diff --git a/frontends/concrete-python/examples/levenshtein_distance/levenshtein_distance.py b/frontends/concrete-python/examples/levenshtein_distance/levenshtein_distance.py
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+++ b/frontends/concrete-python/examples/levenshtein_distance/levenshtein_distance.py
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+# Computing Levenstein distance between strings, https://en.wikipedia.org/wiki/Levenshtein_distance
+
+from concrete import fhe
+from functools import lru_cache
+import numpy
+import time
+
+# Parameters to be set by the user
+max_string_length = 6
+
+# Module FHE
+@fhe.module()
+class MyModule:
+    @fhe.function({"x": "encrypted", "y": "encrypted"})
+    def compare(x, y):
+        return x == y
+
+    @fhe.function(
+        {
+            "is_equal": "encrypted",
+            "if_equal": "encrypted",
+            "case_1": "encrypted",
+            "case_2": "encrypted",
+            "case_3": "encrypted",
+        }
+    )
+    def mix(is_equal, if_equal, case_1, case_2, case_3):
+        min_12 = numpy.minimum(case_1, case_2)
+        min_123 = numpy.minimum(min_12, case_3)
+
+        # FIXME: it should be faster with that, but semantic breaks more often
+        # return fhe.if_then_else(is_equal, if_equal, 1 + min_123)
+
+        return is_equal * if_equal + (1 - is_equal) * (1 + min_123)
+
+
+# For now, we pick only small letters
+def random_letter_as_int():
+    return 97 + numpy.random.randint(26)
+
+
+def random_letter():
+    return chr(random_letter_as_int())
+
+
+def random_string(l):
+    return "".join([random_letter() for _ in range(l)])
+
+
+def map_string_to_int(s):
+    return tuple(ord(si) for si in s)
+
+
+# Compilation
+inputset_compare = [(random_letter_as_int(), random_letter_as_int()) for _ in range(1000)]
+inputset_mix = [
+    (
+        numpy.random.randint(2),
+        numpy.random.randint(max_string_length),
+        numpy.random.randint(max_string_length),
+        numpy.random.randint(max_string_length),
+        numpy.random.randint(max_string_length),
+    )
+    for _ in range(100)
+]
+
+my_module = MyModule.compile(
+    {"compare": inputset_compare, "mix": inputset_mix},
+    show_mlir=True,
+    p_error=10**-20,
+    show_optimizer=True,
+)
+
+# Function in clear, for reference and comparison
+@lru_cache
+def levenshtein_clear(x, y):
+    if len(x) == 0:
+        return len(y)
+    if len(y) == 0:
+        return len(x)
+
+    if x[0] == y[0]:
+        return levenshtein_clear(x[1:], y[1:])
+
+    case_1 = levenshtein_clear(x[1:], y)
+    case_2 = levenshtein_clear(x, y[1:])
+    case_3 = levenshtein_clear(x[1:], y[1:])
+
+    return 1 + min(case_1, case_2, case_3)
+
+
+# Function in FHE-simulate, to debug
+@lru_cache
+def levenshtein_simulate(x, y):
+    if len(x) == 0:
+        return len(y)
+    if len(y) == 0:
+        return len(x)
+
+    if_equal = levenshtein_simulate(x[1:], y[1:])
+    case_1 = levenshtein_simulate(x[1:], y)
+    case_2 = levenshtein_simulate(x, y[1:])
+    case_3 = if_equal
+
+    is_equal = my_module.compare(x[0], y[0])
+    returned_value = my_module.mix(is_equal, if_equal, case_1, case_2, case_3)
+
+    return returned_value
+
+
+# Function in FHE
+@lru_cache
+def levenshtein_fhe(x, y):
+    if len(x) == 0:
+        # In clear, that's return len(y)
+        return my_module.compare.encrypt(len(y), None)[0]
+    if len(y) == 0:
+        # In clear, that's return len(x)
+        return my_module.compare.encrypt(len(x), None)[0]
+
+    if_equal = levenshtein_fhe(x[1:], y[1:])
+    case_1 = levenshtein_fhe(x[1:], y)
+    case_2 = levenshtein_fhe(x, y[1:])
+    case_3 = if_equal
+
+    # In FHE
+    is_equal = my_module.compare.run(x[0], y[0])
+    returned_value = my_module.mix.run(is_equal, if_equal, case_1, case_2, case_3)
+
+    return returned_value
+
+
+# Random patterns of different lengths
+list_patterns = [
+    ("", ""),
+    ("", "a"),
+    ("b", ""),
+    ("a", "a"),
+    ("a", "b"),
+]
+
+for length_1 in range(max_string_length + 1):
+    for length_2 in range(max_string_length + 1):
+        list_patterns += [
+            (
+                random_string(length_1),
+                random_string(length_2),
+            )
+            for _ in range(1)
+        ]
+
+# Checks in simulation
+print("Computations in simulation\n")
+
+for a, b in list_patterns:
+
+    print(f"    Computing Levenshtein between strings '{a}' and '{b}'", end="")
+
+    assert len(a) <= max_string_length
+    assert len(b) <= max_string_length
+
+    a_as_int = map_string_to_int(a)
+    b_as_int = map_string_to_int(b)
+
+    l1_simulate = levenshtein_simulate(a_as_int, b_as_int)
+    l1_clear = levenshtein_clear(a_as_int, b_as_int)
+
+    assert l1_simulate == l1_clear, f"    {l1_simulate=} and {l1_clear=} are different"
+    print(" - OK")
+
+# Key generation: FIXME, to be done calling a keygen function, see https://github.com/zama-ai/concrete-internal/issues/751
+my_module.compare.encrypt(None, None)
+
+# Checks in FHE
+print("\nComputations in FHE\n")
+
+for a, b in list_patterns:
+
+    print(f"    Computing Levenshtein between strings '{a}' and '{b}'", end="")
+
+    assert len(a) <= max_string_length
+    assert len(b) <= max_string_length
+
+    a_as_int = map_string_to_int(a)
+    b_as_int = map_string_to_int(b)
+
+    a_enc = tuple(my_module.compare.encrypt(ai, None)[0] for ai in a_as_int)
+    b_enc = tuple(my_module.compare.encrypt(None, bi)[1] for bi in b_as_int)
+
+    time_begin = time.time()
+    l1_fhe_enc = levenshtein_fhe(a_enc, b_enc)
+    time_end = time.time()
+
+    l1_fhe = my_module.mix.decrypt(l1_fhe_enc)
+
+    l1_clear = levenshtein_clear(a, b)
+
+    assert l1_fhe == l1_clear, f"    {l1_fhe=} and {l1_clear=} are different"
+    print(f" - OK in {time_end - time_begin:.2f} seconds")