Composition is a key technique in automata theory, used in particular in the model-checking, realisability analysis and automatic synthesis of reactive systems. Typically, when it comes to composition, deterministic automata are used as they behave well when composed with other automata or games. However, determinisation is notoriously complex, both conceptually and computationally.
One approach to avoiding determinisation is the notion of Good for Games (GFG) nondeterministic automata, which, despite their nondeterminism, compose well with games. Recent work suggests that the notion of GFG automata, so far only used for composing non-deterministic automata with games, is in fact much more powerful: it generalises to alternating automata---a more general and flexible type of automata that is particularly close to formal logics, and such automata can be used not just in composition with games, but with other automata as well. This means that alternating automata of this type could potentially be used in solutions to parity games, Church's synthesis problem, and, more generally, for turning automata into equivalent automata with simpler acceptance conditions.
We have studied the succinctness of GFG automata, how to recognise compositional automata, and how to exploit compositionality to improve algorithms in verification and synthesis. We have introduced the notion of GFG pushdown automata and studied their computational and descriptive properties.
We co-proposed a successful grant application for the MoVeMnt project, funded by the Icelandic Research Fund, in collaboration with Antonis Achilleos, Luca Aceto, Anna Ingolfsdottir and Adrian Francalanza.
