NFAs with tagged transitions, their conversion to deterministic automata and application to regular expressions

A conservative extension to traditional nondeterministic finite automata (NFAs) is proposed to keep track of the positions in the input string for the last uses of selected transitions, by adding "tags" to transitions. The resulting automata are reminiscent of nondeterministic Mealy machines. A formal semantics of automata with tagged transitions is given. An algorithm is given to convert these augmented automata to the corresponding deterministic automata, which can be used to process strings efficiently. The application to regular expressions is discussed, explaining how the algorithms can be used to implement, for example, substring addressing and a lookahead operator, and an informal comparison to other widely-used algorithms is made.