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Abstract:
We show that unification in certain extensions of shallow equational theories
is decidable. Our extensions generalize the known classes of shallow or
standard equational theories. In order to prove decidability of unification
in the extensions,
a class of Horn clause sets called sorted shallow equational theories is introduced.
This class is a natural extension of tree automata with equality
constraints between brother subterms as well as shallow sort theories.
We show that saturation under sorted superposition is effective on
sorted shallow equational theories.
So called semi-linear equational theories can be effectively transformed into
equivalent sorted shallow equational theories and generalize the classes of
shallow and standard equational theories.
