added suggested changes

burr/core/application.py

@@ -2208,13 +2208,14 @@ def with_state_persister(
         if on_every != "step":
             raise ValueError(f"on_every {on_every} not supported")
 
-        # Check if 'is_initialized' exists and whether it returns False, indicating the persister is uninitialized
-        if hasattr(persister, 'is_initialized'):
+        # Check if 'is_initialized' exists and is False; raise RuntimeError, else continue if not implemented
+        try:
             if not persister.is_initialized():
                 raise RuntimeError(
                     "RuntimeError: Uninitialized persister. Make sure to call .initialize() before passing it to the ApplicationBuilder"
                 )
-        # If the persister is valid and initialized, add it to lifecycle adapters
+        except NotImplementedError:
+             pass
         if not isinstance(persister, persistence.BaseStateSaver):
             self.lifecycle_adapters.append(persister)
         else:

tests/core/test_application.py

@@ -41,7 +41,7 @@
     _validate_start,
 )
 from burr.core.graph import Graph, GraphBuilder, Transition
-from burr.core.persistence import BaseStatePersister, DevNullPersister, PersistedStateData
+from burr.core.persistence import BaseStatePersister, DevNullPersister, PersistedStateData, SQLLitePersister
 from burr.core.typing import TypingSystem
 from burr.lifecycle import (
     PostRunStepHook,
@@ -3230,3 +3230,15 @@ def test_builder_captures_typing_system():
     _, _, state = app.run(halt_after=["result"])
     assert isinstance(state.data, CounterState)
     assert state.data["count"] == 10
+
+# Define a mock persister that does not implement is_initialized
+class PersisterWithoutIsInitialized:
+    def initialize(self):
+        pass
+
+def test_with_state_persister_no_is_initialized_method():
+    builder = ApplicationBuilder()
+    persister = PersisterWithoutIsInitialized()
+
+    # Add the persister to the builder, expecting no exceptions
+    builder.with_state_persister(persister)  # No exception should be raised