@@ -6,6 +6,7 @@ - Standardised CI and Makefile across Miden repos (#323).
 - Added `Smt::compute_mutations()` and `Smt::apply_mutations()` for validation-checked insertions (#327).
 - [BREAKING] Changed return value of the `Mmr::verify()` and `MerklePath::verify()` from `bool` to
   `Result<>` (#).
+- Added `is_empty()` functions to the `SimpleSmt` and `Smt` structures. Added `EMPTY_ROOT` constant to the `SparseMerkleTree` trait (#337).
 
 ## 0.10.1 (2024-09-13)
 

@@ -130,6 +130,12 @@ pub fn open(&self, key: &RpoDigest) -> SmtProof {
         <Self as SparseMerkleTree<SMT_DEPTH>>::open(self, key)
     }
 
+    /// Returns a boolean value indicating whether the SMT is empty.
+    pub fn is_empty(&self) -> bool {
+        debug_assert_eq!(self.leaves.is_empty(), self.root == Self::EMPTY_ROOT);
+        self.root == Self::EMPTY_ROOT
+    }
+
     // ITERATORS
     // --------------------------------------------------------------------------------------------
 
@@ -252,6 +258,7 @@ type Leaf = SmtLeaf;
     type Opening = SmtProof;
 
     const EMPTY_VALUE: Self::Value = EMPTY_WORD;
+    const EMPTY_ROOT: RpoDigest = *EmptySubtreeRoots::entry(SMT_DEPTH, 0);
 
     fn root(&self) -> RpoDigest {
         self.root

@@ -516,6 +516,16 @@ assert_eq!(&(key_2, value_2), entries.next().unwrap());
     assert!(entries.next().is_none());
 }
 
+/// Tests that `EMPTY_ROOT` constant generated in the `Smt` equals to the root of the empty tree of
+/// depth 64
+#[test]
+fn test_smt_check_empty_root_constant() {
+    // get the root of the empty tree of depth 64
+    let empty_root_64_depth = EmptySubtreeRoots::empty_hashes(64)[0];
+
+    assert_eq!(empty_root_64_depth, Smt::EMPTY_ROOT);
+}
+
 // SMT LEAF
 // --------------------------------------------------------------------------------------------
 

@@ -56,6 +56,9 @@
     /// The default value used to compute the hash of empty leaves
     const EMPTY_VALUE: Self::Value;
 
+    /// The root of the empty tree with provided DEPTH
+    const EMPTY_ROOT: RpoDigest;
+
     // PROVIDED METHODS
     // ---------------------------------------------------------------------------------------------
 

@@ -158,6 +158,12 @@ pub fn open(&self, key: &LeafIndex<DEPTH>) -> ValuePath {
         <Self as SparseMerkleTree<DEPTH>>::open(self, key)
     }
 
+    /// Returns a boolean value indicating whether the SMT is empty.
+    pub fn is_empty(&self) -> bool {
+        debug_assert_eq!(self.leaves.is_empty(), self.root == Self::EMPTY_ROOT);
+        self.root == Self::EMPTY_ROOT
+    }
+
     // ITERATORS
     // --------------------------------------------------------------------------------------------
 
@@ -298,6 +304,7 @@ type Leaf = Word;
     type Opening = ValuePath;
 
     const EMPTY_VALUE: Self::Value = EMPTY_WORD;
+    const EMPTY_ROOT: RpoDigest = *EmptySubtreeRoots::entry(DEPTH, 0);
 
     fn root(&self) -> RpoDigest {
         self.root

@@ -444,6 +444,23 @@
     assert_eq!(tree.root(), *EmptySubtreeRoots::entry(DEPTH, 0));
 }
 
+/// Tests that `EMPTY_ROOT` constant generated in the `SimpleSmt` equals to the root of the empty
+/// tree of depth 64
+#[test]
+fn test_simplesmt_check_empty_root_constant() {
+    // get the root of the empty tree of depth 64
+    let empty_root_64_depth = EmptySubtreeRoots::empty_hashes(64)[0];
+    assert_eq!(empty_root_64_depth, SimpleSmt::<64>::EMPTY_ROOT);
+
+    // get the root of the empty tree of depth 32
+    let empty_root_32_depth = EmptySubtreeRoots::empty_hashes(32)[0];
+    assert_eq!(empty_root_32_depth, SimpleSmt::<32>::EMPTY_ROOT);
+
+    // get the root of the empty tree of depth 0
+    let empty_root_1_depth = EmptySubtreeRoots::empty_hashes(1)[0];
+    assert_eq!(empty_root_1_depth, SimpleSmt::<1>::EMPTY_ROOT);
+}
+
 // HELPER FUNCTIONS
 // --------------------------------------------------------------------------------------------