In this paper, we investigate the problem of synthesizing computablefunctions of infinite words over an infinite alphabet . The notion of computability is defined through Turing machines with infinite inputs which can produce the corresponding infinite outputs in the limit . For functions over data $omega$-words, we identify a sufficient condition under which computability and continuity coincide . We also show that theso-called next letter problem is decidable, yielding equivalence between continuity and (uniform) computability . We even show that all these decision problems are PSpace-complete for (N, <) and for a largeclass of oligomorphic data domains, including for instance (Q, <). We also provide characterizations of (Uniform) continuity, which allow us to prove that thesenotions, and thus also (universities) are decidable. We also prove that allThese decision problems, are P space-complete’tundundundable’s decision problems to be PSpace complete for (unibundated’S’N’T’R rational numbers with linear order’. We show that these problems are ‘decidable’

Author(s) : Léo Exibard, Emmanuel Filiot, Nathan Lhote, Pierre-Alain Reynier

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Keywords : infinite - problems - data - computability - decision -

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