Consider the Hamming distance function $h(v),$ defined for finite binary states

in a search graph, where the current state is denoted as $v$ and the target

state as $t.$ Binary representations of states are denoted as $B(v)$ and $B(t).$

$B(v)=v_1{v}_{2}dots{v}_n$

$B(t)=t_1{t}_{2}dots{t}_n$

The Hamming distance function is defined as follows:

$h(v)={\displaystyle \underset{i=1}{\overset{n}{}}}(v_i,t_i)$

where $(v_i,t_i)$ is the Kronecker delta function, which is $0$ if $v_i=t_i($bits are

equal$)$ and $1$ otherwise.