Congruences associated with DOL-schemes
Mario Petrich and Gabriel Thierrin
Proc. Amer. Math. Soc. 102 (1988), 787-793
Primary 68Q45; Secondary 20M05, 20M35
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Abstract: For a DOL-scheme , where is a finite alphabet and is an endomorphism of , we study the properties of the congruence induced by in terms of the properties of . We prove that every submonoid of has a disjunctive subset (for any ) and deduce that is a syntactic congruence. As special cases, we consider the conditions on which are equivalent to being perfect or uniquely perfect or linear. The latter is introduced in the paper together with a ramification.
A. Harrison, Introduction to formal language theory,
Addison-Wesley Publishing Co., Reading, Mass., 1978. MR 526397
T. Herman and Grzegorz
Rozenberg, Developmental systems and languages, North-Holland
Publishing Co., Amsterdam, 1975. With a contribution by Aristid
0495247 (58 #13968)
Petrich and C.
M. Reis, Perfect congruences on a free
monoid, Proc. Amer. Math. Soc.
99 (1987), no. 2,
870772 (87m:20167), http://dx.doi.org/10.1090/S0002-9939-1987-0870772-4
- M. Harrison, Introduction to formal language theory, Addison-Wesley, Reading, Mass., 1978. MR 526397 (80h:68060)
- G. T. Herman and G. Rozenberg, Developmental systems and languages, North-Holland, Amsterdam, 1975. MR 0495247 (58:13968)
- M. Petrich and C. Reis, Perfect congruences on a free monoid, Proc. Amer. Math. Soc. 99 (1987), 205-212. MR 870772 (87m:20167)
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