The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings uxR v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n 3). We establish that the deterministic state complexity of the inversion is 2Ω(n·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.
|Title of host publication||Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings|
|Number of pages||12|
|Publication status||Published - 2014|
|Event||16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014 - Turku, Finland|
Duration: 2014 Aug 5 → 2014 Aug 8
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Other||16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014|
|Period||14/8/5 → 14/8/8|
Bibliographical noteFunding Information:
Cho, Han and Ko were supported by the Basic Science Research Program through NRF funded by MEST ( 2012R1A1A2044562 ), the International Cooperation Program managed by NRF of Korea ( 2014K2A1A2048512 ) and the Yonsei University Future-leading Research Initiative of 2014. Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224 .
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)