diff --git a/aalpy/oracles/kWayStateCoverageEqOracle.py b/aalpy/oracles/kWayStateCoverageEqOracle.py
index e66f404c..d259e53b 100644
--- a/aalpy/oracles/kWayStateCoverageEqOracle.py
+++ b/aalpy/oracles/kWayStateCoverageEqOracle.py
@@ -10,7 +10,7 @@ class KWayStateCoverageEqOracle(Oracle):
     random walk at the end.
     """
 
-    def __init__(self, alphabet: list, sul: SUL, k=2, random_walk_len=20, method='combinations'):
+    def __init__(self, alphabet: list, sul: SUL, k=2, random_walk_len=20, method='permutations'):
         """
 
         Args:
@@ -61,10 +61,23 @@ def find_cex(self, hypothesis):
 
             index = 0
             path = comb[0].prefix
+
+            # in case of non-strongly connected automata test case might not be possible as a path between 2 states
+            # might not exist
+            possible_test_case = True
             while index < len(comb) - 1:
-                path += hypothesis.get_shortest_path(comb[index], comb[index + 1])
+                path_between_states = hypothesis.get_shortest_path(comb[index], comb[index + 1])
                 index += 1
 
+                if not path_between_states:
+                    possible_test_case = False
+                    break
+
+                path += path_between_states
+
+            if possible_test_case is None:
+                continue
+
             path += tuple(choices(self.alphabet, k=self.random_walk_len))
 
             self.reset_hyp_and_sul(hypothesis)