New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics