P. D. Mosses. Denotational Sementics, Handbook of Theoretical Computer Science, Volume B, Chapter 11. Elsevier Science Publishers, Amsterdam; and MIT Press, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....or the other way around. Deciding how these connections are made, either by graph reduction, or by context semantics, must require K (n) steps, no matter how we choose to assign the work associated with this decision problem to the individual parallel steps. 2 1 A rst class machine model [vEB90] is any computational model equal to the power of a Turing Machine, modulo polynomial slowdown. For example, register machines with a logarithmic cost criterion are rst class; counter machines are not. 3 That pictorial diagrams should be a mainstay of formal reasoning has not been entirely ....

....theorem: Theorem 5.3 (Main Theorem) Let 0 be any xed integer. Then there exists a set of explicitly typed, closed terms En : Bool, where jEn j = O(n) En normalizes in O(jEn j) parallel steps, and the time needed to implement the parallel steps, on any rst class machine model [vEB90], grows as K (n) Proof. Let x be a typed, closed term that reduces to true t : o: f : o:t : Bool if and only if an arbitrary, xed Turing Machine M accepts x in K 1 (jxj) steps, where the coding of x is given by Corollary 5.2. By that Corollary and the previous Theorem 5.1, ....

Peter van Emde Boas. Machine models and simulation. Handbook of Theoretical Computer Science, volume A, pp. 1-66. North Holland, 1990.

....is a triple of a function name, a list of formal parameters, and an expression. Expressions can be variables, constants, conditionals, primitive operations, and function calls. Function calls are special. Their rst parameter always accesses the underlying indexed value. The semantics is standard [18], except for the partial function . It is the index function for the underlying indexed value. It is a parameter of the program The startup function (define (main 1 x 3 x 2 x 1) let ( mlet 4 (car x 1) mlet 5 (cdr x 1) mlet 6 (car mlet 5) mlet 7 (cdr mlet 5) mlet 8 (car mlet 7) ....

Peter D. Mosses. Denotational Semantics, volume B of Handbook of Theoretical Computer Science, chapter 11. Elsevier Science Publishers, Amsterdam, 1990.

.... multithreaded slaves architecture for the data parallel evaluation of data field requests. The software architecture described on the right implements the field algebras sketched on the left. Functions i T i 1 are phases of the evaluation. The functions [ i are the semantic functions [31] that map an expression to the denoted element of Z n Value. They are defined such that the diagram commutes, that is [ e i ] i = i T i 1 (e i ) i 1 is true for i 2 f0; 1g and e i 2 L i . This property ensures the soundness of the evaluation process. The evaluation of a L 0 term begins ....

P. D. Mosses. Handbook of Theoretical Computer Science, volume 2, chapter Denotational Semantics, pages 575--631. Elsevier Science, 1990.

.... the jEj parallel fi steps could indeed be implemented at time cost K (jEj) we would then have shown that dtime[K 1 (jxj) dtime[K (jEj) But the time hierarchy theorem from complexity theory (see, e.g. HU79] tells us that this implied conclusion is 1 A first class machine model [vEB90] is any computational model equal to the power of a Turing Machine, modulo polynomial slowdown. For example, register machines with a logarithmic cost criterion are first class; counter machines are not. false, since jEj is polynomial in n; at least K (n) time steps are necessary. Were jEj 2 ....

....most important theorem: Theorem 5. 3 (Main Theorem) There exists a set of closed terms En : Bool, where jEn j = O(n log (c) n) for any integer c 0, such that En normalizes in O(jEn j) parallel fi steps, and the time needed to implement the parallel fi steps, on any first class machine model [vEB90], grows as Omega Gamma K (n) for any fixed integer 0. The Main Theorem must apply to the machine defined by Lamping s algorithm, since the graph reduction operations can be easily implemented with a time complexity that is polynomial in the number of such operations, hence the graph ....

Peter van Emde Boas. Machine models and simulation. Handbook of Theoretical Computer Science, volume A, pp. 1--66. North Holland, 1990.

....equation x = e 1 fby e 2 where fby is a new operator waiting for the first tick in the clock of e 1 and then switching to the stream e 2 . The denotational semantics of L is based on an extension of Kahn s original semantics for dataflow networks [19] The notations are slightly adapted from [28]. 3.1 Stream values and clocks The basic domain consists of finite and infinite sequences over the sets of integer and boolean values extended with the value nil to represent the absence of a value: ScalarValue = Bool [ Int [ fnilg Value = ScalarValue [ ScalarValue 1 The operation : ....

....= Bool [ Int [ fnilg Value = ScalarValue [ ScalarValue 1 The operation : denotes the concatenation of finite or infinite sequences. In Value, u approximates v, written u v if v = u:w. This order is choosen against the more general Scott order (e.g. used for defining domains of functions [28]) in accordance with our interpretation of the succession of elements in the stream as the progression in time of the evaluation process. A first idea to describe timed stream is to associate to the sequence of values, a sequence of boolean flags telling if an element is in the clock of the ....

P. D. Mosses. Handbook of Theoretical Computer Science, volume 2, chapter Denotational Semantics, pages 575--631. Elsevier Science, 1990.

....the contents of the referenced cell to its continuation. The operation fupd t 1 t 2 t 3 updates the heap t 1 at location t 2 with the value of t 3 . It passes the updated heap to its continuation. Lower level definitions of these operations may be found in standard texts on denotational semantics [21, 29]. For example, they can be easily defined in Thiemann terms of sto extended with numbers. We will make use of a pattern matching notation for abstractions, e.g. x; y) t, in order simplify the decomposition of pairs that are passed as arguments. We omit the explicit application . 4.2 ....

Peter D. Mosses. Denotational Semantics, volume B of Handbook of Theoretical Computer Science, chapter 11. Elsevier Science Publishers, Amsterdam, 1990.

....or the other way around. Deciding how these connections are made, either by graph reduction, or by context semantics, must require K (n) steps, no matter how we choose to assign the work associated with this decision problem to the individual parallel fi steps. 2 1 A first class machine model [vEB90] is any computational model equal to the power of a Turing Machine, modulo polynomial slowdown. For example, register machines with a logarithmic cost criterion are first class; counter machines are not. That pictorial diagrams should be a mainstay of formal reasoning has not been entirely ....

....most important theorem: Theorem 5. 3 (Main Theorem) There exists a set of closed terms En : Bool, where jEn j = O(n log (c) n) for any integer c 0, such that En normalizes in O(jEn j) parallel fi steps, and the time needed to implement the parallel fi steps, on any first class machine model [vEB90], grows as Omega Gamma K (n) for any fixed integer 0. Proof. Let Psi x be a typed, closed term that reduces to true j x : y : x : Bool if and only if an arbitrary, fixed Turing Machine M accepts x in K 1 (jxj) steps, where the coding of Psi x is given by Corollary 5.2. By that ....

Peter van Emde Boas. Machine models and simulation. Handbook of Theoretical Computer Science, volume A, pp. 1--66. North Holland, 1990.

....lazy copying can be bounded by a polynomial in the number of unique L evy labels. Polynomial relatedness is the fundamental equivalence relation inherent in the invariance thesis that characterizes first class machine models; this notion is the computer scientist s refinement of Church s thesis [vEB90]. In a recent paper, Asperti has advocated the number of fan interactions as the defining cost metric for calculus reduction [Asp96] He intuitively asserts that Lamping s abstract algorithm performs no useless work. We agree with the assessment of the efficiency of the abstract algorithm. ....

Peter van Emde Boas. Machine models and simulation. Handbook of Theoretical Computer Science, volume A, pp. 1--66. North Holland, 1990.

....we show that they are all inefficient. Machine models: Compiler and interpreter technology relate the two cultures of machines and languages at a theoretical level as well as at a practical one. There is a substantial theory literature on machine simulations (see, e.g. the survey paper [vEB90]) founded on the Invariance Thesis, the modern day version of Church s Thesis: Reasonable universal machines can simulate each other within a polynomially bounded overhead in time and a constant factor overhead in space. Machine simulation is just the theorist s version of hardware emulation, ....

....measure the efficiency of different implementations. Taste and aesthetics govern choice of a model, with a sanity check given by the Invariance Thesis: Reasonable universal machines can simulate each other within a polynomiallybounded overhead in time and a constant factor overhead in space [vEB90]. This sanity check has two basic components: 1) if reducing E requires time t and space s, then there must be an implementation (say, on a Turing machine) using P (t) time and cs space, for some fixed polynomial P and constant c; 2) there must be a coding of Turing machine computations as ....

Peter van Emde Boas. Machine models and simulation. Handbook of Theoretical Computer Science, volume A, pp. 1--66. North Holland, 1990.

....single equation x = e1 fby e2 where fby is a new operator waiting for the first tick in the clock of e1 and then switching to the stream e2 . The denotational semantics of L is based on an extension of Kahn s original semantics for dataflow networks [17] The notations are slightly adapted from [23]. 3.1 Stream Values and Clocks The basic domain consists of finite and infinite sequences over the sets of integer and boolean values extended with the value nil to represent the absence of a value: ScValue = Bool [ Int [ fnilg and Value = ScValue [ ScValue 1 . The operation : denotes the ....

....= Bool [ Int [ fnilg and Value = ScValue [ ScValue 1 . The operation : denotes the concatenation of finite or infinite sequences. In Value, u approximates v, written u v if v = u:w. This order is chosen against the more general Scott order (e.g. used for defining domains of functions [23]) in accordance with our interpretation of the succession of elements in the stream as the progression in time of the evaluation process. A first idea to describe timed stream is to associate to the sequence of values, a sequence of boolean flags telling if an element is in the clock of the ....

P. D. Mosses. Handbook of Theoretical Computer Science, volume 2, chapter Denotational Semantics, pages 575--631. Elsevier Science, 1990.

....based on work of D. Scott and Ch. Strachey, give the meaning of statements or programs at a more abstract level. A semantics consists of a set of functions, defined inductively over the abstract syntax tree, that map language constructs to mathematical values in what are known as domains [20, 6, 26, 30]. One distinguishes between direct style and continuation style semantics. Directstyle semantics are perhaps easier to understand at the beginning but become more complicated as soon as the control constructs of a programming language become more involved (e.g. goto s, exceptions) In contrast, it ....

Peter D. Mosses. Denotational Semantics, volume B of Handbook of Theoretical Computer Science, chapter 11, pages 575 -- 632. The MIT Press / Elsevier, 1990.

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P. D. Mosses. Denotational Sementics, Handbook of Theoretical Computer Science, Volume B, Chapter 11. Elsevier Science Publishers, Amsterdam; and MIT Press, 1990.

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P. D. Mosses. Denotational Semantics, volume B of Handbook of Theoretical Computer Science, chapter 11. Elsevier Science Publishers, Amsterdam, 1990.

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