speculative.txt

No guarantee of accuracy. When in disagreement, anything anywhere else
supercedes that here.

jpt4

UTC20151021

On analog electronic circuits:

Electronic circuits are not particle propagation systems. Although
current is thought of as flowing from source to sink, if a path
doesn't exist, neither does the capacity for work; voltage-encoded
logical HIGH and LOW signal do not test their paths to see if they are
complete. Thus, because a factor at the spatial end of an electrical
circuit (the presence of a sink) effects its beginning (the coursing
of current from source), their exists a non-local effect in analogue
electric circuits compared to the digital logic they support. This
affects the functional formalization of the single transistor RTL NOR
gate, as follows.

In analog reality, voltage level encoded logic values do not exist
independently as point values at the entrance and exit terminals of
circuit elements, and are instead samples of relative potential
between the endpoints of source and ground. Because the endpoints and
the path between them are not guaranteed to be local, a naive
formalization of an analog circuit which attempts to model each
circuit element as a function over its local terminal voltage levels
may be required to break from that approach in some way. When
modelling the single transistor NOR gate (Fig. 1), two possible
deviations from the local, functional method produced an accurate
model:

1. All elements behave as functions, but allow non-local function
inputs (Derivation 1).

2. All inputs are local, but allow relational (bi-directional) element
behavior (Derivation 2).

                       
                           F          Legend:      
                          === V+            ----  := wire
                           |                |     := wire                
                          <R4>              +     := wire junction
                           |   E            o     := connection to 
    A o--<R1>--+        W2 +---o out                 larger circuit
               |           |                ===   := power rail                 
               |         |/                 <R1>  := resistor
    B o--<R2>--+---+-----| T1               T1    := BPJ transistor
               W1  |     |>                 W2    := wire junction
                  <R3>     |                         function
                   |       |                A-F   := input/output
                  === V-  === ground                 labels
                   C       D
                        
                        c                   c,b,e := collector,
                        |                            base, emitter
                      |/                             terminals
                   b--| T1
                      |>
                        |
                        e

    Figure 1. Schematic of the single bipolar junction transistor NOR
    gate using resistor-transistor logic.
                 
Derivation 1: 

Every element is modelled as a function with local inputs and outputs,
except F=NOT(D), E=W2(F)=F, c=W2(F)=F.

UTC20151014
Finite State Machine Representation of a Transistor:
Q={q0}
SIG={0 1 2 3}
GAM={0 1}
DEL={(0,0) (1,0) (2,0) (3,1)}

OR

Q={q0}
SIG={0 1}
GAM={0 1}
DEL=SIG x SIG x Q -> GAM x Q
   ={(0,0,0) (0,1,0) (1,0,0) (1,1,1)}