Synthesis of fast programs for maximum segment sum problems

Abstract

It is well-known that a naive algorithm can often be turned into an efficient program by applying appropriate semanticspreserving transformations. This technique has been used to derive programs to solve a variety of maximum-sum programs. One problem with this approach is that each problem variation requires a new set of transformations to be derived. An alternative approach to synthesis combines problem specifications with flexible algorithm theories to derive efficient algorithms. We show how this approach can be implemented in Haskell and applied to solve constraint satisfaction problems. We illustrate this technique by deriving programs for three varieties of maximum-weightsum problem. The derivations of the different programs are similar, and the resulting programs are asymptotically faster in practice than the programs created by transformation.

Theory and Techniques for Synthesizing a Family of Graph Algorithms

“…Given an appropriate constructive prover (such as the one in KIDS [16]) such a derivation could in fact be automated. Other examples that have been derived using this approach are Activity Selection [11], Integer Linear Programming [15], and variations on the Maximum Segment Sum problem [10].…”

Correctness by Construction for Pairwise Sequence Alignment Algorithm in Bio-Sequence

“…In domestic and foreign research, there have been many works on formalized development of algorithms. For example, Bird et al [25] used calculus of lists in the derivation process, and finally synthesized a very short functional program with a functional version of the Knuth-MorrisPratt algorithm for pattern matching; JE Durán [26] proposed a transformation development method for efficient imperative network algorithms based on the Mller algebra of formal languages and derived the shortest path tree algorithm based on this method; Abrial et al [27] designed and implemented the minimum spanning tree and Prim problem models using the Event-B method and transformed them into the corresponding solution algorithms; Almeida et al [28] demonstrate three known sorting algorithms derived from a similar sequence of transformation steps from a general specification; Nedunuri et al [29] transformed a naive algorithm into an efficient program by applying appropriate semanticpreserving transformations, and deduced three maximum segment sum problems; Mu et al [30] construct a problem specification using equality reasoning the backtracking algorithm of n-queens. These existing works are mainly applied to general areas in combinatorics, but formal methods have not been applied to develop algorithms in the field of bioinformatics.…”