Motivated by work on bio-operations on DNA strings, we consider an outfix-guided insertion operation that can be viewed as a generalization of the overlap assembly operation on strings studied previously. As the main result we construct a finite language L such that the outfix-guided insertion closure of L is nonregular. We consider also the closure properties of regular and (deterministic) context-free languages under the outfix-guided insertion operation and decision problems related to outfix-guided insertion. Deciding whether a language recognized by a deterministic finite automaton is closed under outfix-guided insertion can be done in polynomial time.
KeywordsLanguage operations Closure properties Regular languages
Cho and Han were supported by the Basic Science Research Program through NRF funded by MEST (2015R1D1A1A01060097), the Yonsei University Future-leading Research Initiative of 2015 and the International Cooperation Program managed by NRF of Korea (2014K2A1A2048512). Ng and Salomaa were supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.
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