Institute of Informatics
Acta Cybernetica
Past Issues
Volume 22, Number 3, 2016
On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity
# On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

**Szabolcs Iván and Judit Nagy-György**

### Abstract (in LaTeX format)

We give an upper bound of $n((n-1)!-(n-3)!)$ for the possible largest size of a subsemigroup of the full transformational semigroup over $n$ elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.

### Full text

Available electronic editions: PDF.

### DOI

10.14232/actacyb.22.3.2016.9

DOI link: https://doi.org/10.14232/actacyb.22.3.2016.9

### BibTeX entry
`
@ARTICLE{actacyb_22_3_2016_9,`

author = {Szabolcs Iv\'an and Judit Nagy-Gy\"orgy},

title = {On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity},

journal = {Acta Cybernetica},

year = {2016},

volume = {22},

pages = {687--701},

number = {3},

abstract = {We give an upper bound of $n((n-1)!-(n-3)!)$ for the possible largest size of a subsemigroup of the full transformational semigroup over $n$ elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.},

doi = {10.14232/actacyb.22.3.2016.9}

}