Deductive synthesis

A graph confronting the specification languages with the synthesis mechanisms would be very sparse, because some mechanisms are unique to specification languages. The achievements of inductive and deductive synthesis are surveyed in Chapter 2 and Chapter 3, respectively. 

The theoretical foundations to transformational synthesis are being laid out by [Lau and Omaghi 93, 94ab] [Lau et al. 94]. (Note that their deductive synthesis corresponds to what we here call transformational synthesis.) This work introduces a realistic specification elaboration scenario, based on specification frameworks, where the synthesis process may provide feedback to the specification elaboration process. 

The other major problem with deductive synthesis is related to the formality of the specifications. Where do the formal specifications come from If deductive synthesizers guarantee total correctness of the resulting algorithms with respect to their specifications, what guarantee do we have that these specifications correctly capture our intentions These questions are often either dismissed as irrelevant or considered as intractable issues that are left for future research. But what use are these synthesizers if we don t even know whether they solve our problems or not See [Le Charlier 85] and [Flener and Popelmsky 94] for a detailed discussion of this controversial topic. 

Other researchers have tackled Shapiro s remarks on oracle mechanization [Shapiro 82, Section 3.7] via the incorporation of constraints and partial specifications . The solutions by [Lichtenstein and Shapiro 88], [Drabent et al. 88], and [De Raedt and Bruynooghe 92a] are surveyed in Chapter 6. The solution by [Dershowitz and Lee 93] seems unrealistic in general, because it relies on a complete specification, which could thus rather be used to perform deductive synthesis. 

How to synthesize logic algorithms that are non-determini Stic, such as those for member and permutation As seen in Section 2.4, this is known to be a hard problem for deductive synthesis approaches. 

K.-K. Lau and M. Omaghi. A formal view of specification, deductive synthesis and transformation of logic programs. In [Deville 94], pp. 10-31. 

Z. Manna and R. Waldinger. Deductive synthesis of the unification algorithm. Science of Computer Programming l 5-48, 1981. Also in [Biermann and Guiho 83], pp. 251-307. 

In Chapter 2, we survey the use of deductive inference in automatic programming. Axiomatic specifications are expected to be complete and non-ambiguous, but are usually also quite lengthy and artificial. Deductive synthesis from axiomatic specifications can be classified into transformational synthesis, proofs-as-programs synthesis (or constructive synthesis), and schema-guided synthesis. We survey the achievements of deductive synthesis of LISP functions and Prolog predicates. 

Because of their ease of synthesis and their structural similarity to peptides, many laboratories have used peptoids as the basis for combinatorial drug discovery. Peptoids were among the first non-natural compounds used to establish the basic principles and practical methods of combinatorial discovery [17]. Typically, diverse libraries of relatively short peptoids (< 10 residues) are synthesized by the mix-and-split method and then screened for biological activity. Individual active compounds can then be identified by iterative re-synthesis, sequencing of compounds on individual beads, or indirect deduction by the preparation of positional scanning libraries. 

The analysis of the branching structure turns the preceding deduction process around. We have all the facts available to us at the end of the solution synthesis, i.e., at the end of solving a particular problem. Our task is to select and connect subsets of those facts to prove new results that are useful for deriving new control information. In essence, we have to turn facts about solutions and partial solutions at lower levels in the tree, into constraints on the properties of states and alphabet interpretations higher in the tree. 

The balance of the compounds in Table VIII support the earlier statement that any compound containing fluorine is toxic to moths. These fluorinated hydrocarbons, phenols, acids, sulfonic acids, and sulfones probably act against moths as stomach poisons. The fluorosulfonic acid derivatives and the sulfone with a fluorinated substituent were key compounds whose toxicity to moths laid the groundwork for the deductions which led to the synthesis and testing of DDT as an insecticide. 

The Conceptual Synthesis of Chemical Processing Schemes Michael L. Mavrovouniotis, Symbolic and Quantitative Reasoning Design of Reaction Pathways through Recursive Satisfaction of Constraints Christopher Nagel and George Stephanopoulos, Inductive and Deductive Reasoning ... 

The logical and combinatorial chemical applications of computers are based on integer computation. Storage, retrieval and manipulation of data as well as deductive operations by computers are in that category. Chemical documentation, information oriented synthesis design, and the deductive solution of chemical problems are examples. In the deductive solution of chemical problems the solutions of the individual problems are deduced from general principles. 

In addition to surprisal analysis of measured product energy distributions, surprisal synthesis has been applied [178] to the prediction of energy distributions either by induction from some more limited experimental data or by deduction from some dynamical calculation. In the inductive approach to surprisal synthesis, the available experimental data is used as a constraint to compute the surprisal parameter, X, by ensuring that the entropy is maximised. This surprisal parameter then determines a more detailed distribution. In a more modest way, this approach may be used to extend incomplete product energy distributions. For example, as mentioned before, infrared chemiluminescence measurements are incapable of determining the population of products in the vibrational ground state, v = 0, and this is often induced from the surprisal analysis of the other vibrational levels. 

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