## Real Time Language Recognition on 2D Cellular Automata: Dealing with Non-Convex Neighborhoods

### BibTeX

@MISC{Delacourt_realtime,

author = {Martin Delacourt and Victor Poupet},

title = {Real Time Language Recognition on 2D Cellular Automata: Dealing with Non-Convex Neighborhoods},

year = {}

}

### OpenURL

### Abstract

Abstract. In this paper we study language recognition by two-dimensional cellular automata on different possible neighborhoods. Since it is known that all complete neighborhoods are linearly equivalent we focus on a natural sub-linear complexity class: the real time. We show that any complete neighborhood is sufficient to recognize in real time any language that can be recognized in real-time by a cellular automaton working on the convex hull of V. 1

### Citations

42 |
Real-time computation by n-dimensional iterative arrays of finite-state machines
- Cole
- 1969
(Show Context)
Citation Context ... to the other. As such, it can have a great impact on the possible computations that are held on an automaton. An important result concerning computations on different neighborhoods is due to S. Cole =-=[2]-=- and states that two neighborhoods are either linearly equivalent (any computation that can be done in time T on one can be done in time k · T on the other for some constant k) or that there exists a ... |

32 |
Computation theoretic aspects of cellular automata
- Culik, Hurd, et al.
- 1990
(Show Context)
Citation Context ...s). It has been shown that these two neighborhoods are different [4, 6, 11](mainly because information can only go in one direction on the one-way neighborhood) and many algorithmic results are known =-=[3, 5, 9, 10]-=-. If we only consider neighborhoods that are “complete enough” to perform language recognition (all letters of the input word can affect the outcome of the computation), we have shown in 2005 a strong... |

26 |
One-way bounded cellular automata
- Dyer
- 1980
(Show Context)
Citation Context ... that of its left and right neighbor) and the one-way neighborhood {0, 1} (cells can only see their own state and their right neighbor’s). It has been shown that these two neighborhoods are different =-=[4, 6, 11]-=-(mainly because information can only go in one direction on the one-way neighborhood) and many algorithmic results are known [3, 5, 9, 10]. If we only consider neighborhoods that are “complete enough”... |

22 |
A Simple Universal Cellular Automaton and its One-way and Totalistic Version
- Albert, Culik, et al.
- 1987
(Show Context)
Citation Context ... neighbors. Because of the parallel behavior, it is easy to consider cellular automata in any dimension d ∈ N (the cells are arranged on Z d ). It is known that cellular automata are Turing universal =-=[1, 8]-=-. The neighborhood of a cellular automaton (the set of cells whose states a given cell can see before changing its own) defines the possible communication between all the cells, and therefore the “geo... |

11 |
Relating the power of cellular arrays to their closure properties, Theoret
- Ibarra, Jiang
- 1988
(Show Context)
Citation Context ...s). It has been shown that these two neighborhoods are different [4, 6, 11](mainly because information can only go in one direction on the one-way neighborhood) and many algorithmic results are known =-=[3, 5, 9, 10]-=-. If we only consider neighborhoods that are “complete enough” to perform language recognition (all letters of the input word can affect the outcome of the computation), we have shown in 2005 a strong... |

1 |
6. In: Cellular Automata: a Parallel Model. Mathematics and its applications edn
- Ibarra
- 1999
(Show Context)
Citation Context ... that of its left and right neighbor) and the one-way neighborhood {0, 1} (cells can only see their own state and their right neighbor’s). It has been shown that these two neighborhoods are different =-=[4, 6, 11]-=-(mainly because information can only go in one direction on the one-way neighborhood) and many algorithmic results are known [3, 5, 9, 10]. If we only consider neighborhoods that are “complete enough”... |

1 |
Cellular automata: Real-time equivalence between one-dimensional neighborhoods
- Poupet
(Show Context)
Citation Context ...d can affect the outcome of the computation), we have shown in 2005 a stronger version of Cole’s equivalence: all neighborhoods are real-time equivalent to either the one-way or standard neighborhood =-=[7]-=-. This was done by showing that it was possible to recognize the same languages in real time on non-convex neighborhoods (neighborhoods that had “holes”, for example when a cell c can see (c + 2) but ... |