We want to design a Turing Machine to decide the following language L $=$

$\{$w $|$ w in $\backslash$Sigma $,$ a#$($w$)=$ i$,$ b#$($w$)=$ j$,$ c#$($w$)=$ k$,$ k $>$ i $+$ j$\}$ where a#$($w$)$

indicates the number of a$$s in the string, etc. Describe a TM that decides

the language using a tape$-$level description. Hint: use a Turing machine

with $3$ tapes with tape heads that can traverse L$,$ R$,$ also remain in place

$($S$),$ and reset.

M $=$on input w$1.$ If a or b make x and then make a c x if there are

no c reject and accept if there are only c and x on tape. $2.$ When reach

blank loop back if there are only x or c move right and if get to another

blank accept only if at least one c was found