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"Automata"
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Dynamics of the Box-Ball System with Random Initial Conditions via Pitman’s Transformation
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In
this article, we study the BBS when started from a random two-sided infinite particle configuration. For such a model, Ferrari et al.
recently showed the invariance in distribution of Bernoulli product measures with density strictly less than
eBook
State-conserving one-dimensional cellular automata with radius one
This paper presents a new way of looking at state-conserving one-dimensional cellular automata. Such cellular automata preserve the distribution of states, i.e., the number of cells in each state, throughout the entire evolution of the system. The tools introduced make it possible to fully characterize and enumerate all such cellular automata with radius one, regardless of the number of states. Surprisingly, it turns out that the number of state-conserving one-dimensional cellular automata with radius one and k states is very closely related to the number of labeled directed graphs with k vertices and not containing a directed path of length two.
Journal Article
On Polynomial Recursive Sequences
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is bn = n!. Our main result is that the sequence un = nn is not polynomial recursive.
Journal Article
Automata Field Analysis: Operations, Substructures, and Homomorphisms
This paper introduced the automata field concept and studied its characteristics. In particular, we define new operations by converting finite automata to finite automata field. Additionally, we examine the properties of finite automata field and their relation to field. We also define substructures of the automata field, including sub-automata field and automata field homomorphism.
Journal Article
Fuzzy multiset finite automata with output
Fuzzy multiset finite automata with output represent fuzzy version of finite automata (with output) working over multisets. This paper introduces Mealy-like, Moore-like, and compact fuzzy multiset finite automata. Their mutual transformations are described to prove their equivalent behaviours. Furthermore, various variants of reduced fuzzy multiset finite automata are studied where the reductions are directed to decrease the number of fuzzy components (like fuzzy initial distribution, fuzzy transition relation, or fuzzy output relation) of the fuzzy automata. The research confirmed that all fuzzy multiset finite automata with output can be reduced without change of their behaviours.
Journal Article