were investigated in [Ros91] In ....

....assigned to a wire that leads to an input of a SELECT gate simply has to copy the value it reads to the memory cell assigned to the input of the SELECT gate. 2 Lemma 9 OREW k UnambAC k b (SEL) Proof. Dymond and Ruzzo described the behavior of a CROW PRAM by mutually recursive functions in [DR86]. These functions can be evaluated by a deterministic auxiliary pushdown automaton. A similar technique was used in [Lan90] to describe CREW PRAMs. In contrast to [DR86] here predicates describing the behavior of a CREW PRAM are evaluated by UnambAC circuits rather than AuxPDAs. In case of ....

[Article contains additional citation context not shown here]

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

....In particular we exhibit circuit classes exactly characterizing polynomially time bounded unambiguous augmented push down automata. Introduction An important object in parallel complexity theory, the class NC , can be characterized in terms of Parallel Random Access Machines, see e.g. [3, 4, 9], Boolean Circuits [3, 10] Augmented Pushdown Automata [7, 6] and Alternating Turing Machines [1, 7] There are close connections between these concepts, see e.g. 3, 5] In [5] unambiguous circuits were considered in order to characterize CREW PRAMs and to further relate them with the NC ....

.... why we can use the usual log space uniformity condition of [6] By LOGUCFL we denote the class of all languages log space reducible to any unambiguous context free language and by CREW k the class of languages recognized by some CREW PRAM in time O(log k n) using polynomially many processors [3, 4]. In the following we consider augmented push down automata (see [2] We make the technical assumption that accepting computations always end with an empty stack and an empty working tape and there is exactly one final state, i.e. there is exactly one accepting configuration. In addition we ....

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th ICALP, number 226 in LNCS, pages 95--104. Springer, 1987.

.... Can the inclusion RUSPACE(logn) LOG(DCFL) be extended to SymSPACE(log n) If so, the currently best known CREW PRAM running time for SymSPACE(logn) of O(logn Delta log log n) demonstrated in [5] would be improved to O(logn) and, in addition, the new algorithm would run on the simpler CROW PRAM [8]. ....

P. Dymond and W. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recoginition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in LNCS, pages 95--104. Springer, 1986.

....allowed to write simultaneously into a single memory cell. This type is called CRCW PRAM (concurrent read, concurrent write parallel random access machine) Obviously, CREW PRAMs are more realistic than CRCW PRAMs. An even more restrictive (and realistic) model was introduced by Dymond and Ruzzo [DR86] called CROWPRAM (concurrent read, owner write parallel random access machine) In a CROW PRAM simultaneous write attempts of more than one processor to a single memory cell are also forbidden, but additionally for each memory cell there must be one distinct processor that is the only one allowed ....

.... terms of uniform Boolean circuits [SV84, Lan90] and the language class recognized by CROW PRAMs in logarithmic time is exactly the class of languages reducible to deterministic context free languages in logarithmic space and there is also a characterization in terms of auxiliary pushdown automata [DR86, Sud78]. It is only natural to apply these three different methods to solve write conflicts also to read conflicts. Since the owner write concept is fairly new, this only led to EREW PRAMs by now (see e.g. LPV81, Sni82] but it seems useful to consider EROW and finally OROW PRAMs, too. An OROW PRAM ....

[Article contains additional citation context not shown here]

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

....parallel models were CREW PRAMs, i.e. parallel random access machines with concurrent read and exclusive write access. In [Ryt87] it was shown that CREW PRAMs can recognize any unambiguous context free language. The computational power of CREW PRAMs lies between CRCW PRAMs and CROW PRAMs [Sni82, DR86] For CRCW PRAMs concurrently writing to the same memory cell is allowed. The class of languages accepted by this type of PRAM in O(log k n) time using polynomially many processors is exactly AC k , the class of languages accepted by polynomial size and O(log k n) depth circuits of ....

....this inclusion was conjectured to be wrong or at least very hard to obtain. Furthermore, we show UnambSAC k to be closed under complementation. For nondeterministic and deterministic, polynomially time bounded AuxPDA it is known that their pushdown height can be bounded by O(log 2 n) Ruz80, DR86] In Section 4 we obtain the same result for unambiguous and strongly unambiguous AuxPDA. Moreover, we consider oblivious AuxPDA, i.e. machines where the movements of all heads do not depend on the input except its length. We show that nondeterministic, unambiguous, and strongly unambiguous ....

[Article contains additional citation context not shown here]

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

.... this question affirmatively by showing that RUSPACE(logn) and hence also StUSPACE(log n) is contained in DSPACE(log 2 n= log log n) Since RUSPACE(logn) is a subclass of DAuxPDA TIME Gamma n O(1) Delta we know that there are logtime CROW algorithms for the elements of RUSPACE(logn) [8]. To give better relative upper bounds on the complexity of RUSPACE(logn) it is interesting to consider intermediate classes between DSPACE(logn) and DAuxPDA TIME Gamma n O(1) Delta . Trying to find these classes with sequential models could be difficult, since the usual restrictions of a ....

....of the many varieties of parallel random access machines and their relationship to sequential classes. Let us remark here, that we deal in this paper only with algorithms and classes using PRAMs with a polynomial number of processors. The notion of a CROW PRAM was introduced by Dymond and Ruzzo [8]. This model of PRAM offers many advantages over other models such as CRCW or CREW PRAMs. For instance, although the complexity class NC has a simple characterization on all of these PRAM models (namely: polynomial number of processors and polylog time) SC is known to have a simple ....

[Article contains additional citation context not shown here]

P. Dymond and W. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in LNCS, pages 95--104. Springer, 1986.

....function. We summarize lower and upper bounds up to constant, additive terms in Table 1. Whereas it is open whether there exists a general relationship between the computational power of CREW PRAM s with and without simultaneous reading and writing, such a relation exists for CROW PRAM s [3]. Fich and Wigderson [5] noted that CROW(f) log D(f) where D denotes the decision tree complexity of f . In Section 5 we show that CROW(f) 1:44 logD(f) yielding the general relationship CROW(f) 1:44 CROW(f) We define the speedup SEW (f) 2 CREW(f) CREW(f) resp. SOW (f) All ....

....conflicts. ut 5 CROW PRAM s For CREW PRAM s we conjectured a speedup of 1:44 for all Boolean functions. We couldn t, however, prove it and the reasons that support the conjecture are rather weak. For CROW PRAM s we can prove that all Boolean functions have the same speedup. Dymond and Ruzzo [3] introduced CROW PRAM s (concurrent read, owner write) as a frequently occurring subclass of CREW PRAM s. Here each global memory cell has a unique write owner that is the only processor allowed to write into it. Nisan [10] showed that CREW and CROW PRAM s need the same amount of time up to a ....

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th ICALP, number 226 in LNCS, pages 95--104. Springer-Verlag, 1986.

....cell. We assume that the value of a writer with highest priority is actually stored (Priority CRCW PRAM) A machine with Owner Write access is more restricted by assigning to each cell of global memory a processor, called write owner , that is the only one allowed to write into this memory cell [24]. More common than the owner concept in formulating algorithms is exclusive access, where we only require that for each point of time there is at most one processor writing into a cell. Exclusive write PRAM s are intermediate in computational power between owner write and concurrent write PRAM s ....

....there is at most one processor writing into a cell. Exclusive write PRAM s are intermediate in computational power between owner write and concurrent write PRAM s and the same holds for read access. While the owner and the concurrent concept are closely related to determinism and nondeterminism [24, 42, 59], the concept of exclusiveness corresponds to unambiguity [41, 42, 48] which explains the inconstructive features of this concept. Correspondingly, we get two ways to manage read access: Concurrent Read and Owner Read . In this way, we get four versions of PRAM s, denoted as XRY W PRAM s with X; ....

[Article contains additional citation context not shown here]

P. W. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proceedings of the 13th International Conference on Automata, Languages, and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

....are also valid for the various types of PRAMs defined by the concurrent and the exclusive read and write feature. In 1986, Dymond and Ruzzo introduced the concept of owner write for PRAMs and showed close connections between owner write PRAMs and deterministic auxiliary push down automata [6]. Later, by considering unambiguous circuits it was possible to exhibit similarly close relationships between unambiguous auxiliary push down automata and CREW PRAMs [11,15] Together, these results show the correspondence between determinism, unambiguity, and nondeterminism on the one hand, and ....

....reduction result for deterministic auxiliary push down automata as it was known before in this generality only in the nondeterministic case. The first main ingredient to prove our results will be a simplified and on the other hand much more general version of the algorithms of Dymond and Ruzzo [6], resp. of Monien, Rytter, and Schapers [14] which in turn may be seen as related to the algorithm of Cook [4] Our second main tool is a new circuit like representation of owner write PRAMs which enables us to simplify the presentation and analysis of the recursive structure behind the ....

[Article contains additional citation context not shown here]

P. Dymond and W. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recoginition. In Proc. of the 13th ICALP, number 226 in LNCS, pages 95--104. Springer, 1986.

....tree is bounded from below by its size z. We call the set of nodes being at the same distance t from the root level t nodes. Finally, by w t we understand the number of nodes at level t and w is defined as the average over all widths w t of the recursion tree (1 t h) Dymond and Ruzzo [3] introduced the owner concept for the write access in PRAM s, yielding a frequently occurring subclass of the CREW PRAM called CROW PRAM. Following this line, that idea was also applied with respect to the read access of a PRAM, resulting in the OROW PRAM model [11] For an OROWPRAM (owner read, ....

P. W. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Conference on Automata, Languages, and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

....memory cell. This leaves us with just two strategies: CHAPTER 5. OBJECT COUPLING 19 Thread 1 Thread 2 State Figure 5. 1: Two threads manipulating one memory location ffl When only one processor may write a certain memory cell, we can call it Owner Write, the processor owns the memory location [4]. The resulting value in the memory is deterministic when the order of accesses to the cell is deterministic. This order is determined by the program, in our case using monads. Consequently, the owning processor is also the only one which may read from the cell. When another processor is allowed ....

Dymond, P.W. and W.L. Ruzzo, Parallel RAMs with Owned Global Memory and Deterministic Context-free Language Recognition, Proc. 13th Internat. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 226 (1986) 95-104.

....given in global memory. A PRAM processor is identified by its processor number. We call processors neighbors if their processor numbers differ by one. The most restricted PRAM variant with respect to access possibilities to shared memory is the owner mechanism introduced by Dymond and Ruzzo [7]. Later on, OROW PRAM s (Owner read, Owner write) were introduced as a still more restricted variation of EREW PRAM s [17] Here, a uniquely determined read owner, resp. write owner, processor is assigned to each global memory cell. The read owner is the only processor with read and the write ....

P. W. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th ICALP, number 226 in LNCS, pages 95--104. Springer-Verlag, 1986.

....logspace languages. We answer this question affirmatively by showing that StUSPACE(logn) is contained in DSPACE(log 2 n= log log n) Since StUSPACE(log n) is a subclass of DAuxPDA TIME Gamma n O(1) Delta we know that there are logtime CROW algorithms for the elements of StUSPACE(logn) [7]. To give better relative upper bounds on the complexity of StUSPACE(logn) it is interesting to consider intermediate classes between DSPACE(logn) and DAuxPDA TIME Gamma n O(1) Delta . Trying to find these classes with sequential models could be difficult, since the usual restrictions of ....

....of the many varieties of parallel random access machines and their relationship to sequential classes. Let us remark here, that we deal in this paper only with algorithms and classes using PRAMs with a polynomial number of processors. The notion of a CROW PRAM was introduced by Dymond and Ruzzo [7] and provides the tightest possible connections to deterministic machines [9] CROW PRAMs need only logarithmic time to recognize any given language in DSPACE(logn) There are two important ways to restrict CROW PRAMs and still maintain this property. One way is to restrict the concurrent read ....

[Article contains additional citation context not shown here]

P. Dymond and W. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recoginition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in LNCS, pages 95--104. Springer, 1986.

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P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

No context found.

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th ICALP, number 226 in LNCS, pages 95-104. Springer-Verlag, 1986.

No context found.

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th ICALP, number 226 in LNCS, pages 95--104. Springer, 1987.

No context found.

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

No context found.

P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in Lecture Notes in Computer Science, pages 95--104. Springer, 1986.

No context found.

Patrick W. Dymond and Walter L. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recognition. Journal of the ACM, 47(1):16--45, January 2000.

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