Basic composition operators

To obtain more complex AA, one can define basic primitives for combining attributed automata - the sequential and parallel composition operators.

• In the sequential composition ' ', we apply the second automaton to the result of the first one. We have to take care of flattening the resulting set to make the composed automaton to have correct type:

  

• In the parallel composition ' ', we apply both automata to the same input and take the union of the resulting sets as follows:

  

• An iteration ' ' of the attributed automaton zero or more times can be defined using the serial composition together with parellel composition as follows:

  

For example, automaton recognizing the language can be defined as follows:

First three lines correspondig to the automata counting symbols a, b and c respectively (here the predicate `a`? denotes the checking whether the current symbol of input is a). Then the automaton checks whether the input string is empty and all counters are equal. Finally, it returns the counter as it's final attribute value.