fixed reverse dense fsa and added connect function

sandbox/GNAT.jl

 ### A Pluto.jl notebook ###
-# v0.19.22
+# v0.19.20
 
 using Markdown
 using InteractiveUtils
@@ -73,17 +73,11 @@ C ∩ D
 # ╔═╡ b37d3f48-0b23-4700-bb45-050b08209669
 @time L ∩ C
 
-# ╔═╡ 26a8c2c5-27da-4389-bfd8-ca3793dd994e
-I = FSA(
-	kron(L.α, C.α),
-	kron(L.T, C.T),
-	kron(L.ω, C.ω),
-	L.ρ * C.ρ,
-	kron(L.λ, C.λ)
-)
-
 # ╔═╡ 183f8031-b384-408b-8cd6-c84f23693dfc
+# ╠═╡ disabled = true
+#=╠═╡
 M = sparse([1,1,2,3,4,4,5,6,7,7,8,9],[1,3,2,4,1,3,2,4,1,3,2,4], one(K), nstates(L), nstates(C))
+  ╠═╡ =#
 
 # ╔═╡ b605383a-4080-4916-857c-2528f6ad172c
 M' * L.ω
@@ -122,20 +116,11 @@ G = DenseFSA(H, sort(collect(Σ)), zero(K))
 # ╔═╡ 54888ef8-6ee9-446d-9b78-364fe35e52b6
 G, L
 
-# ╔═╡ b2290feb-24a1-4f7d-8216-7c69ea363a67
-L
-
-# ╔═╡ 5c3893f7-b64f-410f-9be2-5c2023fd9093
-# C = A ∩ B
-
-# ╔═╡ 5ecadd35-feea-459f-9776-3a2762b0de9f
-# FSA(C)
-
-# ╔═╡ 2ea1644a-8836-443b-a1ee-8d13dbd4a534
-H[:, 2]
+# ╔═╡ 40ba3c52-84e0-4d70-8d8e-840ec2225baf
+G ∩ C
 
-# ╔═╡ 68d8f4b3-48e1-49ca-b910-c65c2ec19768
-ones(K, 3) * H[:,2]'
+# ╔═╡ 91b52b46-b8d8-4d14-9f9c-732de9d906ff
+G ∩ C |> connect
 
 # ╔═╡ Cell order:
 # ╠═510f7d8a-ce11-11ed-2832-cdc20fa6f700
@@ -153,15 +138,11 @@ ones(K, 3) * H[:,2]'
 # ╠═b37d3f48-0b23-4700-bb45-050b08209669
 # ╠═049d12b4-0107-4ecc-89e4-45d3955bdd0b
 # ╠═54888ef8-6ee9-446d-9b78-364fe35e52b6
-# ╠═26a8c2c5-27da-4389-bfd8-ca3793dd994e
 # ╠═183f8031-b384-408b-8cd6-c84f23693dfc
 # ╠═b605383a-4080-4916-857c-2528f6ad172c
 # ╠═e91b7104-7149-4770-8abe-fb0a968bd197
 # ╠═49fb8a23-bae8-4c66-8490-01d7e28f25f9
 # ╠═29a16022-6ebc-4e74-8245-e7293fcb160a
 # ╠═ada373ae-0e4e-42ca-80a5-98be29aca610
-# ╠═b2290feb-24a1-4f7d-8216-7c69ea363a67
-# ╠═5c3893f7-b64f-410f-9be2-5c2023fd9093
-# ╠═5ecadd35-feea-459f-9776-3a2762b0de9f
-# ╠═2ea1644a-8836-443b-a1ee-8d13dbd4a534
-# ╠═68d8f4b3-48e1-49ca-b910-c65c2ec19768
+# ╠═40ba3c52-84e0-4d70-8d8e-840ec2225baf
+# ╠═91b52b46-b8d8-4d14-9f9c-732de9d906ff

src/FiniteStateAutomata.jl

@@ -34,6 +34,7 @@ export
     # FSA operations
     addskipedges,
     closure,
+    connect,
     determinize,
     globalrenorm,
     minimize,

src/dense_fsa.jl

@@ -39,6 +39,8 @@ end
 ρ(G::DenseFSA) = G.ρ
 λ(G::DenseFSA) = repeat(G.Σ, size(G.H, 2) - 1)
 
+Base.reverse(A::DenseFSA) = DenseFSA(A.H[:, end:-1:1], A.Σ, A.ρ)
+
 # Intersection with DenseFSA
 struct IntersectedDenseFSA{K, L, T<:AbstractFSA{K, L}} <: IntersectedAbstractFSA{K, L, DenseFSA{K, L}, T}
     A::DenseFSA{K, L}
@@ -72,6 +74,8 @@ end
 Base.intersect(A::DenseFSA, B::AbstractFSA) = IntersectedDenseFSA(A, B)
 Base.intersect(A::AbstractFSA, B::DenseFSA) = IntersectedDenseFSA(B, A) # we assume ∩ to be commutative w.r.t any K
 
+Base.reverse(A::IntersectedDenseFSA) = IntersectedDenseFSA(A.A |> reverse, A.B |> reverse, A.C)
+
 α(I::IntersectedDenseFSA) = begin
     h1 = I.A.H[:, 1]
     Q = nstates(I.B) * (size(I.A.H, 2) - 1)
@@ -113,3 +117,4 @@ end
 λ(I::IntersectedDenseFSA) = repeat(λ(I.B), size(I.A.H, 2) - 1)
 
 ρ(I::IntersectedDenseFSA) = ρ(I.B) * ρ(I.A)
+

src/ops.jl

@@ -224,7 +224,38 @@ end
 Returns a vector `x` of dimension `nstates(A)` where `x[i]` is `one(K)`
 if the state `i` is not accessible, `zero(K)` otherwise.
 """
-coaccessible(A::AbstractFSA) = accessible(A |> reverse)
+function coaccessible(A::AbstractFSA)
+    vₙ = ω(A)
+
+    m = ones(Bool, nstates(A))
+	m[findnz(vₙ)[1]] .= false
+
+	while nnz(vₙ) > 0
+		uₙ = T(A) * vₙ
+		vₙ = uₙ .* m
+		m[findnz(uₙ)[1]] .= false
+	end
+	.! m
+end
+
+"""
+    connect(A::AbstractFSA)
+
+Return a FSA ``B`` equivalent of ``A`` such that all states in ``B``
+are accessible and coaccessible.
+"""
+function connect(A::AbstractFSA{K}) where K
+    m = accessible(A) .* coaccessible(A)
+    I = findall(m)
+    M = sparse(I, 1:length(I), one(K), nstates(A), length(I))
+    FSA(
+        M' * α(A),
+        M' * T(A) * M,
+        M' * ω(A),
+        ρ(A),
+        λ(A)[I]
+    )
+end
 
 """
     renorm(A::FSA)