diff --git a/src/utility/shortestPaths.cpp b/src/utility/shortestPaths.cpp
index 9ff97b4..f0817ca 100644
--- a/src/utility/shortestPaths.cpp
+++ b/src/utility/shortestPaths.cpp
@@ -59,7 +59,8 @@ void define_ksp(py::module& m) {
         .def(py::init<Matrix const&, std::vector<double> const&, BitVector const&, MatrixFormat>(), "transition_matrix"_a, "target_prob_vector"_a, "initial_states"_a, "matrix_format"_a)
         .def(py::init<Matrix const&, StateProbMap const&, BitVector const&, MatrixFormat>(), "transition_matrix"_a, "target_prob_map"_a, "initial_states"_a, "matrix_format"_a)
 
-        // ShortestPathsGenerator(Matrix const& transitionMatrix, std::vector<T> const& targetProbVector, BitVector const& initialStates, MatrixFormat matrixFormat);
-        // ShortestPathsGenerator(Matrix const& maybeTransitionMatrix, StateProbMap const& targetProbMap, BitVector const& initialStates, MatrixFormat matrixFormat);
+        .def("get_distance", &ShortestPathsGenerator::getDistance, "k"_a)
+        .def("get_states", &ShortestPathsGenerator::getStates, "k"_a)
+        .def("get_path_as_list", &ShortestPathsGenerator::getPathAsList, "k"_a)
     ;
 }
\ No newline at end of file
diff --git a/tests/utility/test_shortestpaths.py b/tests/utility/test_shortestpaths.py
index 70451fd..45f4d96 100644
--- a/tests/utility/test_shortestpaths.py
+++ b/tests/utility/test_shortestpaths.py
@@ -6,13 +6,67 @@ from stormpy.utility import MatrixFormat
 from helpers.helper import get_example_path
 
 import pytest
+import math
+
+
+# this is admittedly slightly overengineered
+
+class ModelWithKnownShortestPaths:
+    """Knuth's die model with reference kSP methods"""
+    def __init__(self):
+        self.target_label = "one"
+
+        program_path = get_example_path("dtmc", "die.pm")
+        raw_formula = "P=? [ F \"" + self.target_label + "\" ]"
+        program = stormpy.parse_prism_program(program_path)
+        formulas = stormpy.parse_formulas_for_prism_program(raw_formula, program)
+
+        self.model = stormpy.build_model(program, formulas[0])
+
+    def probability(self, k):
+        return (1/2)**((2 * k) + 1)
+
+    def state_set(self, k):
+        return BitVector(self.model.nr_states, [0, 1, 3, 7])
+
+    def path(self, k):
+        path = [0] + k * [1, 3] + [7]
+        return list(reversed(path))  # SPG returns traversal from back
+
+
+@pytest.fixture(scope="module", params=[1, 2, 3, 3000, 42])
+def index(request):
+    return request.param
+
+
+@pytest.fixture(scope="module")
+def model_with_known_shortest_paths():
+    return ModelWithKnownShortestPaths()
+
+
+@pytest.fixture(scope="module")
+def model(model_with_known_shortest_paths):
+    return model_with_known_shortest_paths.model
+
+
+@pytest.fixture(scope="module")
+def expected_distance(model_with_known_shortest_paths):
+    return model_with_known_shortest_paths.probability
 
 
 @pytest.fixture(scope="module")
-def model(program_path=get_example_path("dtmc", "die.pm"), raw_formula="P=? [ F \"one\" ]"):
-    program = stormpy.parse_prism_program(program_path)
-    formulas = stormpy.parse_formulas_for_prism_program(raw_formula, program)
-    return stormpy.build_model(program, formulas[0])
+def expected_state_set(model_with_known_shortest_paths):
+    return model_with_known_shortest_paths.state_set
+
+
+@pytest.fixture(scope="module")
+def expected_path(model_with_known_shortest_paths):
+    return model_with_known_shortest_paths.path
+
+
+@pytest.fixture(scope="module")
+def target_label(model_with_known_shortest_paths):
+    return model_with_known_shortest_paths.target_label
 
 
 @pytest.fixture
@@ -34,13 +88,6 @@ def state_bitvector(model, state_list):
     return BitVector(length=model.nr_states, set_entries=state_list)
 
 
-@pytest.fixture
-def label(model):
-    some_label = "one"
-    assert some_label in model.labels, "test model does not contain label '" + some_label + "'"
-    return some_label
-
-
 @pytest.fixture
 def transition_matrix(model):
     return model.transition_matrix
@@ -76,8 +123,8 @@ class TestShortestPaths:
     def test_spg_ctor_state_list_target(self, model, state_list):
         _ = ShortestPathsGenerator(model, state_list)
 
-    def test_spg_ctor_label_target(self, model, label):
-        _ = ShortestPathsGenerator(model, label)
+    def test_spg_ctor_label_target(self, model, target_label):
+        _ = ShortestPathsGenerator(model, target_label)
 
     def test_spg_ctor_matrix_vector(self, transition_matrix, target_prob_list, initial_states, matrix_format):
         _ = ShortestPathsGenerator(transition_matrix, target_prob_list, initial_states, matrix_format)
@@ -85,4 +132,14 @@ class TestShortestPaths:
     def test_spg_ctor_matrix_map(self, transition_matrix, target_prob_map, initial_states, matrix_format):
         _ = ShortestPathsGenerator(transition_matrix, target_prob_map, initial_states, matrix_format)
 
-    # TODO: add tests that check actual functionality
+    def test_spg_distance(self, model, target_label, index, expected_distance):
+        spg = ShortestPathsGenerator(model, target_label)
+        assert math.isclose(spg.get_distance(index), expected_distance(index))
+
+    def test_spg_state_set(self, model, target_label, index, expected_state_set):
+        spg = ShortestPathsGenerator(model, target_label)
+        assert spg.get_states(index) == expected_state_set(index)
+
+    def test_spg_state_list(self, model, target_label, index, expected_path):
+        spg = ShortestPathsGenerator(model, target_label)
+        assert spg.get_path_as_list(index) == expected_path(index)