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Degrees of Restriction for Two-Dimensional Automata
[article]

2021
*
arXiv
*
pre-print

In this paper, we introduce the notion

arXiv:2105.01179v1
fatcat:3vkug4xxifgxpaqqhchdko7abm
*of*"*degrees**of**restriction*"*for**two*-*dimensional**automata*, and we develop sets*of*extended*two*-*dimensional*automaton models that allow*for*some bounded number*of**restricted*... extended*two*-way*two*-*dimensional**automata*. ... In the present paper, we consider a similar idea, which we term "*degrees**of**restriction*"*for**two*-*dimensional**automata*. ...##
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Page 416 of Mathematical Reviews Vol. , Issue 91A
[page]

1991
*
Mathematical Reviews
*

*two*-way

*two*-

*dimensional*alternating finite

*automata*through | 80°-rotation. ...

*Two*computing models

*for*the recognition

*of*

*two*-

*dimensional*languages are compared. ...

##
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Universality and Cellular Automata
[chapter]

2005
*
Lecture Notes in Computer Science
*

See also [1]

doi:10.1007/978-3-540-31834-7_4
fatcat:kvezmyeumbfpzazezsysw4baui
*for*a critical analysis*of*frameworks*for*the classification*of*cellular*automata*. ... Since Wolfram relies heavily on discrete dynamical systems such as cellular*automata*in his approach it is interesting to search*for**restricted*classes*of*CA and/or alternative notions*of*universality ... Since Wolfram relies heavily on discrete dynamical systems such as cellular*automata*in his approach it is interesting to search*for**restricted*classes*of*CA and/or alternative notions*of*universality ...##
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Page 5461 of Mathematical Reviews Vol. , Issue 88j
[page]

1988
*
Mathematical Reviews
*

Summary: “We previously introduced a

*two*-*dimensional*automa- ton with the following structure. The*two*-*dimensional*input tape is rotated clockwise by 90, 180 and 270*degrees*. ... Summary: “Exponential lower bounds*for*the lengths*of*diagnostic and synchronizing sequences are derived*for**automata*with a*two*- element input alphabet.” 88j:68125 68Q80 54H20 Goles Ch., Eric (RCH-UCS ...##
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Page 3260 of Mathematical Reviews Vol. , Issue 81H
[page]

1981
*
Mathematical Reviews
*

-Controls 2 (1971), no. 4, 42-48; MR 48 #8211] investi.
gated the decision problems

*for*(four-way)*two*-*dimensional*finite*automata*, and showed,*for*example, that the emptiness problem*for*those*automata*... {*For*the entire collection see MR 81d:03003.} D. Simovici (Roselle, N.J) Inoue, Katsushi; Takanami, Itsuo 81h:68036 A note on decision problems*for*three-way*two*-*dimensional*finite*automata*. Inform. ...##
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Cumulative subject index volumes 64–67

1985
*
Information and Control
*

space,

doi:10.1016/s0019-9958(85)80038-3
fatcat:cnfpoerj4bgahkwbjf5nrkty5e
*of*probabilistic space, lack*of**two*-way random-tape algorithm*for*, 67, 158 real-time, symmetrical one-*dimensional*cellular spaces, 67, 163 Turing machine, space-and time-efficient:*restricted*... classes*of*pushdown*automata*, 67, 126 Space cellular, one-*dimensional*, real-time simulation, 67, 163 probabilistic, polynomial deterministic space simulation, lack*of**two*-way random-tape algorithm ...##
###
Page 982 of Mathematical Reviews Vol. 38, Issue 5
[page]

1969
*
Mathematical Reviews
*

Chapter 13, Stack

*automata*: (13.1) Definitions; (13.2)*Restricted*types*of*stack*automata*; (13.3) The power*of**two*-way stack*automata*; (13.4) The power*of*one-way stack auto- mata ; (13.5) Recursiveness ... problem*for*that class is*of**degree*D. ...##
###
Page 1036 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

Summary: “A

*two*-*dimensional*on-line tessellation acceptor is a*two*-*dimensional*array*of*identical finite*automata*, each connected to its four nearest neighbors. ... Also the relations between languages accepted by*two*-*dimensional*on-line tessellation acceptors and finite*automata*are considered.” 93b:68064 68Q80 58F08 Willson, Stephen J. (1-IASU) Calculating growth ...##
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On Decidability Properties of One-Dimensional Cellular Automata
[article]

2009
*
arXiv
*
pre-print

We give some examples

arXiv:0903.4615v2
fatcat:fc5ccknkefdildt3lk7whl5xfi
*of*new decidable properties*for*one-*dimensional*cellular*automata*. ... In the case*of*surjective cellular*automata*, some more efficient algorithms can be deduced from results*of*Kuske and Lohrey on structures*of*bounded*degree*. ... We hope that the interplay*of*the*two*domains*of*cellular*automata*and*of*automatic structures will be fruitful and will provide new results in both fields*of*research. ...##
###
Page 5701 of Mathematical Reviews Vol. , Issue 99h
[page]

1999
*
Mathematical Reviews
*

Summary: “This paper describes an algorithm

*for*the construction*of*the edges*of*a Voronoi diagram on a*two*-*dimensional*lattice by collectives*of*finite*automata*which pick up and drop pebbles at nodes ... Summary: “This note introduces*two*-*dimensional*probabilistic finite*automata*(2-pfa’s), and investigates several properties*of*them. ...##
###
Page 2672 of Mathematical Reviews Vol. , Issue 82f
[page]

1982
*
Mathematical Reviews
*

Authors’ summary: “We obtain the following

*two*results about one-*dimensional*tessellation*automata*. (1) There is a class*of*one-*dimensional*monogenic cellular*automata*with an arbitrary neighborhood size ... Inoue, Katsushi; Takanami, Itsuo 82f:68053 Erratum: ‘‘A note on deterministic three-way tape-bounded*two*-*dimensional*Turing machines” [Inform. Sci. 20 (1980), no. 1, 41-55; MR 80i:68039]. Inform. ...##
###
Page 7072 of Mathematical Reviews Vol. , Issue 92m
[page]

1992
*
Mathematical Reviews
*

Summary: “Given

*two*cellular*automata*rules represented as op- erators Q and X, together with certain natural*restrictions*on their neighborhood structures, an algorithm is provided which yields*two*other ... -complete*for*NL. (2) Test- ing whether the*degree**of*ambiguity*of*a nondeterministic finite automaton is exponential, or polynomial, or bounded is NC'! ...##
###
Remarks on the structure of Clifford quantum cellular automata
[article]

2008
*
arXiv
*
pre-print

We report here on the structure

arXiv:0812.0714v1
fatcat:choo33d77vcj5px5khikpiua5i
*of*reversible quantum cellular*automata*with the additional*restriction*that these are also Clifford operations. ... In the one*dimensional*case we also find that all 1D Clifford quantum cellular*automata*are generated by a few elementary operations. ... Since we deal here with module homomorphism -a linear structure over the ringD p,d -we have reduced a problem in infinitely many*degrees**of*freedom to an effectively*two*-*dimensional*problem. ...##
###
Page 1110 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

This paper concerns the computational complexity

*of*determining whether a given*two*-*dimensional*cellular automaton is reversible. ... Summary: “We have proposed a new class WSP*of*non-real-time s 68 COMPUTER SCIENCE 1110 deterministic pushdown*automata*(dpda’s) and then have shown the decidability*of*the equivalence*for**two*dpda’s, one ...##
###
Page 4684 of Mathematical Reviews Vol. 58, Issue 6
[page]

1979
*
Mathematical Reviews
*

From the introduction: “This paper considers the problem

*of*whether a finite collection*of*finite*automata*can search all*of*a*two*- or three-*dimensional*obstructed space. ... In contrast, we show that no finite collection*of*finite*automata*is capable*of*searching every finite three-*dimensional*maze.” Cernyi, D. E. 58 #32072 Experiments with superposition*of**automata*. ...
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