Boolean Algebra / Karnaugh Maps with N > 2 (Higher Dimensions)

Most who inhabit this list are probably familiar with standard Boolean
algebra and Karnaugh maps, i.e.

http://en.wikipedia.org/wiki/Karnaugh

Karnaugh maps come up very frequently in the design of microcontroller
software, i.e. on a processor that handles bitfields very efficiently, one
might even implement a 3-state state machine as something like:

if (!x.bf1)
{
if (!x.bf0)
{
/* 0/0 logic, First State */
}
else
{
/* 0/1 logic, Second State */
}
}
else
{
/* 1/X logic, Third State */
}

However, it also occurs frequently that an integer range (x, 0-255, say) is
"paneled" into smaller pieces of significance (0-10, 11-67, and 68-255,
say), and this can lead to truth tables that are a mixture of these
"paneled" ranges and Boolean values. The simplest example would be a table
with 3 columns (corresponding to the three ranges above), and two rows (y,
one for F, one for T).

i.e.
| 0-10 | 11-67 | 68-255
F | 1 | 1 | 0
T | 0 | 1 | 0

In "reducing" a 3 x 2 table like this, one could easily end up with a
Boolean-valued function like:

(!y && x<=67) || (x>=11 && x<=67)

Is there an algebra (similar to Boolean algebra) or a way of thinking that
would allow one to freely mix "Boolean" values and "paneled" values and have
some way of reducing functions, similar to a Karnaugh map with more
dimensions?

Thanks.
------------------------------------------------------------
David T. Ashley (dta@xxxxxxxx)
http://www.e3ft.com (Consulting Home Page)
http://www.dtashley.com (Personal Home Page)
http://gpl.e3ft.com (GPL Publications and Projects)


.

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