feat: Completed the task6

project/task6.py

@@ -0,0 +1,78 @@
+# project/task6.py
+from collections import defaultdict
+from pyformlang.cfg import CFG, Variable, Terminal, Production, Epsilon
+import networkx as nx
+
+
+__all__ = ["cfg_to_weak_normal_form", "hellings_based_cfpq"]
+
+
+def cfg_to_weak_normal_form(cfg: CFG) -> CFG:
+    nullable = cfg.get_nullable_symbols()
+    eps_rules = {Production(v, [Epsilon()]) for v in nullable}
+    cfg_nf = cfg.to_normal_form()
+    cfg_nf = CFG(
+        variables=cfg_nf.variables,
+        terminals=cfg_nf.terminals,
+        start_symbol=cfg_nf.start_symbol,
+        productions=cfg_nf.productions | eps_rules,
+    )
+    return cfg_nf.remove_useless_symbols()
+
+
+def _init_edges(cfg: CFG, graph: nx.MultiDiGraph | nx.DiGraph):
+    term_map = defaultdict(set)
+    for p in cfg.productions:
+        if len(p.body) == 1 and isinstance(p.body[0], Terminal):
+            term_map[p.body[0].value].add(p.head)
+
+    edges = set()
+    for u, v, label in graph.edges(data="label"):
+        for A in term_map.get(label, ()):
+            edges.add((u, A, v))
+
+    for v in graph.nodes:
+        for A in cfg.get_nullable_symbols():
+            edges.add((v, A, v))
+    return edges
+
+
+def _closure(cfg: CFG, edges: set[tuple[int, Variable, int]]):
+    bin_rules = [p for p in cfg.productions if len(p.body) == 2]
+    added = True
+    while added:
+        added = False
+        new_edges = set()
+        for u1, B, v1 in edges:
+            for u2, C, v2 in edges:
+                if v1 == u2:
+                    for p in bin_rules:
+                        if p.body[0] == B and p.body[1] == C:
+                            e = (u1, p.head, v2)
+                            if e not in edges:
+                                new_edges.add(e)
+        if new_edges:
+            edges |= new_edges
+            added = True
+    return edges
+
+
+def hellings_based_cfpq(
+    cfg: CFG,
+    graph: nx.MultiDiGraph | nx.DiGraph,
+    start_nodes: set[int] | None = None,
+    final_nodes: set[int] | None = None,
+) -> set[tuple[int, int]]:
+    cfg = cfg_to_weak_normal_form(cfg)
+    edges = _init_edges(cfg, graph)
+    edges = _closure(cfg, edges)
+
+    start_nodes = start_nodes or set(graph.nodes)
+    final_nodes = final_nodes or set(graph.nodes)
+    start = cfg.start_symbol
+
+    result = set()
+    for u, A, v in edges:
+        if A == start and u in start_nodes and v in final_nodes:
+            result.add((u, v))
+    return result