Decoding the irreversible function.

[SmaranTum]

Description

In this PR, the decoder functionality is included. With the help of this decoder, the irreversible function which was in an encoded form is obtained back. The signatures of certain functions are changed accordingly. Minor changes have been made to the tests.

Checklist:

• The pull request only contains commits that are related to it.
• I have added appropriate tests and documentation.
• I have made sure that all CI jobs on GitHub pass.
• The pull request introduces no new warnings and follows the project's style guidelines.

[codecov]

Codecov Report

Merging #120 (5629005) into main (8cc2c3a) will increase coverage by 0.2%.
The diff coverage is 98.9%.

@@           Coverage Diff           @@
##            main    #120     +/-   ##
=======================================
+ Coverage   92.1%   92.3%   +0.2%     
=======================================
  Files         33      33             
  Lines       2330    2400     +70     
=======================================
+ Hits        2147    2217     +70     
  Misses       183     183             

Impacted Files	Coverage Δ
include/algorithms/synthesis/encoding.hpp	100.0% <ø> (ø)
include/core/truthTable/truth_table.hpp	94.5% <ø> (-0.1%)	⬇️
src/algorithms/synthesis/dd_synthesis.cpp	99.0% <98.5%> (+0.1%)	⬆️
include/algorithms/synthesis/dd_synthesis.hpp	100.0% <100.0%> (ø)
src/algorithms/synthesis/encoding.cpp	100.0% <100.0%> (ø)

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[SmaranTum]

So again let me explain you the changes using an example.

Consider the truth table

0 0 -> 0 0
0 1 -> 1 1
1 0 -> 1 1
1 1 -> 1 1

The primary inputs (n) = 2, the primary outputs (n) = 2, the minimum no. of additional lines (k1) needed to realize the irreversible function is = 2.

encoded output pattern is:
0 0 -> 0 - -
1 1 -> 0 - -

after encoding, we get:

0 0 -> 0 - -
0 1 -> 1 - -
1 0 -> 1 - -
1 1 -> 1 - -

the total number bits = 4

So after the encoding we need to add r = 1 additional bit for decoding purposes.

based on this we augment zeros to the inputs and outputs.

0 0 0 0 -> 0 0 - -
0 0 0 1 -> 0 1 - -
0 0 1 0 -> 0 1 - -
0 0 1 1 -> 0 1 - -

we first synthesis above encoded truthtable (the augmented zeros are passed on since they are considered as identity in our synthesis algorithm)

once the encoded function is synthesized, the decoder is realized (please go through the decoder algorithm mentioned in https://www.cda.cit.tum.de/files/eda/2018_aspdac_coding_techniques_in_synthesis.pdf).

once the decoder is synthesized, we get

0 0 0 0 -> 0 0 - -
0 0 0 1 -> 1 1 - -
0 0 1 0 -> 1 1 - -
0 0 1 1 -> 1 1 - -

Also, as a new addition the don't cares/garbage bits in the decoders are not processed towards identity since it is not required.

[burgholzer]

Thanks for the explanation again. This PR still needs a bit more work before it can be merged.
You can find detailed comments down below.

[burgholzer]

Although an improvement, there are still some issues to be tackled here. See the comments below.

[burgholzer]

A few final change requests.