added test for closure

src/abstractfsa.jl

@@ -89,6 +89,14 @@ Return the indices of the final states `I` and their associated value
 """
 finalstates(A) = findnz(ω(A))
 
+"""
+    emptystring(A)
+
+Return the weight of the empty string "ϵ" in `A`.
+"""
+emptystring(A) = ρ(A)
+
+
 Base.parent(A::AbstractFSA) = A
 
 """

src/fsa.jl

@@ -27,6 +27,8 @@ T(fsa::FSA) = fsa.T
 
 function Base.convert(f::Function, A::AbstractFSA{K,L}) where {K,L}
     l = λ(A)
+    ρ = f(emptystring(A), one(L))
+    U = typeof(ρ)
     α = sparsevec(
         initstates(A)[1],
         [f(v, l[i]) for (i, v) in zip(initstates(A)...)],
@@ -45,6 +47,6 @@ function Base.convert(f::Function, A::AbstractFSA{K,L}) where {K,L}
         nstates(A)
     )
 
-    FSA(α, T, ω, iszero(ρ(A)) ? zero(eltype(α)) : f(ρ(A), one(L)), l)
+    FSA{U,L}(α, T, ω, ρ, l)
 end
 

test/runtests.jl

@@ -18,7 +18,11 @@ Ls = [
 
 f(L, w, l) = begin
     S = UnionConcatSemiring{L}
-    ProductSemiring((w, S(Set(L[l]))))
+    if iszero(w)
+        return ProductSemiring((w, zero(S)))
+    else
+        return ProductSemiring((w, S(Set(L[l]))))
+    end
 end
 
 @testset "FSA" begin
@@ -39,6 +43,9 @@ end
         A2 = FSA(α2, T2, ω2, ρ2, λ2)
         B2 = convert((w, l) -> f(L, w, l), A2)
 
+        Aϵ = FSA(spzeros(K, 0), spzeros(K, 0, 0), spzeros(K, 0), one(K), L[])
+        Bϵ = convert((w, l) -> f(L, w, l), Aϵ)
+
         @test all(α(A1) .≈ α1)
         @test all(T(A1) .≈ T1)
         @test all(ω(A1) .≈ ω1)
@@ -65,6 +72,24 @@ end
         @test cs_B12.tval[1] ≈ cs_B1_B2.tval[1]
         @test cs_B12.tval[2] == cs_B1_B2.tval[2]
 
+        # The number of iteration for the cumulative sum depends on the
+        # structure of the FSA for the test to pass.
+        # It should be 3 times the maximum path length of B2.
+        n = 6
+
+        # closure
+        B2p_n3 = B2 ∪ cat(B2, B2) ∪ cat(B2, B2, B2)
+        B2_n3 = B2 ∪ cat(B2, B2) ∪ cat(B2, B2, B2) ∪ Bϵ
+        cB2p = closure(B2; plus = true)
+        cB2 = closure(B2; plus = false)
+        cs_B2p_n3 = cumsum(B2p_n3; n = n)
+        cs_B2_n3 = cumsum(B2_n3; n = n)
+        cs_cB2p = cumsum(cB2p; n = n)
+        cs_cB2 = cumsum(cB2; n = n)
+        @test cs_cB2p.tval[1] ≈ cs_B2p_n3.tval[1]
+        @test cs_cB2p.tval[2] == cs_B2p_n3.tval[2]
+        @test cs_cB2.tval[1] ≈ cs_B2_n3.tval[1]
+        @test cs_cB2.tval[2] == cs_B2_n3.tval[2]
     end
 end