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51 lines
No EOL
1.9 KiB
Markdown
51 lines
No EOL
1.9 KiB
Markdown
monoid-learner
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==============
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Learns the minimal monoid accepting an unknown language through an orcale.
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Similar to Lstar, but for monoids instead of automata. The output is a monoid
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presentation which is furthermore minimised by the Knuth-Bendix completion.
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Only works for regular languages.
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[Original](https://gist.github.com/Jaxan/d9bb9e3223e8fe8266fe4fe84d357088)
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This algorithm is made more precise and generalised to bimonoids (in the
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sense of a finite set with two binary operations) in
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[this paper.](https://doi.org/10.1007/978-3-030-71995-1_26)
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## To run
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Install Haskell and its cabal tool and clone this repo. Then run:
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```
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cabal run monoid-learner
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```
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## Example output for the example in `app/Main.hs`:
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For the language of non-empty words with an even number of as and a triple
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number of bs. Note that the equations tell us that the language is
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commutative.
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```
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Monoid on the generators:
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fromList "ab"
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with equations:
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[(fromList "ba",fromList "ab"),(fromList "aaa",fromList "a"),(fromList "aab",fromList "b"),(fromList "bbb",fromList "aa")]
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and accepting strings:
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fromList [fromList "aa"]
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```
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For the language where a occurs on position 3 on the right and the empty
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word.
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```
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... (many membership queries) ...
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Monoid on the generators:
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fromList "ab"
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with equations:
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[(fromList "bbbb",fromList "bbb"),(fromList "bbba",fromList "bba"),(fromList "bbab",fromList "bab"),(fromList "bbaa",fromList "baa"),(fromList "babb",fromList "abb"),(fromList "baba",fromList "aba"),(fromList "baab",fromList "aab"),(fromList "baaa",fromList "aaa"),(fromList "abbb",fromList "bbb"),(fromList "abba",fromList "bba"),(fromList "abab",fromList "bab"),(fromList "abaa",fromList "baa"),(fromList "aabb",fromList "abb"),(fromList "aaba",fromList "aba"),(fromList "aaab",fromList "aab"),(fromList "aaaa",fromList "aaa")]
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and accepting strings:
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fromList [fromList "",fromList "aaa",fromList "aab",fromList "aba",fromList "abb"]
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``` |