On Symmetry and Antisymmetry in Strings
by
Marian Alexandru Baroni
"George Cosbuc" High School, Galati, Romania

For a string of symbols of an alphabet V, the symmetry of a subset of V with respect to given positions in that string is considered. Various types of languages related to symmetry in strings, and to its polar opposite (called antisymmetry) have been recently investigated. Like in real analysis, where symmetric and antisymmetric sets have the same topological and measure-theoretic structure, some languages related to symmetry, respectively antisymmetry have the same type in Chomsky hierarchy. Given two subsets U and W of the alphabet V, the antisymmetry of U with respect to W will be examined. Our aim is to prove that from the point of view of Chomsky classification, languages containing such antisymmetric strings are similar to their corresponding languages related to symmetry. Analogous results can be obtained for a type of local symmetry and local antisymmetry in strings.

Date received: March 4, 2000