Cut Points in PEG

This is a short note inspired by some ideas and results from [3,6–8]. It is about Parsing Expression Grammars (PEGs) introduced by Ford in [1]. PEG specifies a language by defining for it a parser with limited backtracking. All of the quoted papers contain a detailed introduction to PEG, so it is not repeated here. Backtracking means that if e1 in a choice expression e1/e2 fails, the parser returns to the position it had before the attempt at e1, and tries e2 on the same input. Limited backtracking means that once e1 succeeded, e2 will not be tried on the same input upon a subsequent failure. In some cases, a failure of e1 may mean that e2 is also bound to fail, so there is no need to try it; one can terminate e1/e2 straight away and return failure. As an example, consider this grammar: