Parameterized Pattern Matching: Algorithms and Applications

Abstract

The problem of finding sections of code that either are identical or are related by the systematic renaming of variables or constants can be modeled in terms of parameterized strings ( p-strings) and parameterized matches ( p-matches). P-strings are strings over two alphabets, one of which represents parameters. Two p-strings are a parameterized match ( p-match) if one p-string is obtained by renaming the parameters of the other by a one-to-one function. In this paper, we investigate parameterized pattern matching via parameterized suffix trees (p-suffix trees). We give two algorithms for constructing p-suffix trees: one (eager) that runs in linear time for fixed alphabets, and another that uses auxiliary data structures and runs in O(n log(n)) time for variable alphabets, where n is input length. We show that using a p-suffix tree for a pattern p-string P, it is possible to search for all p-matches of P within a text p-string T in space linear in |P| and time linear in |T | for fixed alphabets, or O( |T| log(min( |P|, _)) time and O( |P| ) space for variable alphabets, where _ is the sum of the alphabet sizes. The simpler p-suffix tree construction algorithm eager has been implemented, and experiments show it to be practical. Since it runs faster than predicted by the above worst-case bound, we reanalyze the algorithm and show that eager runs in time O(min(t |S | +m(t, S) | t>0) log _)), where for an input p-string S, m(t, S ) is the number of maximal p-matches of length at least t that occur within S, and _ is the sum of the alphabet sizes. Experiments with the author's program dup (B. Baker, in``Comput. Sci. Statist., '' Vol. 24, 1992) for finding all maximal p-matches within a p-string have found m(t, S ) to be less than |S| in practice unless t is small. ]

Parameterized matching on non-linear structures

“…The parameterized matching problem was introduced by Baker [10,11]. Her main motivation lay in software maintenance, where program fragments are to be considered "identical" even if variable names are different.…”

“…An optimal algorithm for exact parameterized matching appeared in [5]. Approximate parameterized matching was investigated in [10,15,8]. Idury and Schäffer [16] considered multiple matching of parameterized patterns.…”

Analyzing Stack Flows to Compare Java Programs

“…Baker and Manber [7] proposed a method to deduce similarities in Java bytecodes by applying text similarity measures, such as Siff [8], parameterized pattern matching [9], and diff. Tamada et al [2], [3] first suggested a practical application of static software birthmarks and presented a method to compare the birthmarks for Java class files.…”

Signature limits: an entire map of clone features and their discovery in nearly linear time

“…The question of how to organize and represent a text corpus for optimized retrieval and search has been motivated by diverse problems in areas of information retrieval Amir et al [1994], Blumer et al [1987] and Ferragina and Grossi [1995], pattern matching Weiner [1973], software analysis Baker [1993], and bioinformatics Bieganski et al [1994] Gusfield [1997 where there are several well developed techniques based on suffix trees McCreight [1976] Ukkonen [1985], compressed suffix trees Navarro and Mäkinen [2007], and suffix arrays Manber and Myers [1990] and Manzini and Ferragina [2004]. In addition indexing for dynamic data sets Amir et al [1994]; Ferragina and Grossi [1995] has been reported.…”