# On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

@article{Ivn2016OnNT, title={On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity}, author={Szabolcs Iv{\'a}n and Judit Nagy-Gy{\"o}rgy}, journal={Acta Cybern.}, year={2016}, volume={22}, pages={687-701} }

We give an upper bound of nn-1!-n-3! for the possible largestsize of a subsemigroup of the full transformational semigroup overn elements consisting only of nonpermutational transformations.As an application we gain the same upper bound for the syntacticcomplexity of generalized definite languages as well.

## 4 Citations

### Large Aperiodic Semigroups

- MathematicsInt. J. Found. Comput. Sci.
- 2015

This work searches for the largest syntactic semigroup of a star-free language having n left quotients of an aperiodic finite automaton with n states.

### Syntactic Complexity of Circular Semi-Flower Automata

- Computer ScienceCIAA
- 2018

It is proved that the syntactic complexity of $n$-state CSFA with two bpis over a binary alphabet is $2n(n+1)$.

### Syntactic Complexity of Bifix-Free Languages

- Mathematics, Computer ScienceCIAA
- 2017

It is proved that the cardinality of the syntactic semigroup of a bifix-free language with state complexity n is at most \((n-1)^{n-3}+(n-2)^{ n-3}) + (n- 3)2-1 - 1, which is the minimal size of the alphabet required to meet the bound for \(n \geqslant 6\).

### Checking Whether an Automaton Is Monotonic Is NP-complete

- Computer ScienceCIAA
- 2015

It is proved that the problem of deciding whether a given automaton is monotonic is NP-complete, and the same result is obtained for oriented automata, whose states can be arranged in a cyclic order.

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