Factorization in the monoid of languages
It is shown that the equation Y1Y2=Y3Y4 over Open image in new window U Q where P is the set of irreducible prefix codes and Q is the set of primitive words admits nor-trivial solutions only when Y1=Y3=Q.
KeywordsTrivial Solution Factor Theorem Empty Word Michigan Math Irreducible Element
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- Clifford, A.H. and Preston, G.B., "The Algebraic Theory of Semigroups", Vol. I, II, Amer. Math. Soc., Providence, RI. (1961).Google Scholar
- Lassez, J.L., A Correspondence on strongly prefix codes, IEEE Transactions on Information Theory, May (1975), 344–345.Google Scholar
- Lentin, A. and Schutzenberger, M.P., A Combinatorial Problem in the Theory of Free Monoid, in "Combinatorial Mathematics and its Applications" (R.C. Bose and T.A. Dowling, Eds.), North Carolina Press, Chapell Hill, NC. (1967) 128–144.Google Scholar
- Sevrin, L.N., On Subsemigroups of Free Semigroups, Soviet Math. Dokl. (1960) 892–894.Google Scholar