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 Zeration = inconsistant ? tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 10/04/2014, 12:11 PM (10/03/2014, 11:29 PM)GFR Wrote: (10/02/2014, 10:58 PM)tommy1729 Wrote: It feels a bit strange ... A so called new concept " zeration " being almost equivalent to max[a,b]. Max[a,b] does not seem so intresting as a function. Max[12,100] = Max[13,100] = Max[91,100] Nothing special. ............... Also there is not much algebra or geometry about Max. Max+ algebra being a big exception. ............... Or ... Finding addional must-have properties. ................ Im sure there are many nice algorithms that use max. ( even without max+ algebra ) Maybe one of those could help us out. --- regards tommy1729 Well, ... why not! As a matter of fact 'Tropical Algebra' and 'Tropical Geometry' seem to use Max-Plus algebra, where the max operation such as: c = a[max]b is one of the basic operations. Together with: d = a[+]b they are used to build an 'Idempotent Semi-Ring'. Not a 'Field', because with [max] we cannot create a 'group' (-oo is the unity element, but there is no 'inverse element'), but a 'monoid'. Nevertheless, the result of this formalism is extremely important, because a lot of successful applications from this new discipline are expected in fields such as the Petri-nets, machine scheduling, discrete event processes (DEP), industrial manufacturing systems, telecommunication networks, parallel processing, coding/decoding systems, traffic control and, last but not least, cellular automata (NKS). Amazing. We need to think about that. Best regards. The max+ algebra is used to find the " shortest path ". Kinda like a discrete version of the calculus of variations , based on isomorphisms with matrices. " shortest paths " are naturally useful in some discrete problems , optimization , graph theory , economics and planning. However saying it is very useful for cellular automatons seems like advertising to me. Afterall many problems in cellular automaton theory , If we can even speak of theory already , do not resemble " shortest paths " but are rather of type halting problems complexity measures randomness measures construction problems problems equivalent to number theory etc. If you can show me how a max+ algebra is used for anything that is quite different from a " shortest path " type of problem that would be appreciated and surprising. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

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