Logic algorithm construction

Task A is done in the same fashion as in manual logic algorithm construction [Deville 90] (see Section 4.2) the induction parameter must be simple, and of an inductive type. This selection can be automated by type inference from the given examples. In case more detailed specification knowledge is available, the Functionality Heuristic (Heuristic 4-1) and the Directionality Heuristic (Heuristic 4-2) may even be used, the latter being of higher precedence in case they yield contradictory results. A reasonable implementation of this synthesis mechanism would actually even accept preference hints from the specifier. We assume that the parameter is selected as induction parameter, where [Pg.162]

We first construct a few alternative logic algorithms for the compress problem. Then we list some logic algorithms for some of the problems posed in Section 1.5. 

The latter task cannot be further explained here, as the heuristics are application-specific. A semantic specialization of LA r) would be T(r) re-expressed as a logic algorithm. The most useful specialization is however a syntactic specialization that only adds atoms to the existing disjuncts of LA(r), and hence preserves the existing computations. Indeed, the ultimate objective is not that LA r) be totally correct wrt fP(r), but that LA" r) be totally correct wrt di. So the construction of LA r) is only a useful intermediate step. 

Let s close in now on the MSG Method. Intuitively, its objective is to infer a logic algorithm of a predicate r n, given a finite set of examples of rhi The method should be applicable if the intended relation (from which the examples are extracted) can be expressed by a logic algorithm that is defined solely in terms of the =/2 primitive (hence is non-recursive, among others). This is feasible iff, in the intended relation, some parameters are somehow syntactically constructed from some other parameters. 

Finally, the methods of tasks A, C, D are non-deterministic, but finite. This means that choice-points are created there, and that the made selections may be reconsidered later, either because synthesis fails, or because synthesis succeeds and the specifier wants more algorithms. Only Task A could possibly fail, namely if there is no parameter of an inductive type. Do not mix up non-deterministic synthesis and a non-deterministic synthesized algorithm. The latter would feature either mutually nonexclusive cases or predicates that are non-deterministic. The logic algorithm synthesized at Step 2 is deterministic, because the two cases are mutually exclusive by construction, and because the introduced predicates are deterministic. 

First, the support of the extrinsic and logarithmic decomposition strategies is quite difficult, as the required knowledge about the intended relation is not available. This apparent drawback may be alleviated however by the observation that the logic algorithms LA r-inhX) and LA r-ext-Y) are by construction quite similar. Compare... 

John von Neumann constructed several models (originally known as kinematic models ) with the goal of incorporating the logical core of self-production into the system. Others studied von Neumann s model and modified it, for example, Walter Fontana, who devised the AlChemy (Algorithmic Chemistry) system. This can be described as artificial chemistry, an evolution reactor in which the objects which react are not molecules but mathematical functions. 

Figure 8 Logical structure of the algorithm for the construction of the numerators in the intermediates FjJKAC...

By definition, the dimension of the DG of an algorithm is identical to the index space dimension. In particular, the bit-level algorithm of equation (14) should be described by a W-D DG. However, the construction of the multidimensional DG is avoided by using combinatorial logic to compute the values of Zk -)j thus reducing the problem to multiple-operand binary addition, which can be represented by a 2-D DG. Moreover, in this DG, the properties of the target architecture may be embodied. 

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