### Abstract

We introduce a new matching criterion - function matching - that captures several different applications. The function matching problem has as its input a text T of length n over alphabet Σ _{T} and a pattern P = P[1]P[2] ⋯ P[m] of length m over alphabet Σ _{P}. We seek all text locations i for which, for some function f : Σ _{P} > Σ _{T} (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2])⋯f(P[m]). We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability 1/n ^{k} of declaring a false positive. We give a deterministic algorithm whose time is O(n|Σ _{P}|log m) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.

Original language | English (US) |
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Pages (from-to) | 929-942 |

Number of pages | 14 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2719 |

State | Published - Dec 1 2003 |

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### Keywords

- Color indexing
- Function matching
- Parameterized matching
- Pattern matching
- Protein folding
- Register allocation

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*2719*, 929-942.