Let $\Sigma  = {1,2,3,4}$  . We say that symbol $\sigma $ bonds with  symbol $\tau$  if $\sigma = \tau$ of $\sigma = \tau +1$ for even  $\sigma$ and $\sigma = \tau -1$ for odd $\sigma$ . In other words  , 1  and 2 bond  , and 3 and 4 bond (in addition to every number bonding  with itself ) . The  Pattern bonding problem is defined as follows:INPUT :  Text $ T = t_{1}  , ..., t_{n}$  and pattern $ P = p_{1}  , ..., p_{m}$ over alphabet  $\Sigma  $ . OUTPUT :  All locations $i$ in the text that bond with the pattern ,   i.e  , where $t_{i+j-1}$ bonds with $p_{j}$ $j=1,...,m$ .Can someone supply an algorithm for the pattern bonding problem (the faster the better   complexity can)  ?  , I thought about Less then matching .  Edit: (Answer)Map $ (1,2) \rightarrow \alpha , (3,4)\rightarrow  \beta$ then the text and the pattern is on $\Sigma = {\alpha , \beta}$ and then we know to solve it in $O(n)$ using witness or KMP . 
Pattern bonding problem
algorithms;pattern recognition
Hint: map $1,2$ to $a$ and $3,4$ to $b$.