Sample Logic Algorithms

In order to motivate this research, in Section 5.2.1, we give sample logic algorithms solving some of the problems posed in Section 1.5. Then, in Section 5.2.2, we give some comments on these logic algorithms. 

In order to give some more insights into Stage B of the existing methodology, we first 

Let s first reconsider Step 2 (Selection of a Well-Founded Relation), and follow the Extrinsic Heuristic when selecting a well-founded relation over the type of the induction parameter L. This means that we want to decompose L into something smaller in a way reflecting the structure of parameter C. Every element of C represents a summary of a plateau of L, so the idea is to decompose L by extracting its first maximal plateau as head of L, and the corresponding suffix as tail of L. This decomposition is non-trivial, but considerably facilitates the rest of the construction. Step 3 is unaffected by this decision, and after Step 4, the result is  

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Table 5-2 Summary of the features of some sample logic algorithms...

Observing the histogram for the distances (in the signal domain) of all data samples collected with the three terminals (Figs. 13.7, 13.8 and 13.9), the best performance of the Sonny Ericsson in what concerns to the precision, using the first Fuzzy Logic Algorithm, since it has more points that will be classified as Very Close was already expected. 

The objective of this book is (semi-)automatic logic algorithm synthesis. First, in Section 5.1, we define this objective in more detail and clearly state its boundaries. In order to motivate this research, we develop a series of sample problems in Section 5.2 and show that non-trivial issues have to be solved. This allows us to identify, in Section 5.3, the challenges of logic algorithm synthesis. 

In this chapter, we develop the Proofs-as-Programs Method, which adds atoms to a logic algorithm so that some correctness criteria wrt a set of properties become satisfied. This method is part of our tool-box of methods for instantiating the predicate-variables of a schema. First, in Section 9.1, we state the problem. Then, in Section 9.2, we explain a method to solve this problem, and discuss its correctness in Section 9.3. In Section 9.4, we illustrate this method on a few sample problems. Future work and related work are discussed in Section 9.5 and Section 9.6, respectively, before drawing some conclusions in Section 9.7. 

In Chapter 5, we formulate the objective of this book in more detail, namely (semi-) automated logic algorithm synthesis. A series of motivating sample scenarios allows us to identify the challenges of this objective. 

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