The Nondeterministic State Complexity of the Site-Directed Deletion Language Operation

Site-directed deletion is a language operation inspired by the laboratory procedures entailed by polymerase chain reaction. Site-directed deletion contextually removes a contiguous substring provided it matches a guiding template string. The matching template must match the non-empty prefix and suffix of the substring, where upon the middle section not contained in the outfix is deleted. We consider the nondeterministic state complexity of site-directed deletion over the general alphabet as well as several special restricted forms. For regular languages recognized by nondeterministic finite automata with N and M states, respectively, we establish a new upper bound of 2 N M + N and a new worst case lower bound of 2 N M. 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.