Group:
artificial intelligence
Topic:
artificial neuron nets
Topic:
history of computers
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Summary
Networks of simulated relays were studied for "interesting" behavior. The most interesting were ring networks with isolated single state equilibriums (singularities). Singular ring networks could be mathematically predicted, but prediction of singularity in general was unsuccessful. When reproduced in physical networks, singular relay networks would often balance at a cyclical equilibrium with eventual collapse into a singular state. Non-singular networks rapidly reached equilibrium. Under repeated disturbances, singular networks remain sensitive to the disturbance while normal networks will reach an insensitive equilibrium state. (cbb 5/80)
The ring networks were random number generators similar to shift-xor generators. So their "interesting" behavior was really just randomness. (cbb 11/92)
Subtopic: Zuse Z3 relay computer 
| Quote: Java simulation of Zuse's Z3 relay computer; circuits validated using a CAD system [»rojaR9_2000]
| | Quote: the Z3 used electromagnetic relays, binary numbers, floating point, punched tape, and a lamp strip for output; one multiply in three seconds [»zuseK_1984]
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Subtopic: relay network
| Quote: networks of relays and switches used for control and protective circuits for telephone exchanges, industrial motor-control, and other automated tasks [»shanCE6_1938]
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Subtopic: math as relays
| Quote: how to construct a relay switching circuit from equations of the independent and dependent variables [»shanCE6_1938]
| | Quote: can use relay circuits for complex mathematical operations; anything using a finite number of steps of 'if', 'or', 'and', etc.; e.g., adding two numbers [»shanCE6_1938]
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Subtopic: analysis of relay network
| Quote: analyze and simplify relay networks as equations; equivalent to calculus of propositions; produces minimal, series and parallel networks
| | Quote: use truth tables to prove theorems about hindrances, i.e., open or closed circuits; e.g., associative and distributive laws [»shanCE6_1938]
| | Quote: X' is the negative of X, i.e., the break contacts of a relay; X+X'=1 [»shanCE6_1938]
| | Quote: perfect analogy between calculus of switching circuits and Boolean logic; Huntington's postulates and De Morgan's theorem [»shanCE6_1938]
| | Quote: series-parallel circuits equivalent to expressions of addition, multiplication, and negation [»shanCE6_1938]
| | Quote: simplify series-parallel circuits by using Shannon's theorems to reduce the number of letters in the expression
| | Quote: sequential circuits built with XY'=0; Y can operate only if X is operated [»shanCE6_1938]
| | Quote: the maximal series-parallel circuits are sum_over_n of X_k and its inverse; O(2^n) elements [»shanCE6_1938]
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Subtopic: flip-flop as relays
| Quote: a lock-in circuit is X=RX+S; X operates from R closing to S opening [»shanCE6_1938]
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Subtopic: random network
| Quote: an unorganized machine has a large number of randomly connected, similar units (e.g., NAND gates); simple model of nervous system [»turiAM9_1947]
| | Quote: turn networks of NAND gates into components that, depending on initial conditions, invert signal, always 1, or alternate; training can create a universal Turing equivalent [»turiAM9_1947]
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Subtopic: random relay networks
| QuoteRef: cbb_1973 ;;1/21/78 going over relay networks--cyclic relays no real difference to relay networks, both worse than random transitions--only interest is singularity
| | QuoteRef: cbb_1973 ;;1/22/78 initial work on singularities in relay networks
| | QuoteRef: cbb_1973 ;;1/26/78 shown that all RQ networks have singularities & how to tell which ones
| | QuoteRef: cbb_1973 ;;1/26/78 singular networks--one or more stable states not reachable from other states except through unusual transitions (eg race transitions)
| | QuoteRef: cbb_1973 ;;1/27/78 interested in relays because show an unusual equilibrium when started from a random state
| | QuoteRef: cbb_1973 ;;2/27/78 A singular system is predictable in the long run but not predictable in the short run.
| | QuoteRef: cbb_1973 ;;8/4/79 determined all 1 and 2 element singularities
| | QuoteRef: cbb_1973 ;;8/4/79 looked at 3 element singularities but didn't find a regularity nor also there was many singularities
| | QuoteRef: cbb_1973 ;;8/4/79 in 1 element systems are singular, in 2 element systems 35/256 system are singular (ca 1/5)
| | QuoteRef: cbb_1973 ;;8/4/79 singularities are very common-- they have lots of similarities but these similarities are not strong enough to generalize, it appears that they occur in classes
| QuoteRef: cbb_1973 ;;8/18/79 non-singular systems under a small disturbance will reach an equilibrium despite the disturbance, singular system will never reach an equilibrium which is insensitive to the disturbance.
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Related Topics
Group: artificial intelligence (14 topics, 500 quotes)
Topic: artificial neuron nets (29 items)
Topic: history of computers
(66 items)
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