  Saturation is a fundamental game-semantic property satisfied by strategies
that interpret higher-order concurrent programs. It states that the strategy
must be closed under certain rearrangements of moves, and corresponds to the
intuition that program moves (P-moves) may depend only on moves made by the
environment (O-moves).
  We propose an automata model over an infinite alphabet, called saturating
automata, for which all accepted languages are guaranteed to satisfy a closure
property mimicking saturation.
  We show how to translate the finitary fragment of Idealized Concurrent Algol
(FICA) into saturating automata, confirming their suitability for modelling
higher-order concurrency. Moreover, we find that, for terms in normal form, the
resultant automaton has linearly many transitions and states with respect to
term size, and can be constructed in polynomial time. This is in contrast to
earlier attempts at finding automata-theoretic models of FICA, which did not
guarantee saturation and involved an exponential blow-up during translation,
even for normal forms.
