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This note introduces the notion of a hyperdecidable pseudovariety. This notion appears naturally in trying to prove decidability of the membership problem of semidirect products of pseudovarieties of semigroups. It turns out to be a generalization of a notion introduced by C. J. Ash in connection with his proof of the \type II" theorem. The main results in… (More)

This article defines the notion of hyperdecidability for a class of finite semigroups, which is closely connected to the notion of decidability. It then proves that the pseudovariety J of J-trivial semigroups is hyperdecidable.

It is widely argued that the ability to recognize and identify manipulable objects depends on the retrieval and simulation of action-based information associated with using those objects. Evidence for that view comes from fMRI studies that have reported differential BOLD contrast in dorsal visual stream regions when participants view manipulable objects… (More)

We study free profinite subgroups of free profinite semi-groups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy.

In this paper, we establish thě Cern´y-Pin conjecture for au-tomata with the property that their transition monoid cannot recognize the language {a, b} * ab{a, b} *. For the subclass of automata whose transition monoids have the property that each regular J-class is a subsemi-group, we give a tight bound on lengths of reset words for synchronizing automata… (More)