# On Upper and Lower Bounds on the Length of Alternating Towers

@inproceedings{Holub2014OnUA, title={On Upper and Lower Bounds on the Length of Alternating Towers}, author={Stepan Holub and Galina Jir{\'a}skov{\'a} and Tomas Masopust}, booktitle={MFCS}, year={2014} }

A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next string in the sequence. It is known that if there are towers of any length, then there also exists an infinite tower. We investigate upper and lower bounds on the length of finite towers between two regular languages with respect to the size of the automata…

## 11 Citations

### Alternating Towers and Piecewise Testable Separators

- Computer ScienceArXiv
- 2014

The complexity of a particular method to compute a piecewise testable separator is investigated, it is shown that it is closely related to the height of maximal finite towers, and the upper and lower bounds with respect to the size of the given nondeterministic automata are provided.

### On the Complexity of k-Piecewise Testability and the Depth of Automata

- Computer ScienceDLT
- 2015

It is shown that the upper bound on k given by the depth of the minimal DFA can be exponentially bigger than the minimal possible k, and the complexity bound and detailed analysis for small k’s are provided.

### Separability by Short Subsequences and Subwords

- Computer ScienceICDT
- 2015

The complexity of separability of regular languages by combinations of subsequences or subwords of a given length k is studied, so that the parameter k can be used to influence the size and simplicity of the separator.

### Deciding Universality of ptNFAs is PSpace-Complete

- Computer ScienceSOFSEM
- 2018

It is shown, using a novel and nontrivial construction, that the universality problem for ptNFAs is PSpace-complete if the alphabet may grow polynomially.

### A combinatorial approach to the separation problem for regular languages. (Une approche combinatoire du problème de séparation pour les langages réguliers)

- Mathematics, Computer Science
- 2014

This thesis provides a generic approach, based on combinatorial arguments, to proving the decidability of the separation problem for several subclasses of the regular languages, including the classes of piecewise testable languages, unambiguous languages, and locally (threshold) testable Languages.

### Piecewise Testable Languages and Nondeterministic Automata

- Computer ScienceMFCS
- 2016

This paper defines a class of NFAs, called ptNFAs, that recognize piecewise testable languages and shows that the depth of a ptNFA provides an (up to exponentially better) upper bound on k than the minimal DFA.

### F L ] 4 D ec 2 01 4 On k-piecewise testability ( preliminary report )

- Mathematics, Computer Science
- 2014

This work provides the complexity bound to decide whether a given minimal DFA represents a k-piecewise testable language for a fixed k, which then results in an algorithm that is single exponential with respect to the size of the DFA and d ouble exponential withrespect to the resulting k.

### On $k$-piecewise testability (preliminary report)

- Computer ScienceArXiv
- 2014

It is shown that the upper bound on $k$ given by the depth of the minimal DFA can be exponentially bigger than the minimal possible $k$, and a tight upper bound is provided on thedepth of the minimum DFA recognizing a piecewise testable language.

### Technical report column

- Computer ScienceSIGA
- 2014

A simple proof that AND-compression of NP-complete problems is hard is hard and can be found in this paper.

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