T h e string-matching problem is a very c o m m o n problem. We are searching for a string P = PtP2. . "Pro i n s i d e a la rge t ex t f i le T = t l t2. . . t . , b o t h sequences of characters from a f i n i t e character set Z. T h e characters may be English characters in a text file, DNA base pairs, lines of source code, angles between edges in polygons, machines or machine parts in a production schedule, music notes and tempo in a musical score, and so fo r th . We w a n t to f i n d a l l occurrences of P i n T; n a m e l y , we are searching for the set of starting posit ions F = {i[1 --i--n m + 1 s u c h t h a t titi+ l " " t i + m 1 = P } " T h e two most famous algorithms for this problem are t h e B o y e r M o o r e algorithm [3] and t h e K n u t h Morris Pratt algorithm [10]. There are many extensions to t h i s problem; for example, we may be looking for a set of patterns, a pattern w i t h "wi ld cards," or a regular expression. String-matching tools are included in every reasonable text editor, word processor, and many other applications.

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Publisher Summary This chapter discusses the algorithms for solving string-matching problems that have proven useful for text-editing and text-processing applications. String pattern matching is an important problem that occurs in many areas of science and information processing. In computing, it occurs naturally as part of data processing, text editing, term rewriting, lexical analysis, and information retrieval. Many text editors and programming languages have facilities for matching strings. In biology, string-matching problems arise in the analysis of nucleic acids and protein sequences, and in the investigation of molecular phylogeny. String matching is also one of the central and most widely studied problems in theoretical computer science. The simplest form of the problem is to locate an occurrence of a keyword as a substring in a sequence of characters, which is called the input string. For example, the input string queueing contains the keyword ueuei as a substring. Even for this problem, several innovative, theoretically interesting algorithms have been devised that run significantly faster than the obvious brute-force method.

Algorithms for finding patterns in strings

Preface. Lecture 1. Bayesian statistical decision making. Lecture 2. Non-Bayesian statistical decision making. Lecture 3. Two statistical models of the recognised object. Lecture 4. Learning in pattern recognition. Lecture 5. Linear discriminant function. Lecture 6. Unsupervised Learning. Lecture 7. Mutual relationship of statistical and structural recognition. Lecture 8. Recognition of Markovian sequences. Lecture 9. Regular languages and corresponding pattern recognition tasks. Lecture 10. Context-free languages, their 2-D generalisation, related tasks. Bibliography. Index.

Ten Lectures on Statistical and Structural Pattern Recognition

This report examines and classi es the characteristics of signatures used in misuse intrusion detection. E cient algorithms to match patterns in some of these classes are described. A generalized model for matching intrusion signatures based on Colored Petri Nets is presented, and some of its properties are derived.

/pdf/an-application-of-pattern-matching-in-intrusion-detection-1c5cxg2eek.pdf

An Application of Pattern Matching in Intrusion Detection

1. The Self-Reducibility Technique.- 2. The One-Way Function Technique.- 3. The Tournament Divide and Conquer Technique.- 4. The Isolation Technique.- 5. The Witness Reduction Technique.- 6. The Polynomial Interpolation Technique.- 7. The Nonsolvable Group Technique.- 8. The Random Restriction Technique.- 9. The Polynomial Technique.- A. A Rogues' Gallery of Complexity Classes.- B. A Rogues' Gallery of Reductions.- References.

The Complexity Theory Companion

Correction of a string x into a language L is the problem of finding a string $y \in L$ to which x can be edited at least cost. The edit operations considered here are single-character deletions, single-character insertions, and single-character substitutions, each at an independent cost that does not depend on context. Employing a linear-time algorithm for solving single-origin graph shortest distance problems, it is shown how to correct a string of length n into the language accepted by a counter automaton in time proportional to $n^2 $ on a RAM with unit operation cost function. The algorithm is uniform over counter automata and edit cost functions; and it is shown how the correction time depends on the size of the automaton, the nature of the cost function, and the correction cost itself. For less general cases, potentially faster algorithms are described, including a linear-time algorithm for the case that very little correction is necessary and that the automaton’s counter activity is determined by ...

Correcting Counter-Automaton-Recognizable Languages

If the time bounds defining two nondeterministic complexity classes are too close for separation by the two known techniques, then they are almost too close for separation by any relativizable technique. Proof of an analogous result for space would be a major breakthrough, implying $\operatorname{NSPACE}(\log n) = \operatorname{DSPACE}(\log n)$.

Limitations on Separating Nondeterministic Complexity Classes

It is shown by simulation that every language accepted within time $n^d$ by a nondeter-ministic one-dimensional Turing machine is accepted in linear time by a nondeterministic d-dimensional iterative array. Conversely, every language accepted in linear time by such an iterative array is accepted within time $n^{d+1}$ by a nondeterministic one-dimensional Turing machine. It follows that the class of languages accepted in linear time by nondeterministic multidimensional iterative arrays is precisely Karp’s class NP, that nondeterministic $(d + 2)$-dimensional iterative arrays are more powerful than nondeterministic d-dimensional iterative arrays, and that nondeterministic two-dimensional iterative arrays are more powerful than the entire class of nondeterministic multidimensional Turing machines. Related deterministic results are surveyed and summarized for comparison.

Linear-Time Computation by Nondeterministic Multidimensional Iterative Arrays

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Correcting Counter-Automaton-Recognizable Languages

Limitations on Separating Nondeterministic Complexity Classes

Linear-Time Computation by Nondeterministic Multidimensional Iterative Arrays