Algorithm 3.5.

Expand: Expand subroutine for heuristic search algorithms.

1:	Function Expand(b)
	Inputs: b: An OR-Node we want to expand.
	Static: bc: The current belief state of the agent.
	T: An AND-OR tree representing the current search tree.
	L: A lower bound on V *.
	U: An upper bound on V *.
2:	for each a ∈ A do
3:	for each z ∈ Z do
4:	b′ ← τ(b, a, z)
5:	UT (b′) ← U(b′)
6:	LT (b′) ← L(b′)
7:	$H_T^{\ast }(b^{\prime })\leftarrow H_T(b^{\prime })$
8:	$b_T^{\ast }(b^{\prime })\leftarrow b^{\prime }$
9:	end for
10:	LT (b, a) ← RB(b, a) + γ Σz ∈ Z Pr(z|b, a)LT (τ(b, a, z))
11:	UT (b, a) ← RB(b, a) + γ Σz ∈ Z Pr(z|b, a)UT (τ(b, a, z))
12:	$z_{b,a}^T\leftarrow {\text{argmax}}_{z\in Z}{H}_T(b,a,z)H_T^{\ast }(\tau (b,a,z))$
13:	$H_T^{\ast }(b,a)=H_T(b,a,z_{b,a}^T)H_T^{\ast }(\tau (b,a,z_{b,a}^T))$
14:	$b_T^{\ast }(b,a)\leftarrow b_T^{\ast }(\tau (b,a,z_{b,a}^T))$
15:	end for
16:	LT (b) ← max{maxa ∈ A LT (b, a), LT (b)}
17:	UT (b) ← min{maxa ∈ A UT (b, a), UT (b)}
18:	$a_b^T\leftarrow {\text{argmax}}_{a\in A}{H}_T(b,a)H_T^{\ast }(b,a)$
19:	$H_T^{\ast }(b)\leftarrow H_T(b,a_b^T)H_T^{\ast }(b,a_b^T)$
20:	$b_T^{\ast }(b)\leftarrow b_T^{\ast }(b,a_b^T)$