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math.GR2023★ 3 cited
Semiring and involution identities of powers of inverse semigroups
Igor Dolinka, Sergey V. Gusev, Mikhail V. Volkov
The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural condition…
cs.FL2023
Synchronization of primitive automata
Mikhail Volkov
We exhibit new conditions under which a primitive automaton is synchronizing. In particular, we show that the primitivity of an automaton forces its synchronizability whenever the…
math.GR2023★ 1 cited
Strongly nonfinitely based monoids
Sergey V. Gusev, Olga B. Sapir, Mikhail V. Volkov
We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based fin…