Corpus ID: 235422324

Automatic winning shifts

@article{Peltomki2021AutomaticWS,
  title={Automatic winning shifts},
  author={Jarkko Peltom{\"a}ki and Ville Salo},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.07249}
}
To each one-dimensional subshift X, we may associate a winning shift W(X) which arises from a combinatorial game played on the language of X. Previously it has been studied what properties of X does W(X) inherit. For example, X and W(X) have the same factor complexity and if X is a sofic subshift, then W(X) is also sofic. In this paper, we develop a notion of automaticity for W(X), that is, we propose what it means that a vector representation of W(X) is accepted by a finite automaton. Let S be… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 34 REFERENCES
Automatic Theorem-Proving in Combinatorics on Words
TLDR
A technique for mechanically proving certain kinds of theorems in combinatorics on words, using finite automata and a software package for manipulating them is described, and the characteristic sequence of least periods of a k-automatic sequence is (effectively) k- automatic. Expand
Playing with Subshifts
TLDR
This work studies the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word, and investigates the relation between the target subshift and the set of turn orders for which the player has a winning strategy. Expand
On Equations for Regular Languages, Finite Automata, and Sequential Networks
TLDR
It is shown that any system of equations of the form X i = ⋃ α∈A α·F i,a ∪δ i i=1,…,n has a unique solution which, moreover, is regular. Expand
On winning shifts of marked uniform substitutions
TLDR
This paper studies the winning shifts of subshifts generated by marked uniform substitutions, and shows that these winning shifts also have a substitutive structure, and gives an explicit description of the winning shift for the generalized Thue-Morse substitutions. Expand
Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance
TLDR
There exists an aperiodic infinite binary word avoiding the pattern x x x^R, which is the first avoidability result concerning a nonuniform morphism proven purely mechanically. Expand
Representations of numbers and finite automata
TLDR
Conditions on the recurrence under which the function of normalization which transforms any representation of an integer into the normal one—obtained by the usual algorithm—can be realized by a finite automaton are given. Expand
Regular sequences and synchronized sequences in abstract numeration systems
TLDR
It is proved that the formal series obtained as the composition of a synchronized relation and a recognizable series is recognizable, which enables us to use recognizable formal series in order to generalize most (if not all) known characterizations of $b-regular sequences to abstract numeration systems. Expand
Automatic sequences based on Parry or Bertrand numeration systems
TLDR
It is proved that the set of Parry-automatic sequences with respect to a fixed Parry numeration system is not closed under taking images by uniform substitutions or periodic deletion of letters, and the result shows that these properties are lost when generalizing to Parry numerical systems and beyond. Expand
Decision algorithms for Fibonacci-automatic Words, I: Basic results
TLDR
A decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) “Fibonacci-automatic”, which includes the famous Fibonacci word f. Expand
Formal Languages, Automata and Numeration Systems 2: Applications to Recognizability and Decidability
The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the crossfertilization between formal logic and finite automata (such as thatExpand
...
1
2
3
4
...