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Automata theory in nominal sets

Mikołaj Bojańczyk ; Bartek Klin ; Sławomir Lasota.

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize&nbsp;[&hellip;]

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Definable isomorphism problem

Khadijeh Keshvardoost ; Bartek Klin ; Sławomir Lasota ; Joanna Ochremiak ; Szymon Toruńczyk.

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying structure of atoms, we prove decidability of the problem. The core&nbsp;[&hellip;]

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Determinisability of register and timed automata

Lorenzo Clemente ; Sławomir Lasota ; Radosław Piórkowski.

The deterministic membership problem for timed automata asks whether the timed language given by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. An analogous problem can be stated in the setting of register automata. We draw the complete&nbsp;[&hellip;]

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Regular Separability of One Counter Automata

Wojciech Czerwiński ; Sławomir Lasota.

The regular separability problem asks, for two given languages, if there exists a regular language including one of them but disjoint from the other. Our main result is decidability, and PSpace-completeness, of the regular separability problem for languages of one counter automata without zero tests&nbsp;[&hellip;]

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