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The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic metalanguage 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 onesymbol 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.

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We present a novel, yet simple, technique for the specification of context in structured documents that we call caterpillar expressions. Although we are primarily applying this technique in the specification of context-dependent style sheets for HTML, SGML and XML documents, it can also be used for query specification for structured documents, as we shall demonstrate, and for the specification of computer program transformations.From a conceptual point of view, structured documents are trees, and one of the oldest and best-established techniques to process trees and, hence, structured documents are tree automata. We present a number of theoretical results that allow us to compare the expressive power of caterpillar expressions and caterpillar automata, their companions, to the expressive power of tree automata. In particular, we demonstrate that each caterpillar expression describes a regular tree language that is, hence, recognizable by a tree automaton.Finally, we employ caterpillar expressions for tree pattern matching. We demonstrate that caterpillar automata are able to solve tree-pattern-matching problems for some, but not all, types of tree inclusion that Kilpeläinen investigated in his Ph.D. thesis. In simulating tree pattern matching with caterpillar automata, we reprove some of Kilpeläinen's results in a uniform framework.

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