Using Pumping Lemma (slides 30-35 of the notes ‘Regular Languages & Finite Automata-IV’) one can show the language L= {a^n b^n | n ϵ N } is not regular (We need this property in the notes ‘Context-free Languages and Pushdown Automata I). This is done by way of contradiction. We assume L is regular. Since L is infinite, Pumping Lemma applies. We then consider the string s=a^m b^m where m is the number of states in the DFA that recognizes L. Since the length of s is bigger than m, by Pumping Lemma, there exists strings x, y and z such that s=xyz, y≠Λ, |xy|≤2m and xy^k z∈L for all k∈N. If |xy|<2m then the first repeated state on the acceptance path cannot be a final state. Is this statement true, why or why not?

Consider the following statements: #include #include class temporary { private: string description; double first; double second; public: temporary(string = "", double = 0.0, double = 0.0); void set(string, double, double); double manipulate(); void get(string& , double& , double& ); void setdescription(string); void setfirst(double); void setsecond(double); }; write the definition of the member function set() so that the instance variables are set according to the parameters. write the definition of the constructor so that it initializes the instance variables using the function set() write the definition of the member function manipulate() that returns a decimal number (double) as follows: if the value of description is "rectangle", it returns first * second if the value of description is "circle" it returns the area of a circle with radius first if the value of description is "cylinder" it returns the volume of a cylinder with radius first and height second. hint: the volume of a cylinder is simply the area of the circle at the base times the height. if the value of description is "sphere" it returns the volume of the sphere with radius first. otherwise it returns -1.0;

A911 dispatcher is the sole sender of messages to all police officers. while on patrol, officers communicate with the dispatcher who, in turn, relays messages to other officers. the officers do not communicate directly with one another. this illustrates a network.

The editing of digital photos us about the same level of difficulty as editing an analog photo