V. Kanovei and M. Reeken. On Ulam's problem of approximation of non-exact homomorphisms. preprint, 2000. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Damage Spreading and µ-sensitivity on Cellular Automata - Martin (1999) (Correct)
....a lim sup in because (of course) generally, the limit does not exist. Thus, for the con gurations such that the lim sup will di er from the lim inf , the result is not really natural. This de nition uses an origin but is independent of it. There exist other shift invariant pseudo distances (see [2, 14]) Formenti suggests Besicovitch point of view in the CA context because of the nicer properties of the induced topology. To save time, we will adopt Besicovitch topology too since the main results related to CA are already proved, although the results of this paper are not speci c to Besicovitch ....
....speci c to Besicovitch topology. We will actually use de nitions based on probability and be interested by almost everywhere sensitivity with respect to some measure. The point is that that these topologies di er on null measure sets. A general study of Besicovitch like topologies has been done in [14] and an interesting question would be to determine those that behave like Besicovitch one and what happens for the other ones. Remark The main reason we point this out here is that there are many ways to extend Besicovitch in higher dimensional grids: the extension of Besicovitch pseudo distance ....
V. Kanovei and M. Reeken. On Ulam's problem of approximation of non-exact homomorphisms. preprint, 2000.
Damage Spreading and µ-sensitivity on CA - Martin (2000) (Correct)
....transition function of a CA is a continuous map from Q Z = into itself. 3 Remark 1.1 Actually, the results of this paper are not speci c to Besicovitch topology, but are true for a wide class of topologies including Weil one. A general study of Besicovitch like topologies has been done in [9] and an interesting question would be to determine those that behave like Besicovitch one and what happens for the other ones. The only reason we point this out here is that there are many ways to extend Besicovitch in higher dimensional grids, but all of them are equivalent for our purpose. 1.3 ....
V. Kanovei and M. Reeken. On Ulam's problem of approximation of non-exact homomorphisms. preprint, 2000.
Damage Spreading and µ-sensitivity on Cellular Automata - Martin (2000) (Correct)
....and the transition function of a CA is a continuous map from Q Z = into itself. Remark 1. Actually, the results of this paper are not speci c to Besicovitch topology, but are true for a wide class of topologies including Weil one. A general study of Besicovitch like topologies has been done in [9] and an interesting question would be to determine those that behave like Besicovitch one and what happens for the other ones. The only reason we point this out here is that there are many ways to extend Besicovitch in higher dimensional grids: the extention of Besicovitch pseudo metric on Q Z ....
V. Kanovei and M. Reeken. On Ulam's problem of approximation of non-exact homomorphisms. preprint, 2000.
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