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Degrees of Restriction for Two-Dimensional Automata [article]

Taylor J. Smith, Kai Salomaa
2021 arXiv   pre-print
In this paper, we introduce the notion 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.  ... 
arXiv:2105.01179v1 fatcat:3vkug4xxifgxpaqqhchdko7abm

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.  ... 

Universality and Cellular Automata [chapter]

K. Sutner
2005 Lecture Notes in Computer Science  
See also [1] 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  ... 
doi:10.1007/978-3-540-31834-7_4 fatcat:kvezmyeumbfpzazezsysw4baui

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  ... 

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.  ... 

Cumulative subject index volumes 64–67

1985 Information and Control  
space, 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  ... 
doi:10.1016/s0019-9958(85)80038-3 fatcat:cnfpoerj4bgahkwbjf5nrkty5e

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  ... 

On Decidability Properties of One-Dimensional Cellular Automata [article]

Olivier Finkel
2009 arXiv   pre-print
We give some examples 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.  ... 
arXiv:0903.4615v2 fatcat:fc5ccknkefdildt3lk7whl5xfi

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]

Dirk-Michael Schlingemann
2008 arXiv   pre-print
We report here on the structure 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.  ... 
arXiv:0812.0714v1 fatcat:choo33d77vcj5px5khikpiua5i

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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