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

2015
*
Godisnjak Uciteljskog fakulteta u Vranju
*

The concept of π-directable

doi:10.5937/gufv1506083b
fatcat:a2myu5w4tjcqpapufefoy4wklq
*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*. ...##
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On Nilpotency and Asymptotic Nilpotency of Cellular Automata

2012
*
Electronic Proceedings in Theoretical Computer Science
*

Richard by showing that cellular

doi:10.4204/eptcs.90.7
fatcat:oswuxldavvcrzmnznvuw7e3kr4
*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. ...##
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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*. ...##
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Conjugacy of one-dimensional one-sided cellular automata is undecidable
[article]

2017
*
arXiv
*
pre-print

following decision problems are undecidable: Given two

arXiv:1710.08111v1
fatcat:cdizyyuryfaoriboabubkmshsm
*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. ...##
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Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable
[chapter]

2017
*
Lecture Notes in Computer Science
*

following decision problems are undecidable: Given two

doi:10.1007/978-3-319-73117-9_16
fatcat:afsytbockbbbfhjd6hirucfhnq
*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. ...##
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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. ...##
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Automata groups generated by Cayley machines of groups of nilpotency class two
[article]

2020
*
arXiv
*
pre-print

We show presentations of

arXiv:2008.02945v1
fatcat:qsaoahoem5fxbkofwikr4lsj7i
*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. ...##
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Characteristic Semigroups of Directable Automata
[chapter]

2003
*
Lecture Notes in Computer Science
*

for dealing with

doi:10.1007/3-540-45005-x_37
fatcat:rvdzox4tdfgvnbcgcgax2mzf2q
*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 ...##
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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}. ...##
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Finitely Generated Synchronizing Automata
[chapter]

2009
*
Lecture Notes in Computer Science
*

We characterize the class of synchronizing

doi:10.1007/978-3-642-00982-2_57
fatcat:j4xa6bojibfojad57evhiqcpcq
*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*. ...##
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Revisiting the Rice Theorem of Cellular Automata
[article]

2011
*
arXiv
*
pre-print

This is a refinement of the classical "Rice Theorem" that Kari proved

arXiv:1001.0253v4
fatcat:gt63drfonzcv3euzkgogglzzsm
*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. ...##
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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. ...##
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Revisiting the Rice Theorem of Cellular Automata

2010
*
Symposium on Theoretical Aspects of Computer Science
*

This is a refinement of the classical "Rice Theorem" that Kari proved

doi:10.4230/lipics.stacs.2010.2474
dblp:conf/stacs/GuillonR10
fatcat:mwmnqjguzbfk5mlbcenzmkaoqy
*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. ...##
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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). ...##
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Trees are nilrigid
[article]

2019
*
arXiv
*
pre-print

after

arXiv:1905.06093v1
fatcat:khrlvcd7nnghxkvs3iikrykd2m
*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. ...
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