P. van Emde Boas, Machine Models and Simulations. In: J. van Leeuwen (ed.). Handbook of Theoretical Computer Science, Vol. A. The MIT Press/Elsevier, 1990, 3--66.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of this paper. Since in the finite model theory literature this issue is usually not addressed, we think it is worthwhile to explain our encoding in some detail. Our underlying model of computation is the standard RAM model with addition and subtraction as arithmetic operations (cf. [2, 20]) As common, we assume that initially all memory registers are set to 0 . In our complexity analysis we use the uniform cost measure. We will carefully distinguish between the size jjojj of an object o, which is the length of its encoding, and, if o is a set, its cardinality, denoted by joj. ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume 1, pages 1--66. Elsevier Science Publishers, 1990.

....by the recent papers [2, 49] which we review. We also discuss Shor s [38] paper, which describes the quantum polynomial time factoring algorithm that has provided a major motivation for much of the recent activity. 1 Introduction Quantitative Church s Thesis. The Quantitative Church s Thesis [50, 48] claims that Turing machines are as efficient as any realistic computer, within a polynomial factor. However, Feynman [25] has pointed out that Turing machines seem to be unable to efficiently simulate quantum physics; that is, they seem to require an exponential slowdown to simulate it (although ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, pages 1--66. Elsevier, Amsterdam, 1990.

....function of a relation is stored in an array whose dimension equals the arity of the relation. For graphs, this means that the graph is described by its adjacency matrix. With array representation, membership of an individual tuple can be checked in constant time on Random Access Machines (cf. [34]) but on the other hand, we obtain a non realistic notion of linear time computability when the adjacency matrix is sparse. However, it is easy to see that a Random Access Machine can translate the list representation into array representation in linear time. A propositional Datalog program is a ....

P. van Emde Boas, Machine models and simulations., in Handbook of Theor.Comp.Science. Vol. A., Elsevier, 1990, pp. 1--66.

....satisfaction problem is generally quite high. THEOREM 1 Let A be any representable relation algebra with jAj 2. The satisfaction problem for A is PSPACE hard. PROOF: We reduce the quantified boolean formulas (QBF) problem to the satisfaction problem for A. QBF is known to be PSPACE complete [vEB94, page 41] So, let OE be any quantified boolean formula using only propositional variables p 0 ; p k Gamma1 . We define a L(A) formula OE in such a way that for any boolean valuation v there is a representation X of A and an assignment v to the free variables of OE such that ....

P van Emde Boas. Machine models and simulations. In van Leeuwen [vL94], pages 1--61.

....that whether a function is computable in polynomial time is independent of the kind of computing device used. This corresponds to a quantitative version of Church s thesis, which Vergis et al. 1986] have called the Strong Church s Thesis and which makes up half of the Invariance Thesis of van Emde Boas [1990]. This quantitative Church s thesis is: Any physical computing device can be simulated by a Turing machine in a number of steps polynomial in the resources used by the computing device. In this thesis, the Turing machine is sometimes augmented with a random number generator, as it has not been ....

....however, it is not particularly useful. Because of the remarkable effectiveness of our mathematical models of computation, computer scientists have tended to forget that computation is dependent on the laws of physics. This can be seen in the statement of the quantitative Church s thesis in van Emde Boas [1990], where the word physical in the above phrasing is replaced with the word reasonable. It is difficult to imagine any definition of reasonable in this context which does not mean physically realizable, i.e. that this computing device could actually be built and would work. Computer ....

P. van Emde Boas (1990) "Machine models and simulations," in Handbook of Theoretical Computer Science, Vol. A (J. van Leeuwen, ed.) Elsevier, Amsterdam, pp. 1--66.

....Yao and Yao in [112] They present for the case d = 1 a data structure supporting queries in time O(m log log n) with space requirement O(nm log m) Their solution was described in the cell probe model of Yao [111] with word size equal to 1. In this paper we adopt the standard unit cost RAM model [105]. For the general case where d 1, d queries can be answered in optimal space O(nm) doing P d i=0 Gamma m i Delta exact queries each requiring time O(m) by using the data structure of Fredman, Komlos Supported by the Danish Natural Science Research Council (Grant No. 9400044) Partially ....

Peter van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity. MIT Press/Elsevier, 1990.

....can create. Rather than define a form of the BM analogous to the pointer machines of Schonhage and others [45, 66, 67, 49, 10] we move straight to a model that uses random access addressing, a mechanism usually considered stronger than pointers (for in depth comparisons, see [9, 10] and also [68]) The following BM form is based on a random access Turing machine (RAM TM; cf. RTM in [30] and indexing TM in [14, 64, 8] and is closest to the BT. Definition 3.5. A RAM BM has one main tape, four address tapes labeled a 1 ; b 1 ; a 2 ; b 2 and given their own heads, and a finite control ....

....R(n) which serves as a measure of parallel time (e.g. R(n) polylog(n) and polynomial work w(n) by deterministic BMs characterizes NC [62] P. van Emde Boas [personal communication, 1994] has observed that while deterministic BMs and NBMs of the weaker kind belong to the second machine class of [68] with R(n) as time measure, NBMs of the stronger kind have properties shown there to place models beyond the second machine class. Related to Problem 2 is whether the classes D d TIME[O(n) differ as d varies. It is also natural to study memory efficient reductions among problems. The following ....

P. van Emde Boas, Machine models and simulations, in Handbook of Theoretical Computer Science, J. V. Leeuwen, ed., Elsevier and MIT Press, 1990, pp. 1--66.

....not implement infinitary term rewriting. Our present definition of an implementation by one system of another (called here an adequate mapping from one to the other) adds to the abundance of concepts of simulation, in term rewriting (e.g. Bar87, ODo85] complexity theory (for an overview see [vEB90]) or programming languages [Mit91] 2. Finitary and infinitary term rewriting 2.1. Basic definitions General introductions to finitary term rewriting may be found in [Der90] and [Klo92] Here we shall define the basic concepts of infinitary term rewriting, which can be seen as including finitary ....

P. VAN EMDE BOAS, Machine models and simulations, in Algorithms and Complexity, in Handbook of Theoretical Computer Science, volume A, ed. J. van Leeuwen, (Elsevier, Amsterdam, 1990).

....and lower bounds are shown for various data processing primitives, and some interesting open problems are given. 1 Introduction Recent years have seen marked dissatisfaction with the computational realism of the classic machine models, such as Turing machines or the standard integer RAM (see [13, 12]) Many algorithms that theoretically run in linear time on the RAM scale non linearly when it comes time to implement them. Cook [5, 6] proposed replacing the usual unit cost RAM measure by the log cost criterion, by which an operation that reads an integer i stored at address a is charged log ....

P. van Emde Boas. Machine models and simulations. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 1--66. Elsevier and MIT Press, 1990.

....size branching programs compute exactly the same class of functions as log space bounded nonuniform Turing machines. The time and space requirements of branching programs give a lower bound on the (respective) time and space requirements of logarithmic cost RAMs. See page 23 of van Emde Boas [vEB90] for a definition of the logarithmic cost RAM model. There are several possible ways of defining space on logarithmic cost RAMs (see the discussion on page 27 of [vEB90] The following proposition holds for any definition of space which ensures that the space requirement of any particular ....

....give a lower bound on the (respective) time and space requirements of logarithmic cost RAMs. See page 23 of van Emde Boas [vEB90] for a definition of the logarithmic cost RAM model. There are several possible ways of defining space on logarithmic cost RAMs (see the discussion on page 27 of [vEB90] The following proposition holds for any definition of space which ensures that the space requirement of any particular computation is greater than or equal to the number of bits needed to describe configurations of the machine during this computation. All reasonable definitions of space on the ....

Peter van Emde Boas. Machine models and simulations. In Jan Van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity, chapter 1, pages 1--66. M.I.T. Press/Elsevier, 1990.

....ffl so that 6 is non singular, the lemma results. 139 Chapter 11 Parallel Time Classes Parallel models have in principle more power than sequential 3 ones. Many Parallel models exist, and not all of them are equivalent. Our parallel models are taken from the so called Second Machine Class [VEB90] This class captures a very frequently observed features of parallelism, characterized by the Parallel Computation Thesis: time on these models corresponds, modulo polynomial overheads, to space on First Class models. Prominent members of the Second Machine Class are the alternating Turing ....

....nondeterministic, e.g. classes like P, PSPACE, or NP. Relativizations of these classes are also used; the oracle machine model used for defining them is standard. All these classes are invariant under changes of the machine model, provided that it stays within the so called First Machine Class [VEB90] they simulate and are simulated by multitape Turing machines within a polynomial time overhead and a linear space overhead. 140 The extended nets we consider in this chapter have processors with either an update equation of the form x i (t 1) oe P i (x 1 (t) xN (t) Q i (x ....

P. Van Emde Boas. Machine models and simulations. In Handbook of Theoretical Computer Science, volume A, pages 1--66. MIT/Elsevier, 1990.

....If g = O(t) O(n) we say that model M 2 simulates M 1 linearly. If g = O(t) the simulation has constant factor overhead ; if g = O(t log t) it has a factor of O(log t) overhead , and so on. The simulation is on line if each step of M 1 is simulated by step(s) of M 2 in some transparent manner see [vEB90, LL92b] for discussion of how to formalize this. The most powerful sequential models in the survey by van Emde Boas [vEB90] are forms of the random access machine (RAM) with the unit cost time measure (RAM TIME) which charges one time unit to execute any instruction. A standard RAM has addition and ....

....g = O(t log t) it has a factor of O(log t) overhead , and so on. The simulation is on line if each step of M 1 is simulated by step(s) of M 2 in some transparent manner see [vEB90, LL92b] for discussion of how to formalize this. The most powerful sequential models in the survey by van Emde Boas [vEB90] are forms of the random access machine (RAM) with the unit cost time measure (RAM TIME) which charges one time unit to execute any instruction. A standard RAM has addition and subtraction as arithmetic operations. 2 For our purpose, the arguments of Cook and Reckhow [CR73] that unit cost is ....

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P. van Emde Boas. Machine models and simulations. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 1--66. Elsevier and MIT Press, 1990.

....(d Gamma1) dimensional tapes. Graedel [Gra90] studied the class of languages L such that for all ffl 0, L is acceptable in time O(n 1 ffl ) by one of the respective kinds of machines, observing a slightly better robustness picture. For background on these machines and simulations, see [WW86, vEB90] For related work on limited nondeterminism classes, see [KF80, DT90, BG93, BG94] Our answer to this problem of non robustness is to arrange that all of our quasilinear time upper bounds be attainable by Turing machines, and that our lower bounds hold even for RAMs. A second difficulty ....

P. van Emde Boas. Machine models and simulations. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, pages 1--66. Elsevier and MIT Press, 1990.

....memory. Here we are only concerned with the complexity measures R(n) and w(n) 3 It has been observed that the distinction between arithmetic and vector registers is inessential, shifts being the same as multiplication and division by powers of 2, and that left shifts are unnecessary see [Sim75, BDG88, vEB90, KR90, TLR92] for these observations and alternate forms of the VM. The original form makes the clearest comparison to the BM. the Pratt Stockmeyer model. The main theorem of this paper is that these adjustments lead to exact characterizations of the classes NC k . 3. Basic List Operations Much of the ....

P. van Emde Boas. Machine models and simulations. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 1--66. Elsevier and MIT Press, 1990.

....infinite seems to be decreasing with respect to the centrality of the numerable infinite N. This centrality is suggested by several facts: the formal definition, within Arithmetic, of important questions about complexity theory [7] the relevance of N in the description of computational processes [6, 18, 23, 4]; the confirmation of the importance of fragments of Arithmetic for Proof Theory [25, 5] On the contrary, results of research on uncountable infinites regard internal aspects of Set Theory [25, 5] moreover, the work focuses more on the concept of self reference, intrinsic to the notion of ....

P. Van Emde Boas. Machine models and simulations. In Van Leeuwen J., editor, Handbook of Theoretical Computer Science, pages 3--61. Elsevier, Amsterdam, 1990.

....problem for N trivially gives a solution for N we assume 0 N M 2 . The membership problem is to answer a query whether a given element x 2 M is in N . The problem has the obvious dynamic extension which also includes the operations insert and delete. We use the standard cell probe model (cf. [6, 10, 15]) with word size dlg Me bits. 2 In other words, one register can be used to represent a single element from the entire domain M, specify all elements which are present in a set of a size lg M elements, refer to some portion of the data structure, or have some other role that is a (dlg Me bit) ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity, chapter 1, pages 1 -- 66. Elsevier, Amsterdam, Holland, 1990.

....the processor s point of view and we assume that the processor performs any operation from its instruction set in one unit of time. It is reasonable to add some theoretical background about the model of computation we are dealing with. The model we use is a cell probe model as it was defined in [2, 3, 8] with a word size m and a usual instruction set including multiplication. 2 New technique Word size parallelism is a programming technique, which is based on a splitting of the word in a number of blocks and on a parallel performing of non interfering operations on these blocks. Obviously, more ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity, chapter 1, pages 1 -- 66. Elsevier, Amsterdam, Holland, 1990.

....6. if d im k then write (d im ; i) end If the starting index of an accepting path is required a backtracking procedure that resolves the minimizing path has to be included in the if statement on the line 6 of the Algorithm 1. Clearly, both the time and space requirements (in RAM machine model [13]) for this algorithm are O(mn) However, if it is enough only to report an occurrence the space requirement can be diminished to O(m) because the book keeping of the table can be done by using only one column and two variables. Also the time requirement can be diminished by using the following ....

....can be calculated in LOGSPACE. It is somewhat bothersome that the space requirements for the Algorithm 1 presented in RAM machine and for the Turing machine calculating the truth of the sentence Phi mis are not directly commensurable. There is a relation between these, as stated by van Emde Boas [13]: Invariance Thesis 7 Reasonable machines can simulate each other within a polynomially bounded overhead in time and a constant factor overhead in space. Furthermore, to quote van Emde Boas [13, p. 5] The study of simulations with polynomial time bounded overhead is a traditional subject in ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science. Volume A: Algorithms and complexity, pages 3--66. Elsevier, Amsterdam, 1990.

....terms of logic, since it circumvents the rather cumbersome translation to the circuit framework. Seen in terms of parallel complexity, our result relating polynomial time reflective machines and PSPACE is a little less surprising, as it falls within the tradition of the second machine class of [vE90], for which polynomial time always coincides with polynomial space. In terms of the computational style of which it is a model (a computer which occasionally interacts with a very powerful machine via powerful but specialized operations) the reflective relational machine is quite close to the ....

....relation, whose tuples correspond to the tape squares of the simulated machine. The queries then repeatedly update the tape according to the moves of the simulated machine. The details are omitted. Lower complexities The reflective relational machine is evidently a machine of the second class [vE90], a parallel model of computation. It is interesting that it can be used to capture feasible parallel computation (notice that, as is typical below NP, we now need order) Theorem 4.6 On ordered structures, reflective relational machines operating within polylogarithmic time, and with a bounded ....

P. van Emde Boas. Machine models and simulations. In Handbook of Theoretical Computer Science, vol. A, ed. J. van Leeuwen, Elsevier Science Publishers B.V., 1990.

....studied in this work, let us only mention that the sorting problem can be solved work optimally with a speedup factor between p=2 and p=3 compared to the best sequential algorithm. Due to the lack of space several details had to be omitted. They will be in the full paper. 1 Van Emde Boas [19] uses the terminus BRAM in order to refer to a kind of Boolean RAM, which should not lead to any confusion with our model. 2 Preliminaries A PRAM (Parallel Random Access Machine) is a set of Random Access Machines, called processors, that work synchronously and communicate via a global, ....

P. van Emde Boas. Machine models and simulations. In van Leeuwen [20], chapter 1, pages 1--66.

....in which every message invokes a message from all components with a higher id. As we have seen before this leads to an exponential worst case message complexity. 2 In complexity theory it is a well known fact that the underlying machine model has a big influence on the complexity of the algorithm [vEB90]. Finite State Machines and ACP both suppose an underlying parallel machine model. The results above show that the execution model of a specification formalism sometimes also has a major influence on the complexity of a distributed algorithm. 6 Verification and Validation in ACP 6.1 ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science (vol. 1). Elsevier Science Publishers, 1990.

....routing methods for read and write requests. But these simulations may be unacceptable slow, since there is a potentially large overhead as part of each instruction for synchronization and communication. 2 A good overview of sequential and earlier parallel machine models can be found in [27]. 3 The EREW PRAM only deals with contention for a single memory location. 6 RELATED WORK 20 Many extensions of the basic PRAM model have been proposed which address one or more of the problems mentioned above. The delay PRAM of Papadimitriou and Yannakakis [16] assumes that there is a ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A. Elsevier Science Publishers and MIT Press, 1990.

....serial machine models, of which the Turing machine is a prime example. The latter corresponds to second class models, with the power of massively parallel computers, in which time is polynomially equivalent to Turing machine (first class) space (see Section 2 for definitions of these classes, and [29] for an exposition of first and second class models) For all we know our class could coincide with P, PSPACE, both, or form a third intermediate class. Yet, if we show that adding threshold strictly increases the power of networks we have actually shown that P 6= PSPACE. Recall, however, that the ....

....uses exponentially many processors, or implicit, in that it sequentially executes operations involving exponentially large objects. The first happens, for example, with the Parallel RAM or PRAM model. The second case is true, for example, for the vector machines of Pratt and Stockmeyer [21] See [29] for more information on second class models. In [2] it was shown that networks with polynomials, division, and bitwise AND operations on rational numbers constitute a second class machine. The proof consisted essentially of an efficient simulation of a vector machine by such a network, with the ....

P. Van Emde Boas, "Machine models and simulations", in Handbook of Theoretical Computer Science, vol. A, MIT/Elsevier, 1990, 1--66. g f h P 2P 0 c d c+P d+P

....increases the space, violating one of our key concerns. Therefore, we develop a solution for L 1 from scratch. We use the extended random access machine model (ERAM) whose instruction set includes integer multiplicationand division, and bitwise Boolean operations (cf. 6] and MBRAM in [14]) We assume that one register is large enough to store one coordinate of a point it is m bits (m = lg M ) wide. Our solutions consist of two parts: first we explain how to search for the closest neighbour in a small, b point universe (b = dm) and second how to search in a big M d point ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity, chapter 1, pages 1 -- 66. Elsevier, Amsterdam, Holland, 1990.

....by Yao and Yao in [15] They present for the case d = 1 a data structure supporting queries in time O(m log log n) with space requirement O(nm log m) Their solution was described in the cell probe model of Yao [14] with word size equal to 1. In this paper we adopt the standard unit cost RAM model [13]. Supported by the Danish Natural Science Research Council (Grant No. 9400044) This research was done while visiting the Max Planck Institut fur Informatik, Saabrucken, Germany. Email: gerth daimi.aau.dk. On leave from Institute of Informatics, Warsaw University, ul. Banacha 2, 02 097, ....

P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity. MIT Press/Elsevier, 1990.

....it is easy to see that the KUM can be easily and efficiently simulated by the SMM; it may be weaker than the latter, but this is also open. 2.8 Pointers to Literature Among the above models, the one most extensively studied is the SMM. Most of the results regarding this model are reported in [15]. Some of these results also pertain to the other, possibly weaker models, while some make use of the full power of the SMM. An interesting discussion of the KUM may be found in [6] Jones [8] presents several results on his I and I su models. 3 Abstract Machines: High Level Models Recall that ....

P. van Emde Boas, "Machine models and simulations," in: Handbook of Theoretical Computer Science, Vol. A, Elsevier, 1990, 1--66.

....Logical Calculi which are used by mathematicians and or logicians for proving theorems or evaluating complex expressions, also can be seen to be specific instances of the abstract framework. For further details and a discussion of the relative merits of the various models I refer to the literature [9, 14, 18, 22, 26, 28]. Inspection of the literature will also eliminate the implicit circularity in the definitions as given in this paper: when referring to structures in the formalization being easy or local I am invoking (be it at the meta level) the very concept of efficient computability I am trying to ....

....exponential time) are generally held to be intractable. The choice for this borderline has the nice property that it is sufficiently large to absorb the simulation overheads which are implicit in the proofs establishing the equivalence between the various models of machine based computation [28], whereas it is narrow enough to become a meaningful boundary between the tractable and the intractable problems. There exists however one feature of the computational model for which this equivalence has not been established: the use of nondeterminism. The class NP consists of those sets which ....

van Emde Boas, P. Machine models and simulations, in J. van Leeuwen (ed.), Handbook of theoretical computer science, Vol. A, North Holland Publ. Comp. (1990), pp. 1--66

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P. van Emde Boas, Machine Models and Simulations. In: J. van Leeuwen (ed.). Handbook of Theoretical Computer Science, Vol. A. The MIT Press/Elsevier, 1990, 3--66.

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P. van Emde Boas, Machine models and simulations. In: van Leeuwen, J., ed., Handbook of Theoretical Computer Science, Vol. A, Elsevier, Amsterdam, 1990, 525--632.

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P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, pages 1-66. Elsevier, Amsterdam, 1990.

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P. van Emde Boas. Machine models and simulations. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, pages 1--66. Elsevier and MIT Press, 1990.

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P. van Emde Boas, "Machine models and simulations," in J. van Leeuwen, Ed., Handbook of Theoretical Computer Science, vol. A: Algorithms and Complexity, Amsterdam: North-Holland (1990), pp. 1--66.

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