Nondeterministic State Complexity of Site-Directed Deletion.

Site-directed deletion is a biologically inspired operation that removes a contiguous substring from the host string guided by a template string. The template string must match the prefix and suffix of a substring. When this occurs the middle section of the substring not contained in the prefix or suffix is removed. We consider the nondeterministic state complexity of the site-directed deletion operation. For regular languages recognized by nondeterministic finite automata with N and M states, respectively, we establish a new upper bound of 2NM + N and a new worst case lower bound of 2NM. The upper bound improves a previously established upper bound, and no non-trivial lower bound was previously known for the nondeterministic state complexity of site-directed deletion.