Termalgebra

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A term algebra is an algebraic structure that is generated from a free signature. The signature gives the operations of algebra with their arities - including zero digit operations, also called constants.

For example, free semigroups are isomorphic to algebras that are generated from a signature that consists of only one binary operation ( the multiplication operation of the semigroup ) and a lot of constants.

Algebras are important in determining the meaning (semantics) of abstract data types ( ADTs ). This provides the ADT declaration of a signature for an algebraic structure with several types. The term algebra is a concrete model of the abstract declaration.

Entscheidbarkeitsfragen

Algebras are decidable under the elimination of quantifiers. The complexity of the decision problem belongs to the class NONELEMENTARY.