By James Kim

As for the algorithm I use to determine the cognitive functions from the types requires some practice. since the MBTI types have binary symmetry, it can get a little hairy. Practice will be very helpful.

ok. summary of steps

0. understand that you only need to identify or correctly position the first 2 cognitive functions. the 3rd and 4th can be determined via positioning rules. and the last 4 via shadow rules, as you have discovered. Basically to flip the e/i valence from the first 4. also the e/i valence rule.

1. Determine Fe/Fi and position.
2. Determing S/N and it's e/i valence, and position
3. extrapolate the other 6 functions
4. check

=====================
details:

0. the cognitive functions actually do follow a pattern. and they are:

***
the positioning rule: focusing on the first 4 only, the F and T are a pair, and the S and N are a pair. forgetting the e/i valence for now, they follow the pattern

Y1 X1 X2 Y2

Each T F S N letter must be used once according to the above pattern

examples:
T S N F correct
S F T N correct
S T N F incorrect
F T S N incorrect
F F N S incorrect

the SN and TF pairs can swap positions and order.

so if you figure out the first 2, using this rule you can derive the next 2.

S T -> S T F N
N F -> N F T S

***
e/i valence rule: within the first four, the e and i always alternates. Also, if the MBTI is extroverted, then the e/i valence starts with e. ditto with introverted and starting with i.

Extroverted : Te Si Ne Fi correct
Introverted : Si Fe Ti Ne correct
Extroverted : Fi Se Ni Te incorrect (should have started the valence with 'e')
Introverted : Si Fi Te Ne incorrect (valence didn't alternate)

***
Shadow rule: the first 4 valences are mirroed, and the STFN are copied in order from the first pair.

=====================
1. Determine Fe/Fi position

Basically, this I commit to memory.

in the first 4 function...
Fi implies Te
Fe implies Ti

and

TP and FJ are Fe/Ti (tend to emit emotional expressions)
Tj and FP are Fi/Te (tend to withold emotional expressions)

remembering the positioning and valence rules, we can now position the Fe/Fi

TP, Ti
ENTP _e Ti
ESTP _e Ti
INTP Ti _e
ISTP Ti _e

FJ, Fe
ENFJ Fe _i
ESFJ Fe _i
INFJ _i Fe
ISFJ _i Fe

TJ, Te
ENTJ Te _i
ESTJ Te _i
INTJ _i Te
ISTJ _i Te

FP, Fi
ENFP _e Fi
ESFP _e Fi
INFP Fi _e
ISFP Fi _e

=====================
2. determine S/N:
basically, if the MBTI type has an N, then a Ne/Ni exists in the first 2 functions. same with S

so to complete the above ...

TP, Ti
ENTP Ne Ti
ESTP Se Ti
INTP Ti Ne
ISTP Ti Se

FJ, Fe
ENFJ Fe Ni
ESFJ Fe Si
INFJ Ni Fe
ISFJ Si Fe

TJ, Te
ENTJ Te Ni
ESTJ Te Si
INTJ Ni Te
ISTJ Si Te

FP, Fi
ENFP Ne Fi
ESFP Se Fi
INFP Fi Ne
ISFP Fi se

=====================
3. determine the other 6 functions
use the positing and valence rules to determine the next 2 functions. then use the shadow rule for the last 4.

after positioning rule
TP, Ti
ENTP Ne Ti Fe Si
ESTP Se Ti Fe Ni
INTP Ti Ne Si Fe
ISTP Ti Se Ni Fe

FJ, Fe
ENFJ Fe Ni Se Ti
ESFJ Fe Si Ne Ti
INFJ Ni Fe Ti Se
ISFJ Si Fe Ti Ne

TJ, Te
ENTJ Te Ni Se Fi
ESTJ Te Si Ne Fi
INTJ Ni Te Fi Se
ISTJ Si Te Fi Ne

FP, Fi
ENFP Ne Fi Te Si
ESFP Se Fi Te Ni
INFP Fi Ne Si Te
ISFP Fi se Ni Te

after shadow rule, you have the complete table and cognitive functions.

===================
4. check: I practice against a table to make sure I was right. after that, it's pretty much second nature.

Reversing the code, cognitive functions to MBTI should be a snap. the key is to memorize the TP/FJ:Ti/Fe and TJ/FP:Te/Fi stuff. then the various rules.

My hunch tells me that there is a more optimized method, however this one works.