replace semiring multiplication with module multiplication

sandbox/autodiff.jl

@@ -109,8 +109,8 @@ begin
 		# (not the log-semiring). `val.(X)` casts `X` in the 
 		# real-semiring while `K.(...)` converts it back 
 		# to the log-semiring.
-		X1 = K.( val.(X1) + (τ ⊗ ∇X1) )
-		X2 = K.( val.(X2) + (τ ⊗ ∇X2) )
+		X1 = K.( val.(X1) + (τ * ∇X1) )
+		X2 = K.( val.(X2) + (τ * ∇X2) )
 	end
 
 	plot(F, ylabel="F", xlabel = "step", legend = false)

src/fst.jl

@@ -31,7 +31,7 @@ function Base.:+(A::AbstractFST, B::AbstractFST)
     FST(α(A) + α(B), T(A) + T(B), ω(A) + ω(B), ρ(A) + ρ(B), λ(A))
 end
 
-function Semirings.:⊗(x::Number, A::AbstractFST)
+function Base.:*(x::Number, A::AbstractFST)
     Q = nstates(A)
     I_α, V_α = findnz(α(A))
     I_T, J_T, V_T = findnz(T(A))