Added semigroup to machine transformation

Author: Unaimend

README.md

@@ -37,6 +37,33 @@ You can plot, layout and export the automata with the `--dot` flag.
 python3 main.py --aut examples/lecture_1.csv -N 5 --dot test.png
 ```
 
+## Running the program on a given semigroup
+Currently you can only specify an semigroup in code.
+
+```python
+states = ["a", "b"]
+semigroup = pd.DataFrame( 
+                         {"0":["0", "1"], 
+                          "1": ["1", "0"]}
+                         )
+semigroup.set_index(["0", "1"])
+
+def action(s: State, sge: SemigroupElement) -> Optional[State]:
+  if str(sge) == "0":
+    return s
+  elif str(sge) == "1":
+    if s == "a":
+      return "b"
+    if s == "b":
+      return "a"
+  else:
+    print(f"SemigroupElement {sge} with State {s}")
+    raise Exception("Operation not defined")
+
+res = semigroup_to_machine((states, semigroup, action))
+plot(res, "test")
+```
+
 
 ## Automate format
 To sepcify an automate via csv use the following format

src/automate.py

@@ -1,15 +1,18 @@
 import pandas as pd
 from graphviz import Digraph
 from itertools import product
-from typing import Dict, Tuple, List
+from typing import Callable, Dict, Tuple, List
 from tabulate import tabulate
 
 State = str
 Letter = str
+SemigroupElement = str
 StateMachine = Dict[Tuple[State, Letter], State]
 
 EqvTable = pd.DataFrame
 Semigroup = pd.DataFrame
+Action = Callable[[State, SemigroupElement], State]
+TransformationSemigroup = (List[State], Semigroup, Action)
 
 
 def get_states(transitions):
@@ -154,9 +157,51 @@ def format_semitable(s: Semigroup):
   s.columns = [f"[{col}]" for col in s.columns]
   return tabulate(s, headers="keys", tablefmt="grid")
 
-#res2 = create_table(l1, ['a','b','c'], N = 5)
-#u, class_, _ = add_representatives(l1, res2)
-#
-##print(u)
-##
-#r = eqv_class_to_semigroup(l1,['a','b','c'], u)
+
+
+def compatability(states: List[State], sg: Semigroup, a: Action, filter_sames = True):
+  pass
+
+def faithfullness(states: List[State], sg: Semigroup, a: Action, filter_sames = True):
+  # TODO Think about this some more
+  action_results = []
+  for s in states:
+    for g1 in sg.index:
+      for g2 in sg.index:
+        if g1 != g2:
+          #q*g1
+          res1 = a(s, g1)
+          #q*g2
+          res2 = a(s, g2)
+          action_results.append([s, g1, res1 == res2, s, g2])
+
+  action_results = pd.DataFrame(action_results)
+  action_results.columns = ['q', 'g1', 'is_same', 'q', 'q2']
+  return action_results[action_results['is_same'] == True]
+
+
+
+
+def execute_semigroup(states: List[State], sg: Semigroup, a: Action, filter_sames = True):
+  # TODO Think about this some more
+  action_results = []
+  for s in states:
+    for g1 in sg.index:
+        res = a(s, g1)
+        action_results.append([s, g1, res])
+
+  action_results = pd.DataFrame(action_results)
+  action_results.columns = ['q', 'g1', 'action_result']
+  return action_results
+
+
+
+def semigroup_to_machine(tsg: TransformationSemigroup):
+  action_table = execute_semigroup(tsg[0], tsg[1], tsg[2])
+  transformations = {}
+
+  for _, q1, l, q2 in action_table.itertuples():
+    transformations[(q1, str(l))] = q2
+  
+  return transformations
+

tests/test.py

@@ -1,5 +1,6 @@
 import unittest
 from src.automate import *
+from typing import Optional
 
 import unittest
 
@@ -62,3 +63,34 @@ def test_two_state_machine_representative(self):
     r = create_table(TestAutomatonToState.one_state_two_trans, ['a', "b"], N = 3)
     _, t, _ = add_representatives(TestAutomatonToState.one_state_two_trans, r)
     self.assertEqual(list(t["eqv_class"]), ["a", "a", "b", "b", "ba", "ba"])
+
+
+
+class TestSemigroupToAutomaton(unittest.TestCase):
+  def semigroup_to_machine(self):
+    states = ["a", "b"]
+    semigroup = pd.DataFrame( 
+                             {"0":["0", "1"], 
+                              "1": ["1", "0"]}
+                             )
+    semigroup.set_index(["0", "1"])
+    
+    def action(s: State, sge: SemigroupElement) -> Optional[State]:
+      if str(sge) == "0":
+        return s
+      elif str(sge) == "1":
+        if s == "a":
+          return "b"
+        if s == "b":
+          return "a"
+      else:
+        print(f"SemigroupElement {sge} with State {s}")
+        raise Exception("Operation not defined")
+
+    res = semigroup_to_machine((states, semigroup, action))
+    print(res)
+    plot(res, "test")
+
+    
+    
+