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...
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...
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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