The Abstraction and Instantiation of String-Matching Programs

Abstract

We consider a naive, quadratic string matcher testing whether a pattern occurs in a text; we equip it with a cache mediating its access to the text; and we abstract the traversal policy of the pattern, the cache, and the text. We then specialize this abstracted program with respect to a pattern, using the off-the-shelf partial evaluator Similix.Instantiating the abstracted program with a left-to-right traversal policy yields the linear-time behavior of Knuth, Morris and Pratt's string matcher. Instantiating it with a right-to-left policy yields the linear-time behavior of Boyer and Moore's string matcher.

Fast partial evaluation of pattern matching in strings

“…To induce this effect, we can either rewrite the matcher so that backtracking only depends on static data (such a rewriting is known as a binding-time improvement or a staging transformation [Mogensen 2000]) and use a simple partial evaluator [Amtoft et al 2002;Consel and Danvy 1989], or keep the matcher as is and use an advanced partial evaluator [Futamura et al 2002a;Secher 2002;Smith 1991;Sørensen et al 1996]. In this article, the starting point is a staged quadratic-time matcher and a simple memoizing partial evaluator such as Similix, where specialization points are dynamic conditional expressions [Bondorf and Danvy 1991].…”

“…In this article, the starting point is a staged quadratic-time matcher and a simple memoizing partial evaluator such as Similix, where specialization points are dynamic conditional expressions [Bondorf and Danvy 1991]. Figure 1 displays a staged matcher similar to the ones developed in the literature [Ager et al 2002;Amtoft et al 2002;Consel and Danvy 1989;Jones et al 1993] (see Appendix A for a more complete picture). Matching is done naively from left to right.…”

DiaSuite

“…This process is most commonly used as an optimization strategy dedicated to removing the interpretation layer. The interpreter paradigm, coupled with partial evaluation, has been successfully applied to a wide range of areas, besides programming language implementations, including string matching [1], networking [2] and operating systems [7]. Although limited in the dimensions covered, this form of a paradigm-oriented software development approach has demonstrated its effectiveness for optimization purposes.…”

Automatic generation of efficient string matching algorithms by generalized partial computation

“…This paper shows that some efficient algorithms can be automatically generated from inefficient ones. Automatic generation of an efficient pattern matcher from a naive one, introduced in [7], is a typical problem for partial evaluation [1,2,5,10,14]. Let m be the length of a given pattern and n be the length of a given text.…”

“…This paper deals with Type 1 problem and reports that, by Generalized Partial Computation (GPC) [8,9], we can generate (1) a Boyer-Moore (BM) type pattern matcher [3] without the bad-character heuristic (the delta 1 table in [3]; see Appendix 1) from a non-linear backward matcher and (2) a Knuth-Morris-Pratt (KMP) matcher from a non-linear forward matcher. Generation of a BM type matcher has been discussed in [2] using off-line partial evaluator. However, there was no proof that every generated matcher runs in the same way as the BM matcher.…”