Algebraic system specification and development: A survey and by Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando

By Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, Donald Sannella

Methods for the algebraic specification of summary information forms have been proposed within the early Nineteen Seventies within the united states and Canada and have become a tremendous examine factor in Europe presently afterwards. on the grounds that then the algebraic procedure has come to play a critical position in examine on formal specification and improvement, as its variety of purposes was once prolonged to the specification of entire software program platforms, to the formal description of this system improvement approach, and to the uniform definition of syntax and semantics of programming languages. at the present time this technique extends past simply software program to the improvement of built-in and software program structures. those flourishing actions within the zone of algebraic necessities have resulted in an abundance of techniques, theories and ideas, that have common algebra, class thought and common sense as a standard mathematical foundation. This quantity is an annotated bibliography which supplies an up to date evaluation of earlier and current paintings on algebraic specification. No test is made to supply a coherent creation to the subject for rookies; the goal is quite to supply a advisor to the present literature for researchers in algebraic specification and neighboring fields. a few symptoms of ways different methods are similar are integrated, including a few principles relating attainable destiny directions.

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10. 11. 12. 13. 14. 5 Divisible Load Modeling for Grids to solve the problem. 0. However speedup is usually less than N because of overhead, communication delays and serialization. In the Gantt type chart there is one graph per processor. Time is on the horizontal axis. Communication is shown above the horizontal axis and computation is shown below it. Usually the chart starts at time t = 0. Speedup increases nonlinearly for nonlinear models because of the nonlinear nature of the computing time.

2 P0 2μ2 λ3 P0 6μ3 (c) P0 + P1 + P2 + P3 + . . μn =1 = from well known summation formula. 34. 35. k P (n) = ani i n! i=1 i P (n) = (1/2)n1 n1 ! G−1 (Ω) (1/3)n2 n2 ! n1 + 3n2 ≤ 1000, n∈Ω (1/2)n1 n1 ! (1/3)n2 n2 ! 36. 0 ρ2 2(1 − ρ) ρ 1−ρ - As ρ → 1 E[n] = 2× E[n] M/M/1 M/D/1 - M/M/1 has larger average queue size because of longer (more variable) distribution tail. 37. 38. 39. Global Balance Equation: M M M μj rji P (n + 1j − 1i )* μi P (n) = i=1 Traffic Equations: ∗ Here 1i = [0, 0, 0 . . 1, .

M j=1 Manipulate the Traffic Equations: M rji 1= j=1 θj θi i = 1, 2, . . M Multiply the left hand side of the global balance equation by this expression for one: M M μi rji i=1 j=1 M θj P (n) θi M μj rji P (n + 1j − 1i ) = i=1 j=1 Rearrange as M M θj μi P (n) − μj P (n + 1j − 1i ) θi rji i=1 j=1 =0 If the parenthesis term is 0, this equation is satisfied when θj μi P (n) = μj P (n + 1j − 1i ) i, j = 1, 2, . . M θi Manipulating: P (n) = θi μi θj μj −1 P (n + 1j − 1i ) i, j = 1, 2, . . M which yields P (n) = θi μi P (n − 1i ) or μi P (n) = θi P (n − 1i ), which is the desired result.

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