Title: An unconventional
1An unconventional computational model
2A self-regulating balance
3Schematic representation
small letters, numerals represent
fixed weights (inputs) capital letters
represent variable weights (outputs)
4The balance can compute!
5The balance can compute!
Weights (or pans) themselves can take the form of
a balance-machine.
- 1) a B A 2) a B
- Therefore, A 2a.
- 1) A B a 2) A B
- Therefore, A a/2.
Note The weight of a balance-machine is the sum
of the individual weights on its pans.
6The balance can compute!
A 4d
D a/4
7Sharing pans between balances
outputs
8Computation universality of balances
NOTE Input true 10 false 5 Output
Interpreted as 1, if gt 5 and as 0, otherwise.
9Computation universality of balances
NOTE Input true 10 false 5 Output
Interpreted as 1, if gt 5 and as 0, otherwise.
10Computation universality of balances
Balance as a transmission line Balance (2) acts
as transmission line, feeding output from (1)
into the input of (3).
11Solving SAT with balances
Consider the satisfiability of (a b) (a b)
Machines 1-3 work together, sharing the variables
A, B, and A. The only possible configuration in
which they can stop is one of the satisfiable
configurations, if any. If the machine keeps
staggering after a fixed time, then one might
conclude that the expression is not satisfiable.
12Balance Machine features
- The balance machine is a closed system unlike
TMs. - It is a closed system with a negative
feed-back.
- The balance machines way of computing is very
human. - Does not require quantification in order
to solve problems.
13Future research
- Balance-machine as a language recognizer
- Balance-machine as an artificial neuron