Merge pull request #33 from nielstron/feat/prefix_cfg

Add a prefix language generation

Author: Aunsiels

pyformlang/cfg/cfg.py

@@ -1106,3 +1106,54 @@ def is_normal_form(self):
         """
         return all(
             production.is_normal_form() for production in self._productions)
+
+    def get_prefix_language(self):
+        """
+        Generates the prefix language of the CFL, i.e., the language of all prefixes of valid words
+        Based on https://cs.uwaterloo.ca/~s4bendav/files/CS360S21Lec10.pdf
+        """
+        if self.is_empty():
+            return CFG()
+        cfg = self
+        if not self.is_normal_form():
+            cfg = cfg.to_normal_form()
+        cfg = cfg.remove_useless_symbols()
+        def to_zero(var: Variable):
+            return Variable((var.value, 0))
+        new_variables = list(cfg.variables) + [to_zero(var) for var in cfg.variables]
+        new_productions = list(cfg.productions)
+        for p in cfg.productions:
+            if len(p.body) == 1:
+                # the production is of the form X -> c
+                new_productions.append(Production(
+                    to_zero(p.head),
+                    p.body
+                ))
+                new_productions.append(Production(
+                    to_zero(p.head),
+                    [Epsilon()]
+                ))
+            else:
+                # the production is of the form X -> Y Z
+                new_productions.append(Production(
+                    to_zero(p.head),
+                    [p.body[0], to_zero(p.body[1])]
+                ))
+                new_productions.append(Production(
+                    to_zero(p.head),
+                    [to_zero(p.body[0])]
+                ))
+        new_productions.append(Production(cfg.start_symbol, [Epsilon()]))
+        new_productions.append(Production(to_zero(cfg.start_symbol), [Epsilon()]))
+        return CFG(
+            variables=set(new_variables),
+            terminals=set(cfg.terminals) | {Epsilon()},
+            productions=new_productions,
+            start_symbol=to_zero(cfg.start_symbol),
+        )
+
+    def get_suffix_language(self):
+        """
+        Generates the suffix language of the CFL, i.e., the language containing all suffixes of valid words
+        """
+        return self.reverse().get_prefix_language().reverse()

pyformlang/cfg/tests/test_cfg.py

@@ -858,6 +858,60 @@ def test_to_text_epsilon(self):
         cfg = CFG.from_text("S -> a S b | a b epsilon")
         assert cfg.contains(["a", "b"])
 
+    def test_prefix_lang(self):
+        cfg = CFG.from_text("S -> a S b | a b | c")
+        prefix_cfg = cfg.get_prefix_language()
+        assert prefix_cfg.contains("")
+        for word in [
+            "ab",
+            "aabb",
+        ]:
+            assert cfg.contains(word)
+            assert prefix_cfg.contains(word)
+        for prefix in [
+            "aaa",
+            "aaac",
+            "aaacb"
+        ]:
+            assert not cfg.contains(prefix)
+            assert prefix_cfg.contains(prefix)
+        for invalid in [
+            "abb",
+            "aba",
+            "aaaba",
+            "bbb",
+        ]:
+            assert not cfg.contains(invalid)
+            assert not prefix_cfg.contains(invalid)
+
+    def test_suffix_lang(self):
+        cfg = CFG.from_text("S -> a S b | a b | c")
+        suffix_cfg = cfg.get_suffix_language()
+        assert suffix_cfg.contains("")
+        for word in [
+            "ab",
+            "aabb",
+        ]:
+            assert cfg.contains(word)
+            assert suffix_cfg.contains(word)
+        for suffix in [
+            "bbb",
+            "cbbb",
+            "acbbb"
+        ]:
+            assert not cfg.contains(suffix)
+            assert suffix_cfg.contains(suffix)
+        for invalid in [
+            "aab",
+            "aba",
+            "aaaba",
+            "abbbba",
+            "bbbbab",
+            "aaa",
+        ]:
+            assert not cfg.contains(invalid)
+            assert not suffix_cfg.contains(invalid)
+
 
 def get_example_text_duplicate():
     """ Duplicate text """