diff --git a/src/ProblemReductions.jl b/src/ProblemReductions.jl
index 0ee2489..9344b2b 100644
--- a/src/ProblemReductions.jl
+++ b/src/ProblemReductions.jl
@@ -30,8 +30,8 @@ export Factoring, is_factoring
 export Matching, is_matching
 export MaximalIS
 export PaintShop
-export BinaryMatrixFactorization, is_binary_matrix_factorization
-export BicliqueCover, is_biclique_cover
+export BinaryMatrixFactorization, is_binary_matrix_factorization, read_solution
+export BicliqueCover, is_biclique_cover, read_solution, biclique_cover_from_matrix
 
 # rules
 export target_problem, AbstractProblem, ConstraintSatisfactionProblem, solution_size, solution_size_multiple, SolutionSize, objectives, constraints, energy_mode
@@ -48,6 +48,7 @@ export ReductionIndependentSetToSetPacking, ReductionSetPackingToIndependentSet
 export ReductionSATToCircuit
 export ReductionIndependentSetToVertexCovering
 export ReductionMatchingToSetPacking
+export ReductionBMFToBicliqueCover, ReductionBicliqueCoverToBMF
 
 # reduction path
 export ReductionGraph, reduction_graph, reduction_paths, ConcatenatedReduction
diff --git a/src/models/BMF.jl b/src/models/BMF.jl
index c17fa53..7b28ccd 100644
--- a/src/models/BMF.jl
+++ b/src/models/BMF.jl
@@ -18,7 +18,7 @@ The Boolean Matrix Factorization (BMF) problem is defined on a binary matrix A i
 struct BinaryMatrixFactorization<: AbstractProblem
     A::BitMatrix
     k::Int
-    function BinaryMatrixFactorization(A::BitMatrix, k::Int) where K
+    function BinaryMatrixFactorization(A::BitMatrix, k::Int)
         new(A, k)
     end
 end
@@ -49,5 +49,27 @@ function is_binary_matrix_factorization(bmf::BinaryMatrixFactorization, b::BitMa
     return solution_size(bmf,b,c) == 0
 end
 
+"""
+
+    read_solution(bmf::BinaryMatrixFactorization, solution::Vector{BitMatrix})
 
+    Read the solution of the BinaryMatrixFactorization problem from the solution of the BMF problem, return a vector of cliques
+"""
+function read_solution(bmf::BinaryMatrixFactorization, a::BitMatrix, b::BitMatrix)
+    @assert size(a,2) == size(b,1) == bmf.k "Dimension mismatch"
+    cliques = [zeros(Int64,size(a,1)+size(b,2)) for i in range(1,bmf.k)]
+    for i in range(1,bmf.k)
+        for j in range(1,size(a,1))
+            if a[j,i]
+                cliques[i][j] = 1
+            end
+        end
+        for j in range(1,size(b,2))
+            if b[i,j]
+                cliques[i][j+size(a,1)] = 1
+            end
+        end
+    end
+    return cliques
+end
 
diff --git a/src/models/BicliqueCover.jl b/src/models/BicliqueCover.jl
index edc1c38..77d7418 100644
--- a/src/models/BicliqueCover.jl
+++ b/src/models/BicliqueCover.jl
@@ -35,7 +35,7 @@ problem_size(c::BicliqueCover) = (; num_vertices=nv(c.graph), num_edges=ne(c.gra
 # Variables Interface
 # each vertex is assigned to a biclique, with k bicliques, variables(c::BicliqueCover) = fill(1,c.k * nv(c.graph)) 
 num_variables(c::BicliqueCover) = nv(c.graph) * c.k
-num_flavors(c::BicliqueCover) = 2
+num_flavors(::Type{<:BicliqueCover}) = 2
 
 # constraints interface
 function constraints(c::BicliqueCover)
@@ -94,3 +94,31 @@ function is_biclique(config,bc::BicliqueCover)
     end
     return true
 end
+
+"""
+
+    read_solution(bicliquecover::BicliqueCover, solution::Vector{Vector{Int64}})
+
+Read the solution of the BicliqueCover problem from the solution of the BMF problem, return a vector of two bit matrix
+"""
+function read_solution(bicliquecover::BicliqueCover, solution::Vector{Vector{Int64}})
+    len_part1 = length(bicliquecover.part1)
+    len_part2 = nv(bicliquecover.graph) - len_part1
+    k = bicliquecover.k
+    B = falses((len_part1,k))
+    C = falses((k,len_part1))
+    # each iteration, we update the a-th column of B and the a-th row of C
+    for a in range(1,k)
+        for i in range(1,len_part1)
+            if solution[a][i] == 1
+                B[i,a] = true
+            end
+        end
+        for j in range(1,len_part2)
+            if solution[a][j+len_part1] == 1
+                C[a,j] = true
+            end
+        end
+    end
+    return [B,C]
+end
diff --git a/src/rules/BMF_BicliqueCover.jl b/src/rules/BMF_BicliqueCover.jl
new file mode 100644
index 0000000..b29e5e7
--- /dev/null
+++ b/src/rules/BMF_BicliqueCover.jl
@@ -0,0 +1,51 @@
+"""
+$TYPEDEF
+
+The reduction result from BinaryMatrixFactorization to BicliqueCover.
+
+### Fields
+- `bicliquecover`: The BicliqueCover problem.
+"""
+struct ReductionBMFToBicliqueCover{Int64} <: AbstractReductionResult
+    bicliquecover::BicliqueCover{Int64}
+end
+Base.:(==)(a::ReductionBMFToBicliqueCover, b::ReductionBMFToBicliqueCover) = a.bicliquecover == b.bicliquecover
+target_problem(res::ReductionBMFToBicliqueCover) = res.bicliquecover
+
+function reduceto(::Type{<:BicliqueCover}, bmf::BinaryMatrixFactorization)
+    bc = biclique_cover_from_matrix(Int.(bmf.A), bmf.k)
+    return ReductionBMFToBicliqueCover(bc)
+end
+
+function extract_solution(res::ReductionBMFToBicliqueCover{Int64}, solution)
+    return solution
+end
+
+"""
+$TYPEDEF
+
+The reduction result from BicliqueCover to BinaryMatrixFactorization.
+
+### Fields
+- `BMF`: The BinaryMatrixFactorization problem.
+"""
+struct ReductionBicliqueCoverToBMF <: AbstractReductionResult
+    BMF::BinaryMatrixFactorization
+end
+Base.:(==)(a::ReductionBicliqueCoverToBMF, b::ReductionBicliqueCoverToBMF) = a.BMF == b.BMF
+target_problem(res::ReductionBicliqueCoverToBMF) = res.BMF
+
+function reduceto(::Type{<:BinaryMatrixFactorization}, biclique::BicliqueCover)
+    len_part1 = length(biclique.part1)
+    A = falses((len_part1,nv(biclique.graph)-len_part1))
+    for e in edges(biclique.graph)
+        if e.src in biclique.part1
+            A[e.src, e.dst-len_part1] = true
+        end
+    end
+    return ReductionBicliqueCoverToBMF(BinaryMatrixFactorization(A, biclique.k))
+end
+
+function extract_solution(res::ReductionBicliqueCoverToBMF, solution)
+    return solution
+end
\ No newline at end of file
diff --git a/src/rules/rules.jl b/src/rules/rules.jl
index a81b74d..9c851f7 100644
--- a/src/rules/rules.jl
+++ b/src/rules/rules.jl
@@ -88,4 +88,5 @@ include("sat_dominatingset.jl")
 include("independentset_setpacking.jl")
 include("circuit_sat.jl")
 include("vertexcovering_independentset.jl")
-include("matching_setpacking.jl")
\ No newline at end of file
+include("matching_setpacking.jl")
+include("BMF_BicliqueCover.jl")
\ No newline at end of file
diff --git a/test/models/BMF.jl b/test/models/BMF.jl
index 86346f6..348d8d1 100644
--- a/test/models/BMF.jl
+++ b/test/models/BMF.jl
@@ -4,32 +4,37 @@ using Test, ProblemReductions
     # test 1
     A = trues(3, 3)
     k = 2
-    bmf = BinaryMatrixFactorization(A, k)
+    bmf1 = BinaryMatrixFactorization(A, k)
 
-    @test variables(bmf) == [i for i in 1:12]
-    @test num_variables(bmf) == 12
+    @test variables(bmf1) == [i for i in 1:12]
+    @test num_variables(bmf1) == 12
     @test flavors(BinaryMatrixFactorization) == (0, 1)
     @test num_flavors(BinaryMatrixFactorization) == 2
-    @test problem_size(bmf) == (num_rows=3, num_cols=3, k=2)
-    @test solution_size(bmf, falses(3, 2), falses(2, 3)) == 9
+    @test problem_size(bmf1) == (num_rows=3, num_cols=3, k=2)
+    @test solution_size(bmf1, falses(3, 2), falses(2, 3)) == 9
     @test energy_mode(BinaryMatrixFactorization) == SmallerSizeIsBetter()
-    @test is_binary_matrix_factorization(bmf, falses(3, 2), falses(2, 3)) == false
-    @test is_binary_matrix_factorization(bmf,trues(3, 2), trues(2, 3)) == true
-    bmf1 = BinaryMatrixFactorization(trues(3,3), 3)
-    @test bmf != bmf1
-    bmf2 = BinaryMatrixFactorization(trues(3,3), 2)
-    @test bmf == bmf2
+    @test is_binary_matrix_factorization(bmf1, falses(3, 2), falses(2, 3)) == false
+    @test is_binary_matrix_factorization(bmf1,trues(3, 2), trues(2, 3)) == true
+    bmf_a = BinaryMatrixFactorization(trues(3,3), 3)
+    @test bmf1 != bmf_a
+    bmf_b = BinaryMatrixFactorization(trues(3,3), 2)
+    @test bmf1 == bmf_b
 
     # test 2
     A = trues(3, 3)
     k = 2
-    bmf = BinaryMatrixFactorization(A, k)
+    bmf2 = BinaryMatrixFactorization(A, k)
 
-    @test num_variables(bmf) == 12
+    @test num_variables(bmf2) == 12
     @test flavors(BinaryMatrixFactorization) == (0, 1)
-    @test problem_size(bmf) == (num_rows=3, num_cols=3, k=2)
-    @test solution_size(bmf, falses(3, 2), falses(2, 3)) == 9
+    @test problem_size(bmf2) == (num_rows=3, num_cols=3, k=2)
+    @test solution_size(bmf2, falses(3, 2), falses(2, 3)) == 9
     @test energy_mode(BinaryMatrixFactorization) == SmallerSizeIsBetter()
-    @test is_binary_matrix_factorization(bmf, falses(3, 2), falses(2, 3)) == false
-    @test is_binary_matrix_factorization(bmf,trues(3, 2), trues(2, 3)) == true
+    @test is_binary_matrix_factorization(bmf2, falses(3, 2), falses(2, 3)) == false
+    @test is_binary_matrix_factorization(bmf2,trues(3, 2), trues(2, 3)) == true
+
+    # test 3
+    A = BitMatrix([1 0;1 1])
+    bmf3 = BinaryMatrixFactorization(A, 2)
+    @test read_solution(bmf3, BitMatrix([1 0 ; 1 1]), BitMatrix([1 0 ; 0 1])) == [[1,1,1,0],[0,1,0,1]]
 end
\ No newline at end of file
diff --git a/test/models/BicliqueCover.jl b/test/models/BicliqueCover.jl
index 711fa53..c49f1fe 100644
--- a/test/models/BicliqueCover.jl
+++ b/test/models/BicliqueCover.jl
@@ -10,6 +10,7 @@ using Test, ProblemReductions, Graphs
     # variable and weight interfaces
     @test num_variables(bc) == 12
     @test num_flavors(bc) == 2
+    @test num_flavors(BicliqueCover{Int64}) == 2
     @test problem_size(bc) == (num_vertices=6, num_edges=5, k=2)
     bc_matrix = ProblemReductions.biclique_cover_from_matrix([1 1 0;1 1 0;0 0 1],2)
     @test bc_matrix == bc
@@ -24,4 +25,6 @@ using Test, ProblemReductions, Graphs
     @test ProblemReductions.is_satisfied(bc,[[1,1,0,1,1,0],[0,0,1,0,0,1]]) == true
     @test solution_size(bc, [[1,1,0,1,1,0],[0,0,1,0,0,1]]) == ProblemReductions.SolutionSize(6, true)
     @test solution_size(bc, [[1,1,0,1,1,0],[0,0,1,0,0,0]]) == ProblemReductions.SolutionSize(5, false)
+    B,C = BitMatrix([1 0;1 0;0 1]), BitMatrix([1 1 0;0 0 1])
+    @test read_solution(bc, [[1,1,0,1,1,0],[0,0,1,0,0,1]]) == [B,C]
 end
diff --git a/test/rules/BMF_BicliqueCover.jl b/test/rules/BMF_BicliqueCover.jl
new file mode 100644
index 0000000..3335a58
--- /dev/null
+++ b/test/rules/BMF_BicliqueCover.jl
@@ -0,0 +1,29 @@
+using Test, ProblemReductions, Graphs
+
+@testset "BMF_BicliqueCover" begin
+    A = [1 0 ; 1 1]
+    A = BitMatrix(A)
+    bmf1 = BinaryMatrixFactorization(A, 2)
+    bc1 = ProblemReductions.biclique_cover_from_matrix(Int.(A), 2)
+    res = reduceto(BicliqueCover, bmf1)
+    res1 = ReductionBMFToBicliqueCover(bc1)
+    @test res == res1
+    @test res.bicliquecover == bc1
+    @test res.bicliquecover.part1 == [i for i in 1:size(A,1)]
+    @test target_problem(res) == bc1
+    @test extract_solution(res,[[1,1,1,0],[0,1,0,1]]) == [[1,1,1,0],[0,1,0,1]]
+end 
+
+@testset "BicliqueCover_BMF" begin
+    g = SimpleGraph(4)
+    for (i,j) in [(1,3),(2,3),(2,4)]
+        add_edge!(g,i,j)
+    end
+    bc = BicliqueCover(g,[1,2], 2)
+    res = reduceto(BinaryMatrixFactorization, bc)
+    res1 = ReductionBicliqueCoverToBMF(BinaryMatrixFactorization(BitMatrix([1 0; 1 1]), 2))
+    @test res == res1
+    @test res.BMF == BinaryMatrixFactorization(BitMatrix([1 0; 1 1]), 2)
+    @test target_problem(res) == BinaryMatrixFactorization(BitMatrix([1 0; 1 1]), 2)
+    @test extract_solution(res,[[1,0,1,0],[0,1,0,1]]) == [[1,0,1,0],[0,1,0,1]]
+end
\ No newline at end of file
diff --git a/test/rules/rules.jl b/test/rules/rules.jl
index 8a24877..32ead72 100644
--- a/test/rules/rules.jl
+++ b/test/rules/rules.jl
@@ -52,6 +52,10 @@ end
     include("matching_setpacking.jl")
 end
 
+@testset "BMF_BicliqueCover" begin
+    include("BMF_BicliqueCover.jl")
+end
+
 @testset "rules" begin
     circuit = CircuitSAT(@circuit begin
         x = a ∨ ¬b