Splicing Systems: Accepting Versus Generating

In this paper we propose a condition for rejecting the input word by an accepting splicing system which is defined by a finite set of forbidding words. More precisely, the input word is accepted as soon as a permitting word is obtained provided that no forbidding word has been obtained so far, otherwise it is rejected. Note that in the new variant of accepting splicing system the input word can be rejected if either no permitting word is ever generated (like in [10]) or a forbidding word has been generated and no permitting word had been generated before. We investigate the computational power of the new variants of accepting splicing systems. We show that the new condition strictly increases the computational power of accepting splicing systems. Rather surprisingly, accepting splicing systems considered here can accept non-regular languages, a situation that has never occurred in the case of (extended) finite splicing systems without additional restrictions.