On the generative capacity of matrix insertion-deletion systems of small sum-norm

Abstract A matrix insertion-deletion system (or ins-del system) is described by a set of rules presented in form, which demands all to be applied the given order. These systems were introduced model very simplistic fragments sequential programs based on insertion and deletion as elementary operations can found biocomputing. We are investigating such with limited resources formalized descriptional complexity. traditional complexity measure its size $$s=(k;n,i',i'';m,j',j'')$$ s = ( k ; n , i ′ m j ) , where parameters from left right represent maximal length, string length contexts rules, rules; last three counterparts previous parameters. call sum $$n+i'+i''+m+j'+j''$$ + sum-norm s . show that 4 sizes (3; 1, 0, 0; 2, 0), 2), (2; 2; 1; 0) describe recursively enumerable languages. Moreover, at least regular closure linear In fact, we if class languages $$\mathrm {LIN}$$ LIN then without any additional resources, also Finally, prove 1)