The nondeterministic state complexity of the site-directed deletion language operation

Abstract

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 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.