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 info varieties have been proposed within the early Seventies within the united states and Canada and have become a huge study factor in Europe almost immediately afterwards. on the grounds that then the algebraic method has come to play a primary function in examine on formal specification and improvement, as its variety of functions used to be prolonged to the specification of whole software program structures, 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 advance of built-in and software program structures. those flourishing actions within the quarter of algebraic requisites have ended in an abundance of ways, theories and ideas, that have common algebra, type conception and good judgment as a standard mathematical foundation. This quantity is an annotated bibliography which gives an updated evaluation of prior and current paintings on algebraic specification. No try is made to supply a coherent creation to the subject for novices; the goal is very to supply a advisor to the present literature for researchers in algebraic specification and neighboring fields. a few symptoms of the way different methods are comparable are integrated, including a few rules pertaining to attainable destiny directions.

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2-2 is shown in Fig. 2-4. F T Figure 2-4. Tree from Fig. 2-2 after reduction This way of representing Boolean functions was originally presented by Akers [Aker78]. By additionally introducing a variable ordering, Bryant further refined this approach such that a normal form results [Brya86]. Imposing a variable ordering requires that for every tree traversal from the root to a leaf the variables in the nodes occur in the same ordering. This property leads to its name: reduced ordered binary decision diagram, abbreviated as ROBDD.

This is repeated until all circuit inputs are reached. It is also possible to combine both approaches [JNCK96]. Example 2-14. We want to construct the Boolean function for the combinational circuit of Fig. 2-1l. The forward approach first creates the Boolean function for the gate with inputs xl and x2: f 1(Xl,X2) := xl/\x2. Then this function is OR-connected with X2 and x3: f2(xl,x2,x3) := (xl/\x2)vx2vx3. Adding X4 by an EXOR operation leads to f(h,x4)= f(xl,x2,x3,x4) := ((xl /\X2)VX2VX3)EBx4· The backward moving approach starts by constructing f(f 2,x4) := f 2 EBx4 for the output gate.

Depending on the actually used representation for Boolean functions the overall efficiency may differ. 2 Relational Cirenit Representation Besides modeling combinational circuits directly by Boolean functions we can use a relational representation. In this case the circuit outputs are modeled explicitly by additional variables. As the circuit output - and thus also its representing variable - 50 2 Boolean Functions always carries the value which is computed by the circuit - and by its corresponding Boolean function - we get an relational representation Y~ f(xj, ...

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