Use the pumping lemma to show that the following languages are not regular.

a a. a1={0^n 1^n 2^n | n≥0}
b. a2 = {www | w ∈ {a, b}∗}

a c. a3 ={a^2^n | n≥0} (here, a^2^n means a string of 2^n a’s.)

a ={a3n |n > 0 }

1. technician a says horsepower information can be used by consumers to compare the power of different automobile engines. technician b says that manufacturers will often list the horsepower output of their engines in the online service information. who is right?

Let r be a robotic arm with a fixed base and seven links. the last joint of r is a prismatic joint, the other ones are revolute joints. give a set of parameters that determines a placement of r. what is the dimension of the configuration space resulting from your choice of parameters?

Define a class named movie. include private fields for the title, year, and name of the director. include three public functions withprototypes void movie: : settitle(cstring); , voidmovie: : setyear(int); , void movie: : setdirector(string); . includeanother function that displays all the information about a movie. write a main() function that declares a movie object namedmyfavoritemovie. set and display the object's fields. this is what i have but know its wrong since it will notcompile: #include#includeusing namespace std; //class declarationclass movie{private: string movietitle ; string movieyear; string directorname; public: void settitle(string title); void setyear(string year); void setdirector(string director); void displayinfo(); }; //class implementationvoid movie: : settitle(string title){ movietitle = title; cout< < "what is the title of themovie? "< > temp; myfavoritemovie. settitle(temp); cout< < "enter movie year"< > temp; myfavoritemovie. setyear(temp); cout< < "enter director'sname"< > temp; myfavoritemovie. setdirector(temp); //display all the data myfavoritemovie. displayinfo(); system("pause"); return 0; this code is not entirely mine someone on cramster edited my firstcode but then i try manipulating the new code and i still get acompile error message : \documents\visual studio 2008\projects\movie\movie\movie. cpp(46) : error c2679: binary '< < ' : no operator found which takes aright-hand operand of type 'std: : string' (or there is no acceptableconversion)c: \program files (x86)\microsoft visual studio9.0\vc\include\ostream(653): could be'std: : basic_ostream< _elem,_traits> & std: : operator< < > (std: : basic_ostream< _elem,_traits> & ,const char *)w