This book presents a practical approach to string matching problems, focusing on the algorithms and implementations that perform best in practice. It covers searching for simple, multiple, and extended strings, as well as regular expressions, exactly and approximately. It includes all of the most significant new developments in complex pattern searching. The clear explanations, step-by-step examples, algorithms pseudo-code, and implementation efficiency maps will enable researchers, professionals, and students in bioinformatics, computer science, and software engineering to choose the most appropriate algorithms for their applications.

Flexible Pattern Matching in Strings: Practical On-Line Search Algorithms for Texts and Biological Sequences

XDuce is a statically typed programming language for XML processing. Its basic data values are XML documents, and its types (so-called regular expression types) directly correspond to document schemas. XDuce also provides a flexible form of regular expression pattern matching, integrating conditional branching, tag checking, and subtree extraction, as well as dynamic typechecking. We survey the principles of XDuce's design, develop examples illustrating its key features, describe its foundations in the theory of regular tree automata, and present a complete formal definition of its core, along with a proof of type safety.

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XDuce: A statically typed XML processing language

Partial derivatives of regular expressions and finite automaton constructions

The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic meta-language for the definition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions, although only regular expressions that denote words unambiguously, in the sense of the ISO standard, are allowed. In general, a word that is denoted by a regular expression is witnessed by a sequence of occurrences of symbols in the regular expression that match the word. In an unambiguous regular expression as defined by Book et al. (1971, IEEE Trans. Comput. C-20 (2), 149–153), each word has at most one witness. But the SGML standard also requires that a witness be computed incrementally from the word with a one-symbol lookahead; we call such regular expressions 1- unambiguous . A regular language is a 1- unambiguous language if it is denoted by some 1-unambiguous regular expression. We give a Kleene theorem for 1-unambiguous languages and characterize 1-unambiguous regular languages in terms of structural properties of the minimal deterministic automata that recognize them. As a result we are able to prove the decidability of whether a given regular expression denotes a 1-unambiguous language; if it does, then we can construct an equivalent 1-unambiguous regular expression in worst-case optimal time.

One-unambiguous regular languages

The availability of summary data for XML documents has many applications, from providing users with quick feedback about their queries, to cost-based storage design and query optimization. StatiX is a novel XML Schema-aware statistics framework that exploits the structure derived by regular expressions (which define elements in an XML Schema) to pinpoint places in the schema that are likely sources of structural skew. As we discuss below, this information can be used to build concise, yet accurate, statistical summaries for XML data. StatiX leverages standard XML technology for gathering statistics, notably XML Schema validators, and it uses histograms to summarize both the structure and values in an XML document. In this paper we describe the StatiX system. We develop algorithms that decompose schemas to obtain statistics at different granularities and discuss how statistics can be gathered as documents are validated. We also present an experimental evaluation which demonstrates the accuracy and scalability of our approach and show an application of these statistics to cost-based XML storage design.

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StatiX: making XML count

Regular expressions into finite automata

It is a well-established fact that each regular expression can be transformed into a nondeterministic finite automaton (NFA) with or without ∈-transitions, and all authors seem to provide their own variant of the construction. Of these, Berry and Sethi [BS86] have shown that the construction of an ∈-free NFA due to Glushkov [Glu61] is a natural representation of the regular expression, because it can be described in terms of the Brzozowski derivatives [Brz64] of the expression. Moreover, the Glushkov construction also plays a significant role in the document processing area: The SGML standard [ISO86], now widely adopted by publishing houses and government agencies for the syntactic specification of textual markup systems, uses deterministic regular expressions, i.e. expressions whose Glushkov automaton is deterministic, as a description language for document types.

Anne Brüggemann-Klein

Papers

Regular expressions into finite automata

Regular Expressions into Finite Automata

Learning Picture Sets from Examples