The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic metalanguage for the de nition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions; although only expressions that denote words unambiguously are allowed. In general, the fact that a word is denoted by an expression is witnessed by a sequence of occurrences of symbols in the expression that matches the word. In an unambiguous expression as de ned by Book, Even, Greibach, and Ott, each word has at most one witness. But the SGML standard also requires that a witness can be computed incrementally from the word with a one-symbol lookahead; we call such expressions 1-unambiguous. A regular language is 1-unambiguous if it is denoted by some 1-unambiguous expression. We give a Kleene theorem for 1-unambiguous languages and characterize them in terms of structural properties of the minimal deterministic automata that recognize them. This result enables us to decide whether a given regular expression denotes a 1-unambiguous language; if it does, then we can construct an equivalent 1-unambiguous expression in worst-case optimal time.
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