A deterministic parsing algorithm for ambiguous regular expressions

We introduce a new parser generator, called Berry–Sethi Parser (BSP), for ambiguous regular expressions (RE). The generator constructs a deterministic finite-state transducer that recognizes an input string, as the classical Berry–Sethi algorithm does, and additionally outputs a linear representation of all the syntax trees of the string; for infinitely ambiguous strings, a policy for selecting representative sets of trees is chosen. To construct the transducer, the RE symbols, including letters, parentheses and other metasymbols, are distinctly numbered, so that the corresponding language becomes locally testable. In this way a deterministic position automaton can be constructed, which recognizes and translates the input into a compact DAG representation of the syntax trees. The correctness of the construction is proved. The transducer operates in a linear time on the input. Its descriptive complexity is analyzed as a function of established RE parameters: the alphabetic width, the number of null string symbols and the height of the RE tree. A condition for checking RE ambiguity on the transducer graph is stated. Experimental results of running the parser generator and the parser on a large RE collection are presented. The POSIX RE disambiguation criterion has also been applied to the parser.