On varieties of completely regular semigroups III.
Weak automorphisms of 1-unary algebras
On varieties of non-indexed algebras
A classification of rational languages by semilattice-ordered monoids
We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.
On biautomata
We initiate the theory and applications of biautomata. A biautomaton can read a word alternately from the left and from the right. We assign to each regular language its canonical biautomaton. This structure plays, among all biautomata recognizing the language , the same role as the minimal deterministic automaton has among all deterministic automata recognizing the language . We expect that from the graph structure of this automaton one could decide the membership of a given language for certain...
The category of nonindexed algebras and weak homomorphisms
On biautomata
We initiate the theory and applications of biautomata. A biautomaton can read a word alternately from the left and from the right. We assign to each regular language its canonical biautomaton. This structure plays, among all biautomata recognizing the language , the same role as the minimal deterministic automaton has among all deterministic automata recognizing the language . We expect that from the graph structure of this automaton one could decide the membership of a given language for certain...
On Varieties of Literally Idempotent Languages
A language is literally idempotent in case that if and only if , for each , . Varieties of literally idempotent languages result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator on classes of languages. We initiate the systematic study of such varieties. Various classes of literally idempotent languages can be characterized using syntactic methods. A starting example is the class of all finite unions of where...
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