diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index c8a7aa7..244d398 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -34,6 +34,9 @@ jobs:
           - python: "3.10"
             toxenv: py310
             os: ubuntu-latest
+          - python: "3.11"
+            toxenv: py311
+            os: ubuntu-latest
           - python: pypy-3.7
             toxenv: pypy37
             os: ubuntu-latest
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0d7b36b..33a8949 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,7 +6,10 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 
 ## Unreleased
 ### Changed
- - Updated dependency on automata-lib to version 6.0.2
+ - Updated dependency on automata-lib to version 7.0.1
+
+### Added
+ - Now testing on Python 3.11
 
 ## 2.2.0 - 2021-10-21
 ### Added
diff --git a/permuta/permutils/pin_words.py b/permuta/permutils/pin_words.py
index cb2192b..8db99b9 100644
--- a/permuta/permutils/pin_words.py
+++ b/permuta/permutils/pin_words.py
@@ -263,13 +263,12 @@ def pinword_contains(cls, word: str, u_word: str):
     @classmethod
     def make_nfa_for_pinword(cls, u_word: str) -> "NFA":
         """NFA for pinword"""
-        prefix = ""
 
         def new_state(states) -> None:
-            states.add(prefix + str(len(states)))
+            states.add(len(states))
 
-        def last_state(states) -> str:
-            return prefix + str(len(states) - 1)
+        def last_state(states) -> int:
+            return len(states) - 1
 
         def add_a_star(states, transitions) -> None:
             new_state(states)
@@ -308,19 +307,19 @@ def add_sp(u_i, states, transitions) -> None:
                     position = nxt
 
         decomp = [cls.sp_to_m(x) for x in cls.factor_pinword(u_word)]
-        input_symbols = set(DIRS)
-        initial_state = "0"
-        states: Set[str] = set()
-        transitions: DefaultDict[str, dict] = defaultdict(dict)
+        input_symbols = frozenset(DIRS)
+        initial_state = 0
+        states: Set[int] = set()
+        transitions: DefaultDict[int, dict] = defaultdict(dict)
 
         add_a_star(states, transitions)
         for u_i in decomp:
             add_sp(u_i, states, transitions)
 
-        final_states = {last_state(states)}
+        final_states = frozenset({last_state(states)})
 
         return NFA(
-            states=states,
+            states=frozenset(states),
             input_symbols=input_symbols,
             transitions=transitions,
             initial_state=initial_state,
@@ -328,88 +327,57 @@ def add_sp(u_i, states, transitions) -> None:
         )
 
     @staticmethod
-    def dfa_name_reset(dfa_in: "DFA", minimize=True) -> "DFA":
-        """DFA name reset."""
-        if minimize:
-            return dfa_in.minify()
-        m_dict: Dict[str, str] = {}
-        for state in dfa_in.states:
-            m_dict[state] = str(len(m_dict))
-
-        return DFA(
-            states={m_dict[x] for x in dfa_in.states},
-            input_symbols=dfa_in.input_symbols,
-            transitions={
-                m_dict[x]: {k: m_dict[v] for k, v in dfa_in.transitions[x].items()}
-                for x in dfa_in.transitions
-            },
-            initial_state=m_dict[dfa_in.initial_state],
-            final_states={m_dict[x] for x in dfa_in.final_states},
-        )
-
-    @staticmethod
+    @lru_cache(maxsize=None)
     def make_dfa_for_m() -> "DFA":
         """Returns DFA for M."""
         return DFA(
-            states={"0", "1", "2", "3"},
-            input_symbols=set(DIRS),
+            states=frozenset({0, 1, 2, 3}),
+            input_symbols=frozenset(DIRS),
             transitions={
-                "0": {"U": "1", "D": "1", "L": "2", "R": "2"},
-                "1": {"U": "3", "D": "3", "L": "2", "R": "2"},
-                "2": {"U": "1", "D": "1", "L": "3", "R": "3"},
-                "3": {"U": "3", "D": "3", "L": "3", "R": "3"},
+                0: {"U": 1, "D": 1, "L": 2, "R": 2},
+                1: {"U": 3, "D": 3, "L": 2, "R": 2},
+                2: {"U": 1, "D": 1, "L": 3, "R": 3},
+                3: {"U": 3, "D": 3, "L": 3, "R": 3},
             },
-            initial_state="0",
-            final_states={"0", "1", "2"},
+            initial_state=0,
+            final_states=frozenset({0, 1, 2}),
         )
 
     @classmethod
     def make_dfa_for_pinword(cls, word: str) -> "DFA":
         """Returns DFA for pinword."""
-        return cls.dfa_name_reset(DFA.from_nfa(cls.make_nfa_for_pinword(word)))
+        return DFA.from_nfa(cls.make_nfa_for_pinword(word))
 
     @classmethod
     def make_dfa_for_perm(cls, perm: "Perm") -> "DFA":
         """Returns DFA for Perm."""
         pinwords = cls.pinwords_for_basis((perm,))
-        out_dfa: "DFA" = None
+        out_dfa: "DFA" = DFA.empty_language(frozenset(DIRS))
         sorted_pinwords = sorted(pinwords)
         for word in sorted_pinwords:
-            if out_dfa is None:
-                out_dfa = cls.make_dfa_for_pinword(word)
-            else:
-                out_dfa2 = cls.make_dfa_for_pinword(word)
-                for_union = out_dfa.union(out_dfa2)
-                out_dfa = cls.dfa_name_reset(for_union)
+            out_dfa2 = cls.make_dfa_for_pinword(word)
+            out_dfa = out_dfa.union(out_dfa2)
         return out_dfa
 
     @classmethod
     def make_dfa_for_basis_from_pinwords(cls, basis: List["Perm"]) -> "DFA":
         """Returns DFA for basis from list of pinwords"""
         pinwords = cls.pinwords_for_basis(basis)
-        out_dfa: "DFA" = None
+        out_dfa: "DFA" = DFA.empty_language(frozenset(DIRS))
         sorted_pinwords = sorted(pinwords)
         for word in sorted_pinwords:
-            if out_dfa is None:
-                out_dfa = cls.make_dfa_for_pinword(word)
-            else:
-                out_dfa2 = cls.make_dfa_for_pinword(word)
-                out_dfa = out_dfa.union(out_dfa2)
-                # out_dfa = cls.dfa_name_reset(for_union)
+            out_dfa2 = cls.make_dfa_for_pinword(word)
+            out_dfa = out_dfa.union(out_dfa2)
         return out_dfa
 
     @classmethod
     def make_dfa_for_basis_from_db(cls, basis: List["Perm"]) -> "DFA":
         """Returns DFA for basis from db."""
-        out_dfa: "DFA" = None
+        out_dfa: "DFA" = DFA.empty_language(frozenset(DIRS))
         sorted_basis = sorted(basis)
-        for word in sorted_basis:
-            if out_dfa is None:
-                out_dfa = cls.load_dfa_for_perm(word)
-            else:
-                out_dfa2 = cls.load_dfa_for_perm(word)
-                for_union = out_dfa.union(out_dfa2)
-                out_dfa = cls.dfa_name_reset(for_union)
+        for perm in sorted_basis:
+            out_dfa2 = cls.load_dfa_for_perm(perm)
+            out_dfa = out_dfa.union(out_dfa2)
         return out_dfa
 
     @classmethod
@@ -495,8 +463,7 @@ def has_finite_pinperms(cls, basis, use_db=False, dfa: "DFA" = None) -> bool:
         """Check if basis has finite pinperms"""
         if dfa is None:
             dfa = cls.make_dfa_for_basis(basis, use_db)
-        dfa = dfa.complement()
-        dfa = cls.dfa_name_reset(cls.make_dfa_for_m() & dfa)
+        dfa = cls.make_dfa_for_m().difference(dfa)
         return dfa.isfinite() is True
 
     @classmethod
@@ -521,15 +488,10 @@ def store_dfa_for_perm(cls, perm, in_dfa=None) -> None:
         if in_dfa is None:
             in_dfa = cls.make_dfa_for_perm(perm)
         with open(str(path), "w") as file_object:
-            file_object.write(
-                f"DFA(states={in_dfa.states}, "
-                + f"input_symbols={in_dfa.input_symbols}, "
-                + f"transitions={dict(in_dfa.transitions)}, "
-                + f"initial_state='{in_dfa.initial_state}', "
-                + f"final_states={in_dfa.final_states})\n"
-            )
+            file_object.write(repr(in_dfa))
 
     @classmethod
+    @lru_cache(maxsize=None)
     def load_dfa_for_perm(cls, perm) -> "DFA":
         """Loads the DFA for the specified Perm from file."""
         directory = f"dfa_db/S{len(perm)}/"
diff --git a/setup.py b/setup.py
index 1cb14fb..66337ef 100755
--- a/setup.py
+++ b/setup.py
@@ -51,6 +51,6 @@ def get_version(rel_path):
         "Topic :: Education",
         "Topic :: Scientific/Engineering :: Mathematics",
     ],
-    install_requires=["automata-lib==6.0.2"],
+    install_requires=["automata-lib==7.0.1"],
     entry_points={"console_scripts": ["permtools=permuta.cli:main"]},
 )
diff --git a/tests/permutils/test_pinwords.py b/tests/permutils/test_pinwords.py
index 4145770..3e6ec04 100644
--- a/tests/permutils/test_pinwords.py
+++ b/tests/permutils/test_pinwords.py
@@ -3277,859 +3277,6 @@ def test_make_dfa_for_pinword():
     )
 
 
-def test_dfa_name_reset():
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("1UR2")) == DFA(
-        states={
-            "{0,1}",
-            "{0,4,5}",
-            "{{0,2,4},{0,4}}",
-            "{0,2}",
-            "{0,1,3}",
-            "{{0,1,3,4,6},{0,1,4,6}}",
-            "{0}",
-            "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0,1}", "R": "{0}"},
-            "{0,1}": {"L": "{0}", "D": "{0}", "U": "{0,1}", "R": "{0,2}"},
-            "{0,2}": {"L": "{0}", "D": "{0}", "U": "{0,1,3}", "R": "{0}"},
-            "{0,1,3}": {"L": "{0}", "D": "{0}", "U": "{0,1}", "R": "{{0,2,4},{0,4}}"},
-            "{0,4,5}": {
-                "L": "{0,4,5}",
-                "D": "{{0,2,4},{0,4}}",
-                "U": "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-                "R": "{{0,2,4},{0,4}}",
-            },
-            "{{0,1,3,4,6},{0,1,4,6}}": {
-                "L": "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-                "D": "{{0,2,4},{0,4}}",
-                "U": "{{0,1,3,4,6},{0,1,4,6}}",
-                "R": "{{0,2,4},{0,4}}",
-            },
-            "{{0,2,4},{0,4}}": {
-                "L": "{0,4,5}",
-                "D": "{{0,2,4},{0,4}}",
-                "U": "{{0,1,3,4,6},{0,1,4,6}}",
-                "R": "{{0,2,4},{0,4}}",
-            },
-            "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}": {
-                "L": "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-                "D": "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-                "U": "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-                "R": "{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3,4,6,7},{0,1,4,6,7},{0,2,4,7},{0,4,5,7},{0,4,7}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("3D23")) == DFA(
-        states={
-            "{0,1}",
-            "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}",
-            "{{0,1,3},{0,3}}",
-            "{{0,2,3,4},{0,3,4}}",
-            "{0,1,3,6,8}",
-            "{0,2}",
-            "{0,3,4,6,7}",
-            "{0}",
-            "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-            "{0,3,5}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0,1}", "U": "{0}", "R": "{0}"},
-            "{0,1}": {"L": "{0,2}", "D": "{0,1}", "U": "{0}", "R": "{0}"},
-            "{0,2}": {"L": "{0}", "D": "{{0,1,3},{0,3}}", "U": "{0}", "R": "{0}"},
-            "{0,3,5}": {
-                "L": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3},{0,3}}",
-                "U": "{0,3,5}",
-                "R": "{{0,1,3},{0,3}}",
-            },
-            "{0,3,4,6,7}": {
-                "L": "{0,3,4,6,7}",
-                "D": (
-                    "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},"
-                    "{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-                ),
-                "U": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{0,1,3,6,8}": {
-                "L": (
-                    "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},"
-                    "{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-                ),
-                "D": "{0,1,3,6,8}",
-                "U": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{{0,2,3,4},{0,3,4}}": {
-                "L": "{{0,2,3,4},{0,3,4}}",
-                "D": "{{0,1,3},{0,3}}",
-                "U": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,1,3},{0,3}}",
-            },
-            "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}": {
-                "L": (
-                    "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},"
-                    "{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-                ),
-                "D": (
-                    "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},"
-                    "{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-                ),
-                "U": (
-                    "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},"
-                    "{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-                ),
-                "R": (
-                    "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},"
-                    "{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-                ),
-            },
-            "{{0,3,4,6},{0,3,5,6},{0,3,6}}": {
-                "L": "{0,3,4,6,7}",
-                "D": "{0,1,3,6,8}",
-                "U": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,3,4,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{{0,1,3},{0,3}}": {
-                "L": "{{0,2,3,4},{0,3,4}}",
-                "D": "{{0,1,3},{0,3}}",
-                "U": "{0,3,5}",
-                "R": "{{0,1,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={
-            "{{0,1,3,6,8,9},{0,2,3,4,6,7,9},{0,3,4,6,7,9},{0,3,5,6,9},{0,3,6,9}}"
-        },
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("141R4")) == DFA(
-        states={
-            "{0,1}",
-            "{0,2,3,6,8}",
-            "{0}",
-            "{0,1,3,4,6,7}",
-            "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-            "{{0,1,3},{0,2,3},{0,3}}",
-            "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-            "{0,1,3,4}",
-            "{0,2}",
-            (
-                "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-            ),
-            "{0,1,10,3,4,6,7,9}",
-            "{0,3,5}",
-            "{0,11,3,5,6,9}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0,2}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0}",
-                "U": "{0,2}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{0,1}": {
-                "L": "{0}",
-                "D": "{0}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{0,1}",
-            },
-            "{0,3,5}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{0,3,5}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{0,1,3,4}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{0,1,3,4}",
-            },
-            "{0,1,3,4,6,7}": {
-                "L": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,2,3,6,8}",
-                "R": "{0,1,3,4,6,7}",
-            },
-            "{0,2,3,6,8}": {
-                "L": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "U": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-            },
-            "{0,11,3,5,6,9}": {
-                "L": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-                "D": "{0,11,3,5,6,9}",
-                "U": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-                "R": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                    "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{0,1,10,3,4,6,7,9}": {
-                "L": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-                "D": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                    "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "U": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-                "R": "{0,1,10,3,4,6,7,9}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{0,3,5}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{0,1,3,4}",
-            },
-            "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}": {
-                "L": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "U": "{{0,1,3,4,6},{0,2,3,6},{0,3,5,6},{0,3,6}}",
-                "R": "{0,1,3,4,6,7}",
-            },
-            (
-                "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-            ): {
-                "L": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                    "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "D": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                    "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "U": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                    "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "R": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},"
-                    "{0,12,2,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}": {
-                "L": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-                "D": "{0,11,3,5,6,9}",
-                "U": "{{0,1,3,4,6,7,9},{0,2,3,6,8,9},{0,2,3,6,9},{0,3,6,9}}",
-                "R": "{0,1,10,3,4,6,7,9}",
-            },
-        },
-        initial_state="{0}",
-        final_states={
-            (
-                "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,9},{0,12,2,3,6,8,9},"
-                "{0,12,2,3,6,9},{0,12,3,6,9}}"
-            )
-        },
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("1R")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,1}": {"L": "{0}", "D": "{0}", "U": "{0,2}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("2L")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0,1}", "D": "{0}", "U": "{0}", "R": "{0}"},
-            "{0,1}": {"L": "{0,1}", "D": "{0}", "U": "{0,2}", "R": "{0}"},
-            "{0,2}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{0}",
-                "U": "{0}",
-                "R": "{0}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("4L2")) == DFA(
-        states={
-            "{0,1}",
-            "{0,2}",
-            "{0,3,4}",
-            "{0,3,5}",
-            "{{0,1,3},{0,2,3},{0,3}}",
-            "{0}",
-            "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,1}": {"L": "{0}", "D": "{0,2}", "U": "{0}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{0}",
-                "U": "{0}",
-                "R": "{0,1}",
-            },
-            "{0,3,4}": {
-                "L": "{0,3,4}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{0,3,5}": {
-                "L": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{0,3,5}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{0,3,4}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{0,3,5}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}": {
-                "L": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "U": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-                "R": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6},{0,3,6}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("3R")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0,1}", "D": "{0}", "U": "{0}", "R": "{0}"},
-            "{0,1}": {"L": "{0,1}", "D": "{0,2}", "U": "{0}", "R": "{0}"},
-            "{0,2}": {
-                "L": "{0,1}",
-                "D": "{0}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("41R11")) == DFA(
-        states={
-            "{{0,3,5,6,8},{0,3,6,8}}",
-            "{0,1}",
-            "{0}",
-            "{0,1,3,4,6,7}",
-            "{{0,1,3},{0,2,3},{0,3}}",
-            "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-            "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-            "{0,1,3,4}",
-            "{0,2}",
-            "{{0,11,3,5,6,8,9},{0,11,3,6,8,9}}",
-            (
-                "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},{0,11,12,3,6,8,9},"
-                "{0,12,2,3,6,9},{0,12,3,6,9}}"
-            ),
-            "{0,1,10,3,4,6,7,9}",
-            "{0,3,5}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0,2}", "U": "{0}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0,2}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{0,1}": {
-                "L": "{0}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{0}",
-                "R": "{0,1}",
-            },
-            "{0,1,3,4}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{0,3,5}",
-                "R": "{0,1,3,4}",
-            },
-            "{0,3,5}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-            },
-            "{0,1,3,4,6,7}": {
-                "L": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-                "U": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "R": "{0,1,3,4,6,7}",
-            },
-            "{0,1,10,3,4,6,7,9}": {
-                "L": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "D": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "U": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},"
-                    "{0,11,12,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "R": "{0,1,10,3,4,6,7,9}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{0,1,3,4}",
-            },
-            "{{0,3,5,6,8},{0,3,6,8}}": {
-                "L": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-                "U": "{{0,3,5,6,8},{0,3,6,8}}",
-                "R": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-            },
-            "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}": {
-                "L": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,6},{0,3,6}}",
-                "U": "{{0,3,5,6,8},{0,3,6,8}}",
-                "R": "{0,1,3,4,6,7}",
-            },
-            (
-                "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},{0,11,12,3,6,8,9},"
-                "{0,12,2,3,6,9},{0,12,3,6,9}}"
-            ): {
-                "L": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},"
-                    "{0,11,12,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "D": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},"
-                    "{0,11,12,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "U": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},"
-                    "{0,11,12,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-                "R": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},"
-                    "{0,11,12,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}": {
-                "L": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "D": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "U": "{{0,11,3,5,6,8,9},{0,11,3,6,8,9}}",
-                "R": "{0,1,10,3,4,6,7,9}",
-            },
-            "{{0,11,3,5,6,8,9},{0,11,3,6,8,9}}": {
-                "L": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "D": "{{0,1,3,4,6,7,9},{0,2,3,6,9},{0,3,5,6,8,9},{0,3,6,9}}",
-                "U": "{{0,11,3,5,6,8,9},{0,11,3,6,8,9}}",
-                "R": (
-                    "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},"
-                    "{0,11,12,3,6,8,9},{0,12,2,3,6,9},{0,12,3,6,9}}"
-                ),
-            },
-        },
-        initial_state="{0}",
-        final_states={
-            (
-                "{{0,1,10,12,3,4,6,7,9},{0,11,12,3,5,6,8,9},{0,11,12,3,6,8,9},"
-                "{0,12,2,3,6,9},{0,12,3,6,9}}"
-            )
-        },
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("4L41D4")) == DFA(
-        states={
-            "{0,3,6,7}",
-            "{0,1}",
-            "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            "{0,1,3,4,6,8}",
-            "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-            (
-                "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-            ),
-            "{0,3}",
-            "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}",
-            "{0,1,3,4}",
-            "{0,2}",
-            "{0}",
-            "{0,3,5}",
-            "{0,11,3,5,6,9}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,1}": {"L": "{0}", "D": "{0,2}", "U": "{0}", "R": "{0,1}"},
-            "{0,2}": {"L": "{0,3}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,3}": {"L": "{0,3}", "D": "{0,3,5}", "U": "{0,3}", "R": "{0,1,3,4}"},
-            "{0,3,5}": {
-                "L": "{0,3}",
-                "D": "{0,3,5}",
-                "U": "{0,3}",
-                "R": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{0,1,3,4}": {
-                "L": "{0,3}",
-                "D": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,3}",
-                "R": "{0,1,3,4}",
-            },
-            "{0,3,6,7}": {
-                "L": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,3,6,7}",
-                "R": "{0,1,3,4,6,8}",
-            },
-            "{0,1,3,4,6,8}": {
-                "L": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "U": "{0,3,6,7}",
-                "R": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{0,11,3,5,6,9}": {
-                "L": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "D": "{0,11,3,5,6,9}",
-                "U": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "R": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}": {
-                "L": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "D": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "U": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "R": "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}",
-            },
-            (
-                "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-            ): {
-                "L": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "D": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "U": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "R": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}": {
-                "L": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,3,6,7}",
-                "R": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}": {
-                "L": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "D": "{0,11,3,5,6,9}",
-                "U": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "R": "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={
-            (
-                "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-            )
-        },
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("4")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0,2}", "U": "{0}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0,2}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{0,1}": {
-                "L": "{0}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{0}",
-                "R": "{0,1}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("1R")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,1}": {"L": "{0}", "D": "{0}", "U": "{0,2}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("4L41D4")) == DFA(
-        states={
-            "{0,3,6,7}",
-            "{0,1}",
-            "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            "{0,1,3,4,6,8}",
-            "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-            (
-                "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-            ),
-            "{0,3}",
-            "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}",
-            "{0,1,3,4}",
-            "{0,2}",
-            "{0}",
-            "{0,3,5}",
-            "{0,11,3,5,6,9}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,1}": {"L": "{0}", "D": "{0,2}", "U": "{0}", "R": "{0,1}"},
-            "{0,2}": {"L": "{0,3}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,3}": {"L": "{0,3}", "D": "{0,3,5}", "U": "{0,3}", "R": "{0,1,3,4}"},
-            "{0,3,5}": {
-                "L": "{0,3}",
-                "D": "{0,3,5}",
-                "U": "{0,3}",
-                "R": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{0,1,3,4}": {
-                "L": "{0,3}",
-                "D": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,3}",
-                "R": "{0,1,3,4}",
-            },
-            "{0,3,6,7}": {
-                "L": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,3,6,7}",
-                "R": "{0,1,3,4,6,8}",
-            },
-            "{0,1,3,4,6,8}": {
-                "L": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "U": "{0,3,6,7}",
-                "R": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{0,11,3,5,6,9}": {
-                "L": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "D": "{0,11,3,5,6,9}",
-                "U": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "R": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}": {
-                "L": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "D": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "U": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "R": "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}",
-            },
-            (
-                "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-            ): {
-                "L": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "D": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "U": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-                "R": (
-                    "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                    "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-                ),
-            },
-            "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}": {
-                "L": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "D": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-                "U": "{0,3,6,7}",
-                "R": "{{0,1,3,4,6},{0,2,3,5,6},{0,3,5,6},{0,3,6}}",
-            },
-            "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}": {
-                "L": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "D": "{0,11,3,5,6,9}",
-                "U": "{{0,2,3,5,6,9},{0,3,6,7,9},{0,3,6,9}}",
-                "R": "{{0,1,10,3,4,6,8,9},{0,1,10,3,4,6,9}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={
-            (
-                "{{0,1,10,12,3,4,6,8,9},{0,1,10,12,3,4,6,9},{0,11,12,2,3,5,6,9},"
-                "{0,11,12,3,5,6,9},{0,12,3,6,7,9},{0,12,3,6,9}}"
-            )
-        },
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("4")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0,2}", "U": "{0}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0,2}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{0,1}": {
-                "L": "{0}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{0}",
-                "R": "{0,1}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("31")) == DFA(
-        states={
-            "{0,1}",
-            "{0,2}",
-            "{0,3,4}",
-            "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-            "{{0,1,3},{0,2,3}}",
-            "{0}",
-            "{0,3,5}",
-        },
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0,1}", "D": "{0,2}", "U": "{0}", "R": "{0}"},
-            "{0,1}": {"L": "{0,1}", "D": "{{0,1,3},{0,2,3}}", "U": "{0}", "R": "{0}"},
-            "{0,2}": {"L": "{{0,1,3},{0,2,3}}", "D": "{0,2}", "U": "{0}", "R": "{0}"},
-            "{0,3,5}": {
-                "L": "{{0,1,3},{0,2,3}}",
-                "D": "{{0,1,3},{0,2,3}}",
-                "U": "{0,3,5}",
-                "R": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-            },
-            "{0,3,4}": {
-                "L": "{{0,1,3},{0,2,3}}",
-                "D": "{{0,1,3},{0,2,3}}",
-                "U": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-                "R": "{0,3,4}",
-            },
-            "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}": {
-                "L": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-                "D": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-                "U": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-                "R": "{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}",
-            },
-            "{{0,1,3},{0,2,3}}": {
-                "L": "{{0,1,3},{0,2,3}}",
-                "D": "{{0,1,3},{0,2,3}}",
-                "U": "{0,3,5}",
-                "R": "{0,3,4}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3,6},{0,2,3,6},{0,3,4,6},{0,3,5,6}}"},
-    )
-    assert PinWords.dfa_name_reset(PinWords.make_dfa_for_pinword("1R")) == DFA(
-        states={"{{0,1,3},{0,2,3},{0,3}}", "{0,1}", "{0}", "{0,2}"},
-        input_symbols={"L", "D", "U", "R"},
-        transitions={
-            "{0}": {"L": "{0}", "D": "{0}", "U": "{0}", "R": "{0,1}"},
-            "{0,1}": {"L": "{0}", "D": "{0}", "U": "{0,2}", "R": "{0,1}"},
-            "{0,2}": {
-                "L": "{0}",
-                "D": "{0}",
-                "U": "{0}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-            "{{0,1,3},{0,2,3},{0,3}}": {
-                "L": "{{0,1,3},{0,2,3},{0,3}}",
-                "D": "{{0,1,3},{0,2,3},{0,3}}",
-                "U": "{{0,1,3},{0,2,3},{0,3}}",
-                "R": "{{0,1,3},{0,2,3},{0,3}}",
-            },
-        },
-        initial_state="{0}",
-        final_states={"{{0,1,3},{0,2,3},{0,3}}"},
-    )
-
-
 def test_make_dfa_for_perm():
     assert PinWords.make_dfa_for_perm(Perm.from_string("1032")) == DFA(
         states={
diff --git a/tox.ini b/tox.ini
index 7d88729..db5a6fe 100644
--- a/tox.ini
+++ b/tox.ini
@@ -6,7 +6,7 @@
 [tox]
 envlist =
     flake8, mypy, pylint, black
-    py{37,38,39, 310},
+    py{37,38,39, 310, 311},
     pypy37
 
 [default]
@@ -19,6 +19,7 @@ basepython =
     py38: python3.8
     py39: python3.9
     py310: python3.10
+    py311: python3.11
     pypy37: pypy3
 deps =
     pytest==7.2.0