Compiling Regular Patterns to Sequential Machines

Pattern matching combined with regular expressions has many applications including text and XML processing, lexical analysis, classification of DNA segments and content-based routing. Patterns contain variables to refer to parts of the matching input. But regular patterns pose the problem of ambiguity: Words can be matched against 'overlapping' sections of the pattern in several ways, yielding different variable bindings. A match policy like shortest or longest match disambiguates the outcome of matching. In order to implement the longest/shortest match policies, we propose to compile regular patterns to sequential machines. This intuitive approach %to resolving ambiguities by means of shortest/longest match %policies (and the slightly different ungreedy/greedy match), with lets us derive a compilation scheme with linear runtime complexity. \par The main contributions of this paper are firstly, a decision procedure for unambiguous regular patterns, which can be matched with a single traversal of the input, and secondly, algorithms to obtain deterministic sequential machines from ambiguous patterns. These produce the shortest(longest) match in two consecutive runs. The first run produces an intermediary result from which all possible variable bindings can be reproduced. The second run then chooses the unique binding which adheres to the given match policy. In the general case, this approach is optimal.

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