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Abstract In [2] the notion of an ”-semigroup (epsilon semigroup) is de ned as a semigroup S with a unary operation ” : S ! S; x ! ”x that satis es a set of axioms, extending the notion of an identity in a monoid. The necessarily unique element ”x (may be also written x”) associated with x 2 S is called the partial identity of x. A partial monoid is de ned as an ”-semigroup in which every ”x is central, characterized as a strong semilattice of monoids and proved to be embedded in a certain partial monoid whose elements are partial mappings. In [3] the strong semilattice of the free monoids over the non empty nite subsets of a set A is de ned and proved to be the free object in the category of partial monoids and homomorphisms of partial monoids, denoted FPM (A), and called the free partial monoid on A. This notion is used to develop a theory of a generalized code, called a partial code, in analogy with the corresponding classical theory. With the usual notion of a ”language” as a subset of a free monoid A on a set A, a subset of free partial monoid on a could be regarded as a language in the ordinary sense (unless A is a singleton). In that, a subset of FPM(A) is actually a (disjoint) union of sets, which are subset of (di¤erent) free monoids (on di¤erent alphabets). Whence a subset of FPM(A) might be viewed as a generalized language which could not be recognized by an ordinary automaton. With the aim of developing a ”generalized” automata (machines) that could recognize(accepted) generalized language in a free partial monoid on a set A ,the two structures (machines) so called a ”perfectly generalized au- tomaton over A” and has been rst created in [1] and characterized as a ”strong semilattice of automata over A”. Languages of these two (equiv- alent) machines have been de ned in a rather general setting and called P-languages. Some algebra of P-languages has been developed in analogy with the corresponding properties in the classical automata-language theory. The general concept of P recognizability de ned in [1] has laid to establish the most motivated result, that is, if M is a strong semilattice of automata over the non empty nite subsets of A, then the union of the language of the maximal automata in M is a (possibly proper) subset of the P-language of M. Evidently more deeper result concerning the new developed machine. |