Logic algorithm transformation

Stage B Design of a logic algorithm (and possibly its transformation) ... 

This chapter is organized as follows. In Section 4.1, we discuss the elaboration of specifications. Section 4.2 is about the design of logic algorithms, whereas Section 4.3 is about their transformation. Section 4.4 describes the derivation of logic programs, whereas Section 4,5 describes their transformation. 

In the case of incremental synthesis, let s view the steps of one synthesis increment as a macro-step performing a transformation trans. Synthesis is then the design of a series of logic algorithms ... 

Reality is more complex, however. Function-variables and predicate-variables may have any arity, and this calls for schema-variables to denote these arities. Conjunctions, disjunctions, or quantifications of any length may appear, and this calls for schema-variables to denote the ranges of such ellipses. Permutations of parameters, conjuncts, disjuncts, or quantifications may have to be performed in order to see why a logic algorithm is an instance of some schema. Unfold transformations may have to be performed in order to see why a logic algorithm is an instance of some schema. 

A possible enhancement is a schema that automatically introduces an additional parameter to the specified predicate, hence covering LA(split) (LA 5-19). Such an extension is discussed by [Summers 77]. This schema could still be considered a design schema, rather than a transformation schema, as it is not possible to design a logic algorithm for split/3 that is covered by one of the given versions. 

Molecular descriptors are formally mathematical representations of a molecule obtained by a well-specified algorithm applied to a defined molecular representation or a well-specified experimental procedure the molecular descriptor is the final result of a logical and mathematical procedure which transforms chemical information encoded within a symbolic representation of a molecule into a useful number or the result of some standardized experiment. 

In the previous chapter we saw how the matrix elements of a NMR density matrix relate to spectral lines. In the context of NMR QIP, an algorithm is nothing but a radiofrequency pulse sequence which encodes quantum logic gates. Each radiofrequency pulse implements an unitary transformation, which is used to prepare the initial state, and process the information and the computation. Under a sequence of unitary operators U (ti), U(t2), U(t ), the initial equilibrium density matrix transforms according to ... 

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