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.

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Also there is not much algebra or geometry about Max.

Max+ algebra being a big exception.

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Or ...

Finding addional must-have properties.

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Im sure there are many nice algorithms that use max.

( even without max+ algebra )

Maybe one of those could help us out.

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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