Added description of AutomataMatcher

README.md

@@ -37,23 +37,26 @@ $matcher = AutomataMatcher::build($owners->getRules());
 $rule = $matcher->match($relative_path);
 ```
 
-## TODO
-
-- [x] Add comments to the structure
-- [x] Complete phpdocs
-- [x] Add error checking on `match` to normalize or reject impossible patterns (i.e. "" and "/...")
-- [ ] Explain how `AutomataMatcher` works in this file.
-- [x] Should I support whitespace escaping in patterns?
-- [x] Add ability to turn `Owners` into string.
-- [x] Test owners entries.
-- [x] Test entries to string.
-- [x] Test pattern escaping.
-- [x] Test no-owners rules
-- [x] Remove ext-json from requires.
-- [x] Add ext-ctype to requires.
-- [x] Convert json tests to PHP arrays.
-- [ ] Add a command line tool for dot-renderer
-- [x] Add tests for all entries.
+#### What does the AutomataMatcher do?
+
+Each of the patterns in a `CODEOWNERS` rule is a simplified regular expression and, thus, it could be represented as a
+fininte automata. In fact, the `SimpleMatcher` turns each of the patterns into a regular expression and then iteratively
+matches the path against those regular expressions. In other words, the `SimpleMatcher` executes the finite automata
+of each rule independently. The `AutomataMatcher`, on the other hand, combines all of the patterns into a single finite
+automata. For example, here is the state machine for Github's [exmaple CODEOWNERS](tests/CODEOWNERS.example).
+
+![Automata for CODEOWNERS.example](tests/CODEOWNERS.example.png)
+
+The image was rendered with the following command:
+
+```bash
+bin/render-nfa tests/CODEOWNERS.example | dot -Tpng -o tests/CODEOWNERS.example.png
+```
+
+## Acknowledgements
+
+The code in `SimpleMatcher` that converts patterns to regular expressions owes a debt of gratitude
+to https://github.com/hmarr/codeowners.
 
 ## Author(s)