Hi I have a notation question.

I've recently come across the '*-operation' (star-operation) in the context of a binary operation on two automata e.g., **A*B** and I'm not sure exactly what it means (and it's rather difficult to google).

In the context of a unary operation on a single transducer/acceptor **A*** generally refers to the kleene closure, but I'm not familiar with the binary context. Further, in the context of a binary operation, this is distinct from general composition or weighted composition.

edit: after some furious googling, i found that the binary kleene * is described in,

"Representation of Events in Nerve Nets and Finite Automata", Kleene, 1956

http://www.dlsi.ua.es/~mlf/nnafmc/papers/kleene56representation.pdf

from page 24, paragraph 3:

If

EandFare sets of tables,E*F( theiterateofEonF, or brieflyEiterateF) shall be in the infinite sum of the setsF, EF, EEF, EEEF, ...,or in self-explanatory symbolism,FvEFvEEFv ... or $\sum_{n=0}^{\infty} E^{n}F$.