Nasu, Masakazu, "Local maps inducing surjective global maps of one-dimensional tessellation automata, " Math. Systems Theory 11 (1978), 327-351.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in [61] which brought to light a number of subtle issues somehow related to invertibility. But invertibility was explicitly addressed only in 1972, in seminal papers by Richardson[60] and Amoroso and Patt[2] #4 After that, theoretical work on invertibility in cellular automata proliferated[3,61,54,46 48,90,35]. In spite of that work, however, for many #4 Unbeknownst to those authors, systems that are in essence one dimensional cellular automata had already been studied in an abstract mathematical context by Hedlund and associates as early as 1963[30,31] both Richardson s results on invertibility ....

....results to higher dimensions would most likely require a different approach. Since then, for almost twenty years a quest for these generalizations to more than one dimension went on with little success. Invertibility and related properties for the one dimensional case were revisited in [54,87,14,29]. Many equivalent characterizations of ica were given[90,47,48,35] but none that offered a finitary handle on invertibility. Finally, quite recently, Kari proved that Theorem 4.5 (Kari[38,39] There is no effective procedure for deciding whether or not an arbitrary two dimensional cellular ....

Nasu, Masakazu, "Local maps inducing surjective global maps of one-dimensional tessellation automata, " Math. Systems Theory 11 (1978), 327-351.

....instance, 55, 7, 8, 10] to light a number of subtle issues somehow related to invertibility. But invertibility was explicitly addressed only in 1972, in seminal papers by Richardson[60] and Amoroso and Patt[2] 4 After that, theoretical work on invertibility in cellular automata proliferated[3, 61, 54, 46, 47, 48, 90, 35]. In spite of that work, however, for many years the most interesting ica actually exhibited remained an extremely simpleminded one (the longest orbit is of period two ) discovered by Patt through brute force enumeration[56] Ica continued to appear to be quite rare [2] Not only rare, but also ....

....their results to higher dimensions would most likely require a different approach. Since then, for almost twenty years a quest for these generalizations to more than one dimension went on with little success. Invertibility and related properties for the onedimensional case were revisited in [54, 87, 14, 29]. Many equivalent characterizations of ica were given[90, 47, 48, 35] but none that offered a finitary handle on invertibility. Finally, quite recently, Kari proved that Theorem 4.5 (Kari[38, 39] There is no effective procedure for deciding whether or not an arbitrary twodimensional cellular ....

Nasu, Masakazu, "Local maps inducing surjective global maps of one-dimensional tessellation automata," Math. Systems Theory 11 (1978), 327-351.

....can also be used to study the reversibility. A more detailed elaboration will replace this informal discussion) 4 Future Research . Study the injectivity and surjectivity of GCAs. It is expected that the methods developed for CAs can also be used to give answers for one dimensional GCAs ( 1] [6]) Use regular expressions to describe configurations. Apply the methods, found in Wolfram [7] to the class of GCAs. What is the connection between the time and the space evolution in GCAs . Study the connection between CAs and GCAs. Is is possible, given an arbitrary CA, to find a ....

Masakazu Nasu. Local maps inducing surjective global maps of one-dimensional tesselation automata. Mathematical Systems Theory, 11:327--351, 1978.

No context found.

-130 #1987#. #12# Masakazu Nasu, #Local Maps Inducing Surjective Global Maps of OneDimensional Tessellation Automata," Mathematical Systems Theory 11

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC