diff --git a/lcn/generator.py b/lcn/generator.py
index b050a1a..33dd887 100644
--- a/lcn/generator.py
+++ b/lcn/generator.py
@@ -194,7 +194,7 @@ def make_lcn_random2(
     count = 0
     while count < c:
         child = ordering[np.random.randint(n - p)]
-        if cpts[child] is True:
+        if cpts[child]:
             continue
         cpts[child] = True
         num_higher_vars = n - position[child] - 1
@@ -218,7 +218,7 @@ def make_lcn_random2(
     
     # Add the roots
     for i in range(n):
-        if cpts[i] is False:
+        if not cpts[i]:
             scopes[i] = [i]
     
     # Create extra knowledge: l <= P(x) <= u
@@ -341,7 +341,7 @@ def make_lcn_dag(
     count = 0
     while count < c:
         child = ordering[np.random.randint(n - p)]
-        if cpts[child] is True:
+        if cpts[child]:
             continue
         cpts[child] = True
         num_higher_vars = n - position[child] - 1
@@ -367,7 +367,7 @@ def make_lcn_dag(
     
     # Add the roots
     for i in range(n):
-        if cpts[i] is False:
+        if not cpts[i]:
             scopes[i] = [i]
     
     # Create extra knowledge: l <= P(x) <= u
@@ -489,7 +489,7 @@ def make_lcn_polytree(
             u = ordering[i]
             v = ordering[j]
             edge = (u, v)# if np.random.uniform() <= 0.5 else (v, u)
-            if G.has_edge(edge[0], edge[1]) is False:
+            if not G.has_edge(edge[0], edge[1]):
                 UG = nx.to_undirected(G)
                 paths = list(nx.all_simple_paths(UG, u, v))
                 assert(len(paths) == 1)
diff --git a/lcn/model.py b/lcn/model.py
index 652111a..e9caa61 100644
--- a/lcn/model.py
+++ b/lcn/model.py
@@ -51,8 +51,13 @@ def __init__(
         self.label = label # unique identifier of the formula (is the atom if atomic)
         self.input_formula = formula # store the formula
         output, atoms = parse_formula(formula) # parse the formula
-        if output is None or vars is None:
+        if output is None or atoms is None:
             raise ValueError(f"Malformed formula: {formula}")
+
+        # Reject empty / whitespace-only formulas that parse as valid but have no content
+        stripped = formula.strip()
+        if not stripped:
+            raise ValueError(f"Empty formula: {formula!r}")
         
         self.parsed_formula = output # parse tree of the formula
         self.atoms = atoms # a dict indexed by 'Vi' where i is the i-th variable
@@ -892,7 +897,11 @@ def parse_sentence(line: str):
             tau = False
             if ";" in line:
                 pos = line.find(";")
-                tau = bool(line[pos+1:].strip())
+                tau_str = line[pos+1:].strip()
+                # Parse "tau=true" or "tau=false" correctly — bool() of any
+                # non-empty string (including "False") returns True, so we
+                # must split on "=" to get the actual boolean value.
+                tau = tau_str.split("=")[1].lower() == 'true'
                 line = line[:pos]
 
             # Get the lower and upper bounds