Connecting Partial Words and Regular Languages

@inproceedings{Dassow2012ConnectingPW,
  title={Connecting Partial Words and Regular Languages},
  author={J{\"u}rgen Dassow and Florin Manea and Robert Mercas},
  booktitle={CiE},
  year={2012}
}
We initiate a study of languages of partial words related to regular languages of full words. First, we study the possibility of expressing a regular language of full words as the image of a partial-words-language through a substitution that only replaces the hole symbols of the partial words with a finite set of letters. Results regarding the structure, uniqueness and succinctness of such a representation, as well as a series of related decidability and computational-hardness results, are… 
Deterministic finite H-Automata and ω-regular partial languages
TLDR
This paper introduces the subclass of ω-regular partial languages called Büchi local υ-partial languages, and defines deterministic finite H-automaton with acceptance condition on ψ-partial words and deterministic infinite H-local automaton.
Partial Word DFAs
TLDR
This paper investigates a question of Dassow et al. as to how these sizes are related and creates so-called ⋄-DFAs which are smaller than the DFAs recognizing the original language L, which recognize the compressed language.

References

SHOWING 1-9 OF 9 REFERENCES
Freeness of partial words
Hard Counting Problems for Partial Words
TLDR
This paper shows that finding a full word that is not compatible with any word from a given list of partial words, all having the same length, is NP-complete; from this it is derived that counting the number of words that are compatible with at least one words from aGiven list of Partial Words is #P-complete.
Algorithmic Combinatorics on Partial Words
TLDR
This paper focuses on two areas of algorithmic combinatorics on partial words, namely, pattern avoidance and subword complexity, and discusses recent contributions as well as a number of open problems.
Restorations of punctured languages and similarity of languages
TLDR
It is proved the existence of linear languages which are not δ -similar to any regular language for any δ < ½ and for δ ≥ ½ this is unknown but it could only be possible in the case of non-slender linear languages.
Handbook of Formal Languages
TLDR
This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field.
On the Maximal Number of Cubic Runs in a String
TLDR
C cubic runs are investigated, in which the shortest period p satisfies 3p≤|v|, and the upper bound of 0.5 n is shown on the maximal number of such runs in a string of length n, and an infinite sequence of words over binary alphabet is constructed.
STRING-MATCHING AND OTHER PRODUCTS
TLDR
By exploiting the formal similarity of string-matching with integer multiplication, a new algorithm has been obtained with a running time which is only slightly worse than linear.
Partial Words and a Theorem of Fine and Wilf
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
TLDR
This book lucidly develops the central ideas and results of combinatorics on partial words and explores up-and-coming techniques for solving partial word problems as well as the future direction of research.