Existence of arbitrarily long square-free words with one possible mismatch
-
Nikita V. Kotlyarov
Abstract
We are concerned with problems of the existence of periodic structures in words from formal languages. We consider both squares (that is, fragments of the form xx, where x is an arbitrary word) and squares with one mismatch (that is, fragments of the form xy, where a word x differs from a word y by exactly one letter). Given natural numbers l0 and l1, we study conditions for the existence of arbitrarily long words not containing squares with length larger than l0 and squares with one mismatch and length larger than l1. For all possible pairs l1 ≥ l0 a minimal alphabet cardinality is found which permits to construct such a word.
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00598) and of the Branch of Mathematics of the Russian Academy of Sciences Program “Algebraic and combinatorial methods of mathematical cybernetics and new generation information systems” (the project “Problem of optimal synthesis of control systems”).
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Cardinality estimates for some classes of regular languages
- On large deviations of a branching process in random environments with immigration at moments of extinction
- Existence of arbitrarily long square-free words with one possible mismatch
- On frequencies of elements in multicyclic random sequence modulo 4
- Single tests for logical gates
- On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
Articles in the same Issue
- Frontmatter
- Cardinality estimates for some classes of regular languages
- On large deviations of a branching process in random environments with immigration at moments of extinction
- Existence of arbitrarily long square-free words with one possible mismatch
- On frequencies of elements in multicyclic random sequence modulo 4
- Single tests for logical gates
- On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
