91Ó°ÊÓ

Using construction theory, prove the Theorem 1.47. Construct the diagram NFA recognize the languages that describes concatenation of the languages given.

Consider the languages $L_1=\left\{w|\text{thelengthof}w\text{isatmost}5\right\}\text{on}∑=\left\{0,1\right\}$and $L_2=\left\{w|\text{alloddplaces}\text{of}w\text{isa}1\right\}\text{on}∑=\left\{0,1\right\}$.

The NFA $M_1$recognizes the language $L_1$and the NFA $M_2$recognizes the language $L_2$.

The concatenation of the languages $L_1$and $L_2$
is represented as $L$.

The NFA $M_1$is as follows,

The NFA is as follows,

The state diagram that recognizes is as follows,

Consider that $L_1=\left\{w|w\text{carryatleastthree}1\text{s}\right\}\text{on}∑=\left\{0.1\right\}$and $L_2=\left\{w|\text{alloddplacesofwisa}1\right\}\text{on}∑=\left\{0,1\right\}$. The NFA $M_1$recognizes the language $L_1$and the NFA $M_2$recognizes the language $L_2$. The concatenation of the languages $L_1\text{and}{L}_2$is $L$that is recognized by the NFA $M$.

The NFA $M_1$is as follows,

The NFA $M_2$is follows,

Therefore, the state diagram of $M$is as follows,