GEKLA in Il'apoli (Italy)
IntrodrictioiiThe research of suitable free subsemigroups of a given free semigroup is an important I)ranch of C'ommnnication Theory [ 5 ] . In fact let B+ be the free semigroup of alphatjet b ' and S a free subsemigroup of B+. then the set C = X -X2, named code, is a base of S and therefore every word y of S is univocally factorized by elements of C'. Moreover. if S is another alphabet, every bijective map e : X + C' deterniines a n e,t,corliq. i.e. an isomorphism among St and S. I n this case me say t.ha.t, a, word (or message) .I' of 9+ is codified by t'lie word e(.r). The decodification of a u-ord y of A' requires a decomposition of y as product of elements of the code C. Kamely, if y = c , . . . c , . with ci E C'. thc word .I' = e-' (c,) . . . e-'(c,) is the result of t'he dccodification of y. Since S is free. t'liis decodification is nnivocally determined. If e arid P-are computable, t'lien the codification and the decodification are cffectiye oprrat ions.