On the relations between the degree of synchronization and the degree of nondeterminism in k-limited and uniformly k-limited tol systems

Abstract

k-limited and uniformly k-limited TOL systems provide limitations of the parallel rewriting of TOL systems. According to these systems the rewriting is carried out in a manner which lies between fully parallel and sequential rewriting. The degree ofsynchronization of such a system or of a TOL system is given by the number of its tables and the degree of nondeterminism is defined by the maximum, taken over all tables, of the maximal number of productions with the same left side in such a table. For a language L generated by such a system, taking the minimum of the corresponding degree of all such systems generating L, we get the corresponding complexity measures of the languages of the appropriate language families. As a new complexity measure we introduce the product of both degrees. The relations between these different measures are investigated.

Keywords:

• Formal languages
• limited TOL systems
• complexity of languages

C.R. Categories:

• F.4.2