Partial Evaluation of Pattern Matching in Strings, revisited

Grobauer, Bernd; Lawall, Julia

doi:10.7146/brics.v7i31.20165

Cited by 7 publications

(16 citation statements)

References 14 publications

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“…After 15 years, however, we observe that 1. the KMP test, as it is called, appears to have had little impact, if any, on the development of algorithms outside the field of partial evaluation, and that 2. except for Grobauer and Lawall's recent work [13], issues such as the precise characterization of time and space of specialized string matchers have not been addressed.…”

Section: List Of Figuresmentioning

confidence: 99%

“…The resulting residual program is displayed in Figure 5, after lambda-dropping [8] and renaming (the character following the "|", in the subscripts, is the next character in the pattern to be matched against the text-an intuitive notation suggested by Grobauer and Lawall [13]). The specialized string matcher traverses the text linearly and compares characters in the text and literal characters from the pattern.…”

Section: Program Specializationmentioning

confidence: 99%

“…(Indeed, Grobauer and Lawall have shown that the size of these residual programs is bounded by |pat | × |Σ|, where pat denotes the pattern and Σ denotes the alphabet [13]. )…”

Section: This Workmentioning

confidence: 99%

“…We relate the original KMP algorithm [18] to a staged quadratic string matcher that keeps one character of negative information (essentially Consel and Danvy's original solution [7]; there are many ways to stage a string matcher [1,13], and we show one in Appendix A). Our approach is semantic rather than algorithmic or intuitive:…”

Section: This Workmentioning

confidence: 99%

“…In their revisitation of partial evaluation of pattern matching in strings [13], Grobauer and Lawall analyzed the size and complexity of the residual code produced by Similix, measured in terms of the number of residual tests. They showed that the size of a residual program is linear in the length of the pattern, and that the time complexity is linear in the length of the text.…”

Section: Program Specializationmentioning

confidence: 99%

See 4 more Smart Citations

On Obtaining Knuth, Morris, and Pratt's String Matcher by Partial Evaluation

Ager¹,

Danvy²,

Rohde³

2002

BRICS

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We present the first formal proof that partial evaluation of a quadratic string matcher can yield the precise behaviour of Knuth, Morris, and Pratt's linear string matcher.Obtaining a KMP-like string matcher is a canonical example of partial evaluation: starting from the naive, quadratic program checking whether a pattern occurs in a text, one ensures that backtracking can be performed at partial-evaluation time (a binding-time shift that yields a staged string matcher); specializing the resulting staged program yields residual programs that do not back up on the text,à la KMP. We are not aware, however, of any formal proof that partial evaluation of a staged string matcher precisely yields the KMP string matcher, or in fact any other specific string matcher.In this article, we present a staged string matcher and we formally prove that it performs the same sequence of comparisons between pattern and text as the KMP string matcher. To this end, we operationally specify each of the programming languages in which the matchers are written, and we formalize each sequence of comparisons with a trace semantics. We also state the (mild) conditions under which specializing the staged string matcher with respect to a pattern string provably yields a specialized string matcher whose size is proportional to the length of this pattern string and whose time complexity is proportional to the length of the text string. Finally, we show how tabulating one of the functions in this staged string matcher gives rise to the 'next' table of the original KMP algorithm.The method scales for obtaining other linear string matchers, be they known or new. * Extended version of an article

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Section: List Of Figuresmentioning

confidence: 99%

Section: Program Specializationmentioning

confidence: 99%

“…(Indeed, Grobauer and Lawall have shown that the size of these residual programs is bounded by |pat | × |Σ|, where pat denotes the pattern and Σ denotes the alphabet [13]. )…”

Section: This Workmentioning

confidence: 99%

Section: This Workmentioning

confidence: 99%

Section: Program Specializationmentioning

confidence: 99%

See 3 more Smart Citations

On Obtaining Knuth, Morris, and Pratt's String Matcher by Partial Evaluation

Ager¹,

Danvy²,

Rohde³

2002

BRICS

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Fast partial evaluation of pattern matching in strings

Ager

Danvy

Rohde

2006

ACM Trans. Program. Lang. Syst.

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We show how to obtain all of Knuth, Morris, and Pratt's linear-time string matcher by specializing a quadratic-time string matcher with respect to a pattern string. Although it has been known for fifteen years how to obtain this linear matcher by partial evaluation of a quadratic one, how to obtain it in linear time has remained an open problem.Obtaining a linear matcher by the partial evaluation of a quadratic one is achieved by performing its backtracking at specialization time and memoizing its results. We show (1) how to rewrite the source matcher such that its static intermediate computations can be shared at specialization time and (2) how to extend the memoization capabilities of a partial evaluator to static functions. Such an extended partial evaluator, if its memoization is implemented efficiently, specializes the rewritten source matcher in linear time. Finally, we show that the method also applies to a variant of Boyer and Moore's string matcher.

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An Analytical Approach to Programs as Data Objects

Danvy¹

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This essay accompanies a selection of 32 articles (referred to in bold face in the text and marked with " √ " in the bibliographic references) submitted to the University of Aarhus towards a Doctor Scientiarum degree in Computer Science. The author's previous academic degree, beyond a doctoral degree in June 1986, is an Habilitationà diriger les recherches from the Université Pierre et Marie Curie (Paris VI) in France; the corresponding material was submitted in September 1992 and the degree was obtained in January 1993. The present 32 articles have all been written since 1993 and while at DAIMI. Except for one other PhD student, all co-authors are or have been the author's students here in Aarhus. * Technical summaryThis work presents an analytical approach to programs as data objects, i.e., to programs whose representation is operated upon by other programs. The approach is analytical in that a variety of program manipulations is considered and their impact on program understanding, design, and efficiency is measured.Most of the programs considered here are language processors, i.e., programs interpreting, translating, or transforming other programs. As for the program manipulations, they concern block structure and lexical scope, the representation of functions at run time, and the representation of control.ii Teknisk résuméDette arbejde praesenterer en analytisk tilgang til programmer som dataobjekter, dvs, til programmer hvis repraesentation bliver behandlet af andre programmer. Tilgangen er analytisk i og med at et udvalg af programmanipulationer bliver betragtet og deres indflydelse på program-forståelse, -design og -effektivitet bliver vurderet.De fleste programmer, der betragtes her, er sprogbehandlingsprogrammer, dvs, programmer der fortolker, oversaetter eller transformerer andre programmer. Hvad angår programmanipulationerne, vedrører de blokstruktur og leksikalsk virkefelt, repraesentation af funktioner på køretidspunktet og repraesentation af kontrol.iii

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Partial Evaluation of Pattern Matching in Strings, revisited

Cited by 7 publications

References 14 publications

On Obtaining Knuth, Morris, and Pratt's String Matcher by Partial Evaluation

On Obtaining Knuth, Morris, and Pratt's String Matcher by Partial Evaluation

Fast partial evaluation of pattern matching in strings

An Analytical Approach to Programs as Data Objects

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