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Some remarks on the π-directable automata and definite automata: A survey

Milena Bogdanovic
2015 Godisnjak Uciteljskog fakulteta u Vranju  
The concept of π-directable automata is a concomitant specialization concept of the directable automata and generalization of the concept definite automata.  ...  Various specializations and generalizations of directable automata are an interesting field of Automata theory. They have useful applications in industrial context and still offer open questions.  ...  The transition semigroup of the automata A is a nil-semigroup. On the other hand, A is a finite automata, so the transition semigroup is finite.  ... 
doi:10.5937/gufv1506083b fatcat:a2myu5w4tjcqpapufefoy4wklq

On Nilpotency and Asymptotic Nilpotency of Cellular Automata

Ville Salo
2012 Electronic Proceedings in Theoretical Computer Science  
Richard by showing that cellular automata that eventually fix all cells to a fixed symbol 0 are nilpotent on S^Z^d for all d.  ...  We also briefly discuss nilpotency on other subshifts, and show that weak nilpotency implies nilpotency in all subshifts and all dimensions, since we do not know a published reference for this.  ...  And of course, I would like to thank all three for their comments on this article.  ... 
doi:10.4204/eptcs.90.7 fatcat:oswuxldavvcrzmnznvuw7e3kr4

Page 2129 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
From the text: “We consider the isomorphic and homomorphic realizations of finite nilpotent automata. First we characterize all finite subdirectly irreducible nilpotent automata.  ...  We characterize all subdirectly irreducible commutative automata and hence all subdirectly irreducible commutative semigroups as well.” Imreh, B. 83e:68068 On finite nilpotent automata.  ... 

Conjugacy of one-dimensional one-sided cellular automata is undecidable [article]

Joonatan Jalonen, Jarkko Kari
2017 arXiv   pre-print
following decision problems are undecidable: Given two one-dimensional one-sided cellular automata F and G over a full shift: Are F and G conjugate?  ...  It also immediately follows that these results hold for one-dimensional two-sided cellular automata.  ...  Conjugacy of periodic cellular automata on one-or two-sided subshifts of finite type is decidable.  ... 
arXiv:1710.08111v1 fatcat:cdizyyuryfaoriboabubkmshsm

Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable [chapter]

Joonatan Jalonen, Jarkko Kari
2017 Lecture Notes in Computer Science  
following decision problems are undecidable: Given two one-dimensional one-sided cellular automata F and G over a full shift: Are F and G conjugate?  ...  It also immediately follows that these results hold for one-dimensional two-sided cellular automata.  ...  Conjugacy of periodic cellular automata on one-or two-sided subshifts of finite type is decidable.  ... 
doi:10.1007/978-3-319-73117-9_16 fatcat:afsytbockbbbfhjd6hirucfhnq

Page 5798 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
We show that all the automata belonging to a finite definable class, except for the limit automata, form a finitely recognizable class of automata.  ...  A tree automaton over a ranked alphabet © is essentially a finite algebra (A,2) on the set A of states.  ... 

Automata groups generated by Cayley machines of groups of nilpotency class two [article]

Ning Yang
2020 arXiv   pre-print
We show presentations of automata groups generated by Cayley machines of finite groups of nilpotency class two and these automata groups are all cross-wired lamplighters.  ...  The author [19] gave the automata group presentations for finite step-2 nilpotent groups with central squares.  ...  The automata groups generated by Cayley machines of finite step-2 nilpotent groups are cross-wired lamplighter groups.  ... 
arXiv:2008.02945v1 fatcat:qsaoahoem5fxbkofwikr4lsj7i

Characteristic Semigroups of Directable Automata [chapter]

Tatjana Petković, Miroslav Ćirić, Stojan Bogdanović
2003 Lecture Notes in Computer Science  
for dealing with automata satisfying some irregular identities.  ...  Finally, a correspondence between irregular varieties of automata and certain varieties of semigroups is given.  ...  To the pseudo-σ C -varieties of all finite definite and finite nilpotent automata correspond pseudo-κ C -varieties of all finite semigroups that are nilpotent 0-free extensions of right zero bands and  ... 
doi:10.1007/3-540-45005-x_37 fatcat:rvdzox4tdfgvnbcgcgax2mzf2q

Page 185 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
) On absolutely-nilpotent of class k groups.  ...  Then either (a) dimp(V) is finite, or (b) G is imprimitive, or (c) G acts fixed point freely on V — {0}.  ... 

Finitely Generated Synchronizing Automata [chapter]

Elena V. Pribavkina, Emanuele Rodaro
2009 Lecture Notes in Computer Science  
We characterize the class of synchronizing automata having finite language of minimal synchronizing words (such automata are called finitely generated ).  ...  We also prove that checking whether a given DFA A is finitely generated is co-NPhard, and provide an algorithm for this problem which is exponential in the number of states A .  ...  In the following lemma we state without proof some simple known properties of nilpotent automata.  ... 
doi:10.1007/978-3-642-00982-2_57 fatcat:j4xa6bojibfojad57evhiqcpcq

Revisiting the Rice Theorem of Cellular Automata [article]

Pierre Guillon, Gaétan Richard
2011 arXiv   pre-print
This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets.  ...  A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors.  ...  Given some partial cellular automaton G on some subshift of finite type Σ, some cellular automata N and S on alphabets A ∋ θ and B ∋ γ, κ. Considering C = A × B, we can build E, k, ξ as in Lemma 3.1.  ... 
arXiv:1001.0253v4 fatcat:gt63drfonzcv3euzkgogglzzsm

Page 1375 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
Zil/ber that a soluble group of finite Morley rank which is not nilpotent-by-finite interprets an al- gebraically closed field [see e.g., B.  ...  The present authors establish a similar result for probability models that take on at most a finite number of values on definable sets.  ... 

Revisiting the Rice Theorem of Cellular Automata

Pierre Guillon, Gaétan Richard, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets.  ...  A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors.  ...  Given some partial cellular automaton G on some subshift of finite type Σ, some cellular automata N and S on alphabets A ∋ θ and B ∋ γ, κ. Considering C = A × B, we can build E, k, ξ as in Lemma 3.1.  ... 
doi:10.4230/lipics.stacs.2010.2474 dblp:conf/stacs/GuillonR10 fatcat:mwmnqjguzbfk5mlbcenzmkaoqy

Page 7336 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
(UKR-AOS; Kiev) On locally finite groups factorized by locally nilpotent subgroups. (English summary) J. Pure Appl. Algebra 106 (1996), no. 1, 45—56.  ...  One of the consequences is that the isomorphism problem for finitely generated virtually free groups is primitive recursive (in the push-down automata for the groups).  ... 

Trees are nilrigid [article]

Ville Salo
2019 arXiv   pre-print
after finite time.  ...  We study cellular automata on the unoriented k-regular tree T_k, i.e. continuous maps acting on colorings T_k which commute with all automorphisms of the tree.  ...  By similar abuse of notation, cellular automata on the k-ary tree are cellular automata f : A T k → A T k on the action G k T k . Definition 2. Let X be a topological space and f : X → X a function.  ... 
arXiv:1905.06093v1 fatcat:khrlvcd7nnghxkvs3iikrykd2m
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