From 32e6ca3de6e8ab683954af40886e7ed2f737d187 Mon Sep 17 00:00:00 2001
From: Lucas ONDEL YANG <lucas.ondel@cnrs.fr>
Date: Fri, 31 Mar 2023 12:32:41 +0200
Subject: [PATCH] fixed reverse dense fsa and added connect function
---
sandbox/GNAT.jl | 39 ++++++++++----------------------------
src/FiniteStateAutomata.jl | 1 +
src/dense_fsa.jl | 5 +++++
src/ops.jl | 33 +++++++++++++++++++++++++++++++-
4 files changed, 48 insertions(+), 30 deletions(-)
diff --git a/sandbox/GNAT.jl b/sandbox/GNAT.jl
index 4f95a03..167f19c 100644
--- a/sandbox/GNAT.jl
+++ b/sandbox/GNAT.jl
@@ -1,5 +1,5 @@
### A Pluto.jl notebook ###
-# v0.19.22
+# v0.19.20
using Markdown
using InteractiveUtils
@@ -73,17 +73,11 @@ C ∩ D
# â•”â•â•¡ b37d3f48-0b23-4700-bb45-050b08209669
@time L ∩ C
-# â•”â•â•¡ 26a8c2c5-27da-4389-bfd8-ca3793dd994e
-I = FSA(
- kron(L.α, C.α),
- kron(L.T, C.T),
- kron(L.ω, C.ω),
- L.Ï * C.Ï,
- kron(L.λ, C.λ)
-)
-
# â•”â•â•¡ 183f8031-b384-408b-8cd6-c84f23693dfc
+# â• â•â•¡ disabled = true
+#=â• â•â•¡
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))
+ â• â•â•¡ =#
# â•”â•â•¡ b605383a-4080-4916-857c-2528f6ad172c
M' * L.ω
@@ -122,20 +116,11 @@ G = DenseFSA(H, sort(collect(Σ)), zero(K))
# â•”â•â•¡ 54888ef8-6ee9-446d-9b78-364fe35e52b6
G, L
-# â•”â•â•¡ b2290feb-24a1-4f7d-8216-7c69ea363a67
-L
-
-# â•”â•â•¡ 5c3893f7-b64f-410f-9be2-5c2023fd9093
-# C = A ∩ B
-
-# â•”â•â•¡ 5ecadd35-feea-459f-9776-3a2762b0de9f
-# FSA(C)
-
-# â•”â•â•¡ 2ea1644a-8836-443b-a1ee-8d13dbd4a534
-H[:, 2]
+# â•”â•â•¡ 40ba3c52-84e0-4d70-8d8e-840ec2225baf
+G ∩ C
-# â•”â•â•¡ 68d8f4b3-48e1-49ca-b910-c65c2ec19768
-ones(K, 3) * H[:,2]'
+# â•”â•â•¡ 91b52b46-b8d8-4d14-9f9c-732de9d906ff
+G ∩ C |> connect
# â•”â•â•¡ Cell order:
# â• â•510f7d8a-ce11-11ed-2832-cdc20fa6f700
@@ -153,15 +138,11 @@ ones(K, 3) * H[:,2]'
# â• â•b37d3f48-0b23-4700-bb45-050b08209669
# â• â•049d12b4-0107-4ecc-89e4-45d3955bdd0b
# â• â•54888ef8-6ee9-446d-9b78-364fe35e52b6
-# â• â•26a8c2c5-27da-4389-bfd8-ca3793dd994e
# â• â•183f8031-b384-408b-8cd6-c84f23693dfc
# â• â•b605383a-4080-4916-857c-2528f6ad172c
# â• â•e91b7104-7149-4770-8abe-fb0a968bd197
# â• â•49fb8a23-bae8-4c66-8490-01d7e28f25f9
# â• â•29a16022-6ebc-4e74-8245-e7293fcb160a
# â• â•ada373ae-0e4e-42ca-80a5-98be29aca610
-# â• â•b2290feb-24a1-4f7d-8216-7c69ea363a67
-# â• â•5c3893f7-b64f-410f-9be2-5c2023fd9093
-# â• â•5ecadd35-feea-459f-9776-3a2762b0de9f
-# â• â•2ea1644a-8836-443b-a1ee-8d13dbd4a534
-# â• â•68d8f4b3-48e1-49ca-b910-c65c2ec19768
+# â• â•40ba3c52-84e0-4d70-8d8e-840ec2225baf
+# â• â•91b52b46-b8d8-4d14-9f9c-732de9d906ff
diff --git a/src/FiniteStateAutomata.jl b/src/FiniteStateAutomata.jl
index 0d9da08..3e2beca 100644
--- a/src/FiniteStateAutomata.jl
+++ b/src/FiniteStateAutomata.jl
@@ -34,6 +34,7 @@ export
# FSA operations
addskipedges,
closure,
+ connect,
determinize,
globalrenorm,
minimize,
diff --git a/src/dense_fsa.jl b/src/dense_fsa.jl
index dbef9e2..a044b3e 100644
--- a/src/dense_fsa.jl
+++ b/src/dense_fsa.jl
@@ -39,6 +39,8 @@ end
Ï(G::DenseFSA) = G.Ï
λ(G::DenseFSA) = repeat(G.Σ, size(G.H, 2) - 1)
+Base.reverse(A::DenseFSA) = DenseFSA(A.H[:, end:-1:1], A.Σ, A.Ï)
+
# 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)
Ï(I::IntersectedDenseFSA) = Ï(I.B) * Ï(I.A)
+
diff --git a/src/ops.jl b/src/ops.jl
index f44d17e..400b06b 100644
--- a/src/ops.jl
+++ b/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(vâ‚™)[1]] .= false
+
+ while nnz(vâ‚™) > 0
+ uâ‚™ = T(A) * vâ‚™
+ vâ‚™ = uâ‚™ .* m
+ m[findnz(uâ‚™)[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),
+ Ï(A),
+ λ(A)[I]
+ )
+end
"""
renorm(A::FSA)
--
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