diff --git a/include/fiction/algorithms/iter/bdl_input_iterator.hpp b/include/fiction/algorithms/iter/bdl_input_iterator.hpp
index 16aff0a9d..3ac04a6eb 100644
--- a/include/fiction/algorithms/iter/bdl_input_iterator.hpp
+++ b/include/fiction/algorithms/iter/bdl_input_iterator.hpp
@@ -23,7 +23,8 @@ namespace fiction
  * set. To this end, the iterator alters the given layout. The state enumeration wraps around, i.e. after the last
  * possible input state, the first input state is set again.
  *
- * The iterator is bidirectional and can be used in iterator-based `for` loops.
+ * The iterator satisfies the requirements of `LegacyRandomAccessIterator` and can be used in iterator-based `for`
+ * loops.
  *
  * @tparam Lyt SiDB cell-level layout type.
  */
@@ -49,6 +50,15 @@ class bdl_input_iterator
 
         set_all_inputs();
     }
+    /**
+     * Dereference operator. Returns a reference to the layout with the current input state.
+     *
+     * @return Reference to the current layout.
+     */
+    [[nodiscard]] Lyt& operator*() const noexcept
+    {
+        return layout;
+    }
     /**
      * Prefix increment operator. Sets the next input state.
      *
@@ -75,6 +85,20 @@ class bdl_input_iterator
 
         return result;
     }
+    /**
+     * Addition assignment operator. Sets a next input state.
+     *
+     * @param m The amount of input states to skip.
+     * @return Reference to `this`.
+     */
+    bdl_input_iterator& operator+=(const uint64_t m) noexcept
+    {
+        current_input_index += m;
+
+        set_all_inputs();
+
+        return *this;
+    }
     /**
      * Prefix decrement operator. Sets the previous input state.
      *
@@ -102,13 +126,42 @@ class bdl_input_iterator
         return result;
     }
     /**
-     * Dereference operator. Returns a reference to the layout with the current input state.
+     * Subtraction assignment operator. Sets a previous input state.
      *
-     * @return Reference to the current layout.
+     * @param m The amount of input states to skip.
+     * @return Reference to `this`.
      */
-    [[nodiscard]] Lyt& operator*() const noexcept
+    bdl_input_iterator& operator-=(const uint64_t m) noexcept
     {
-        return layout;
+        current_input_index -= m;
+
+        set_all_inputs();
+
+        return *this;
+    }
+    /**
+     * Subscript operator. Sets the input state to the current one plus the given subscript.
+     *
+     * @param m The amount of input states to skip.
+     * @return Reference to `this`.
+     */
+    bdl_input_iterator& operator[](const uint64_t m) noexcept
+    {
+        current_input_index += m;
+
+        set_all_inputs();
+
+        return *this;
+    }
+    /**
+     * Subtraction operator. Computes the difference between the current input index and the given iterator ones.
+     *
+     * @param other Iterator to compute the difference with.
+     * @return The difference between the current input index and the given iterator ones.
+     */
+    [[nodiscard]] std::size_t operator-(const bdl_input_iterator& other) const noexcept
+    {
+        return current_input_index - other.current_input_index;
     }
     /**
      * Equality operator. Compares the current input index with the given integer.
@@ -225,7 +278,8 @@ namespace std
 template <typename Lyt>
 struct iterator_traits<fiction::bdl_input_iterator<Lyt>>
 {
-    using iterator_category = std::bidirectional_iterator_tag;
+    using iterator_category = std::random_access_iterator_tag;
+    using difference_type   = std::size_t;
     using value_type        = Lyt;
 };
 }  // namespace std
diff --git a/test/algorithms/iter/aspect_ratio_iterator.cpp b/test/algorithms/iter/aspect_ratio_iterator.cpp
index 2e3f85003..fb2140c96 100644
--- a/test/algorithms/iter/aspect_ratio_iterator.cpp
+++ b/test/algorithms/iter/aspect_ratio_iterator.cpp
@@ -7,8 +7,19 @@
 #include <fiction/algorithms/iter/aspect_ratio_iterator.hpp>
 #include <fiction/layouts/coordinates.hpp>
 
+#include <iterator>
+#include <type_traits>
+
 using namespace fiction;
 
+TEST_CASE("Traits", "[bdl-input-iterator]")
+{
+    CHECK(std::is_same_v<std::iterator_traits<aspect_ratio_iterator<offset::ucoord_t>>::iterator_category,
+                         std::forward_iterator_tag>);
+
+    CHECK(std::is_same_v<std::iterator_traits<aspect_ratio_iterator<offset::ucoord_t>>::value_type, offset::ucoord_t>);
+}
+
 TEST_CASE("Aspect ratio iteration", "[aspect-ratio-iterator]")
 {
     aspect_ratio_iterator<offset::ucoord_t> ari{1};
diff --git a/test/algorithms/iter/bdl_input_iterator.cpp b/test/algorithms/iter/bdl_input_iterator.cpp
index 825e23ef3..43202f80d 100644
--- a/test/algorithms/iter/bdl_input_iterator.cpp
+++ b/test/algorithms/iter/bdl_input_iterator.cpp
@@ -8,8 +8,100 @@
 #include <fiction/technology/cell_technologies.hpp>
 #include <fiction/types.hpp>
 
+#include <cstdint>
+#include <iterator>
+#include <type_traits>
+
 using namespace fiction;
 
+TEST_CASE("Traits", "[bdl-input-iterator]")
+{
+    using layout = sidb_cell_clk_lyt_siqad;
+
+    CHECK(std::is_same_v<std::iterator_traits<bdl_input_iterator<layout>>::iterator_category,
+                         std::random_access_iterator_tag>);
+
+    CHECK(std::is_same_v<std::iterator_traits<bdl_input_iterator<layout>>::value_type, layout>);
+
+    CHECK(std::is_same_v<std::iterator_traits<bdl_input_iterator<layout>>::difference_type, std::size_t>);
+}
+
+TEST_CASE("Operators", "[bdl-input-iterators]")
+{
+    using layout = sidb_cell_clk_lyt_siqad;
+
+    layout lyt{};
+
+    bdl_input_iterator<layout> bii{lyt};
+
+    CHECK(bii == 0ull);
+    CHECK(bii != 1ull);
+
+    CHECK(bii < 1ull);
+    CHECK(bii <= 1ull);
+
+    CHECK(bii >= 0ull);
+
+    // increment
+    ++bii;
+
+    CHECK(bii == 1ull);
+    CHECK(bii != 0ull);
+
+    CHECK(bii < 2ull);
+    CHECK(bii <= 2ull);
+
+    CHECK(bii > 0ull);
+    CHECK(bii >= 0ull);
+
+    // decrement
+    --bii;
+
+    CHECK(bii == 0ull);
+    CHECK(bii != 1ull);
+
+    CHECK(bii < 1ull);
+    CHECK(bii <= 1ull);
+
+    CHECK(bii >= 0ull);
+
+    // increment assignment
+    bii += 2ull;
+
+    CHECK(bii == 2ull);
+    CHECK(bii != 1ull);
+
+    CHECK(bii < 3ull);
+    CHECK(bii <= 3ull);
+
+    CHECK(bii > 1ull);
+    CHECK(bii >= 1ull);
+
+    const auto bii_cp = bii;
+
+    // decrement assignment
+    bii -= 2ull;
+
+    CHECK(bii == 0ull);
+    CHECK(bii != 1ull);
+
+    CHECK(bii < 1ull);
+    CHECK(bii <= 1ull);
+
+    CHECK(bii >= 0ull);
+
+    // difference
+    CHECK(bii_cp - bii == 2ull);
+
+    // subscript
+    CHECK(bii[0] == 0ull);
+    CHECK(bii[1] == 1ull);
+    CHECK(bii[2] == 3ull);
+    CHECK(bii[3] == 6ull);
+    CHECK(bii[4] == 10ull);
+
+}
+
 TEST_CASE("Empty layout iteration", "[bdl-input-iterator]")
 {
     using layout = sidb_cell_clk_lyt_siqad;
@@ -20,6 +112,8 @@ TEST_CASE("Empty layout iteration", "[bdl-input-iterator]")
 
     CHECK((*bii).num_cells() == 0);
 
+    // increment
+
     ++bii;
 
     CHECK((*bii).num_cells() == 0);
@@ -28,6 +122,18 @@ TEST_CASE("Empty layout iteration", "[bdl-input-iterator]")
 
     CHECK((*bii).num_cells() == 0);
     CHECK((*bii_cp).num_cells() == 0);
+
+    // decrement
+
+    --bii;
+
+    CHECK((*bii).num_cells() == 0);
+
+    auto bii_cm = bii--;
+
+    CHECK((*bii).num_cells() == 0);
+
+    CHECK((*bii_cm).num_cells() == 0);
 }
 
 TEST_CASE("BDL wire iteration", "[bdl-input-iterator]")
@@ -49,6 +155,9 @@ TEST_CASE("BDL wire iteration", "[bdl-input-iterator]")
     lyt.assign_cell_type({20, 0, 0}, sidb_technology::cell_type::OUTPUT);
 
     bdl_input_iterator<layout> bii{lyt};
+    CHECK(bii == 0ull);
+
+    // start by incrementing over all input states
 
     // layout at input state 0
     const auto& lyt_0 = *bii;
@@ -58,6 +167,7 @@ TEST_CASE("BDL wire iteration", "[bdl-input-iterator]")
     CHECK(lyt_0.get_cell_type({2, 0, 0}) == sidb_technology::cell_type::EMPTY);
 
     ++bii;
+    CHECK(bii == 1ull);
 
     // layout at input state 1
     const auto& lyt_1 = *bii;
@@ -68,11 +178,30 @@ TEST_CASE("BDL wire iteration", "[bdl-input-iterator]")
 
     // doing another iteration should overflow and set it back to 0
     ++bii;
+    CHECK(bii == 2ull);
 
     const auto& lyt_2 = *bii;
 
     CHECK(lyt_2.get_cell_type({0, 0, 0}) == sidb_technology::cell_type::INPUT);
     CHECK(lyt_2.get_cell_type({2, 0, 0}) == sidb_technology::cell_type::EMPTY);
+
+    // finally, decrement back to the initial state, doing another wrap-around
+
+    --bii;
+    CHECK(bii == 1ull);
+
+    const auto& lyt_1_1 = *bii;
+
+    CHECK(lyt_1_1.get_cell_type({0, 0, 0}) == sidb_technology::cell_type::EMPTY);
+    CHECK(lyt_1_1.get_cell_type({2, 0, 0}) == sidb_technology::cell_type::INPUT);
+
+    --bii;
+    CHECK(bii == 0ull);
+
+    const auto& lyt_0_1 = *bii;
+
+    CHECK(lyt_0_1.get_cell_type({0, 0, 0}) == sidb_technology::cell_type::INPUT);
+    CHECK(lyt_0_1.get_cell_type({2, 0, 0}) == sidb_technology::cell_type::EMPTY);
 }
 
 TEST_CASE("SiQAD's AND gate iteration", "[bdl-input-iterator]")