Ambiguity refers to the property whereby regular expressions or patterns have multiple matching possibilities. As discussed in Chapter 5, ambiguity can make the behavior of a program harder to understand and can actually be the result of a programming error. Therefore it is often useful to report it to the user. However, when we come to ask exactly what we mean by ambiguity, there is no consensus. In this chapter, we review three different definitions, strong ambiguity, weak ambiguities and binding ambiguity, and discuss how these notions are related to each other and how they can be checked algorithmically.

Caveat: In this chapter, we concentrate on regular expressions and patterns on strings rather than on trees in order to highlight the essence of ambiguity. The extension for the case of trees is routine and can be found in the literature.

Ambiguities for regular expressions

In this section, we study strong and weak ambiguities and how they can be decided by using an ambiguity checking algorithm for automata.

14.1.1 Definitions

Ambiguity arises when a regular expression has several occurrences of the same label. Therefore we need to be able to distinguish between these occurrences.