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Concatenation Operations and Restricted Variants of Two-Dimensional Automata [article]

Taylor J. Smith, Kai Salomaa
2020 arXiv   pre-print
In this paper, we investigate closure properties of restricted models of two-dimensional automata under various concatenation operations.  ...  Finally, we study closure properties of diagonal concatenation on both two- and three-way two-dimensional automata.  ...  By restricting the movement of the input head to move in fewer than four directions, we obtain the aforementioned restricted variants of the two-dimensional automaton model.  ... 
arXiv:2008.11164v1 fatcat:ybgjpyqiordfdpebtnza6zbvm4

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  ...  Lastly, we consider closure properties for some operations on languages recognized by extended three-way two-dimensional automata.  ...  By restricting the movement of the input head, we obtain the aforementioned restricted variants of the two-dimensional automaton model.  ... 
arXiv:2105.01179v1 fatcat:3vkug4xxifgxpaqqhchdko7abm

Closure properties of cellular automata

Véronique Terrier
2006 Theoretical Computer Science  
In this paper we investigate the question of equality of real time CA and linear time CA with respect to the operations of concatenation and cycle.  ...  Moreover, in the case of two-dimensional CA recognizers, we investigate how restricted communication reduces the computational power.  ...  The two natural restrictions of CA are the one-way cellular automata (OCA) and the iterative array (IA).  ... 
doi:10.1016/j.tcs.2005.10.039 fatcat:45ddnvtzb5dillgobun33k2c4y

Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata [article]

Taylor J. Smith, Kai Salomaa
2020 arXiv   pre-print
Finally, we study the state complexity of projection languages for two-way two-dimensional automata, focusing on the language operations of union and diagonal concatenation.  ...  The operation of row projection has previously been studied under the name "frontier language", and previous work has focused on one- and two-dimensional language classes.  ...  In this section, therefore, we will focus on the state complexity of projections of union and concatenation operations for nondeterministic two-way two-dimensional automata.  ... 
arXiv:2009.00602v1 fatcat:mh6piu4lpvhhjndhtqk2cjcx44

Page 4194 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
The need to dispose of heat restricts com- puting chips to two dimensions, which would make this method depend on linear arrays of automata to preserve each bit reliably.  ...  Namely, we formalize primitive corecursive functions as apomorphisms, and show their utility on several simple examples (the ‘standard’ example being the concatenation of two colists).  ... 

Page 5118 of Mathematical Reviews Vol. , Issue 83m [page]

1983 Mathematical Reviews  
We show that some properties of two-dimensional array patterns do not coincide with their one-dimensional counterparts.”  ...  . } Ruohonen, Keijo 83m:68142 On a variant of a method of Berstel’s and Nielsen’s.  ... 

Page 8094 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
It comprises a next operator and two versions of until (existentially and universally quantified over computations).  ...  The paper studies the state-complexity of languages accepted by different variants of systolic tree automata.  ... 

Cellular automata with limited inter-cell bandwidth

Martin Kutrib, Andreas Malcher
2011 Theoretical Computer Science  
Furthermore, the computational capacity of the one-dimensional devices in question is compared with the power of two-way and one-way cellular automata with restricted communication.  ...  In this paper, d-dimensional iterative arrays and onedimensional cellular automata are investigated which operate in real and linear time and whose inter-cell communication bandwidth is restricted to some  ...  Here, we investigate d-dimensional IAs and one-dimensional cellular automata operating in real and linear time.  ... 
doi:10.1016/j.tcs.2011.02.026 fatcat:ayfzataxwzdnvd7g3djjv23ygq

Real-time reversible iterative arrays

Martin Kutrib, Andreas Malcher
2010 Theoretical Computer Science  
It is shown that real-time reversible iterative arrays can simulate restricted variants of stacks and queues.  ...  Iterative arrays are one-dimensional arrays of interconnected interacting finite automata. The cell at the origin is equipped with a one-way read-only input tape.  ...  Several closure properties of the language families in question are derived in Section 4, whereas Section 3 is devoted to the simulation of restricted variants of stacks and queues by real-time reversible  ... 
doi:10.1016/j.tcs.2009.10.017 fatcat:bhuhagke4vfurf3b6fjqjzkz6u

Two-Dimensional Languages [chapter]

Dora Giammarresi, Antonio Restivo
1997 Handbook of Formal Languages  
Inoue sent us many bibliographic references on two-dimensional automata. Finally, we thank O. Matz for his careful reading and valuable comments.  ...  Simplot for sending us a copy of 25], and for many useful comments on domino systems, and to V. Bruyere for sending us a copy of A. Gilon's Thesis 16]. K.  ...  We now de ne some concatenation operations between pictures and two-dimensional languages.  ... 
doi:10.1007/978-3-642-59126-6_4 fatcat:ymevasf56jbxfkqnos6wvzlocu

Low complexity classes of multidimensional cellular automata

Véronique Terrier
2006 Theoretical Computer Science  
We present also a correspondence between a main variant of multidimensional real-time cellular automata and one-way multihead alternating finite automata.  ...  However, we compare different variants and study their closure properties.  ...  Other variants of k-dimensional CA have been investigated [1] [2] [3] 9, 13] .  ... 
doi:10.1016/j.tcs.2006.07.061 fatcat:jpah3wn3tvbxlldqoybk7rcc4y

Weighted finite transducers in image processing

Karel Culik, Ivan Friš
1995 Discrete Applied Mathematics  
Culik and Karhumiki studied weighted finite automata (WFA) as devices computing real functions. The main motivation was to give specifications of graytone images as local grayness functions.  ...  We also show that WFT transformations are closed under union and composition and that the family of WFA images is closed under WFT transformations.  ...  The operation of concatenation of WFA, or more generally concatenation of weighted functions jr ,f2 : C* + R, does not seem to have a natural interpretation as an operation on images.  ... 
doi:10.1016/0166-218x(93)e0149-s fatcat:xr5r2z2awbexpl2i4ul3yu6ccu

Tight Bounds on the Descriptional Complexity of Regular Expressions [chapter]

Hermann Gruber, Markus Holzer
2009 Lecture Notes in Computer Science  
In particular we consider the conversion of planar deterministic finite automata to regular expressions, study the effect of the complementation operation on the descriptional complexity of regular expressions  ...  , and the conversion of regular expressions extended by adding intersection or interleaving to ordinary regular expressions.  ...  The priority of operators is specified in the usual fashion: concatenation is performed before union, and star before both product and union.  ... 
doi:10.1007/978-3-642-02737-6_22 fatcat:zo6ay47qazekvixb2m5flrwlku

A New Representation of Two-Dimensional Patterns and Applications to Interactive Programming [chapter]

I.T. Banu-Demergian, C.I. Paduraru, G. Stefanescu
2013 Lecture Notes in Computer Science  
In this paper we present a new type of regular expressions for two-dimensional patterns based on contours and their composition.  ...  Regular expressions and the associated regular algebra provide a rich formalism for specifying and analysing sequential models of computation.  ...  We thank the anonymous reviewers for their suggestions for improving the presentation of the results.  ... 
doi:10.1007/978-3-642-40213-5_12 fatcat:gb7phmrnvvcwho4ogvmcu7rqwa


Mark Burgin, Cristian S. Calude
2007 Theoretical Computer Science  
There is a dependency between computability of algorithmic complexity and decidability of different algorithmic Acknowledgements Finally, we warmly thank the referees for their reports and comments leading  ...  to better presentations of the accepted papers, as well as to Giorgio Ausiello for important technical advice.  ...  For the building blocks of this automaton, John von Neumann decided on identical chips (finite automata) placed in a rigid two-dimensional array and connected to their four nearest neighbors.  ... 
doi:10.1016/j.tcs.2007.04.018 fatcat:p7e6qof5pja4tceanzn44nwxam
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