Regular Expressions with Finite State Machines

Let's make a "Finite State Machine" which is used to check "a*b" regular expression.
At first we must design the FSM.

class State {
protected:
 State * const nextState;
 bool isFinal;
public:
 State( State & next, bool _isFinal ) : nextState( &next ) { isFinal = _isFinal; }
 virtual State * transition( char in ) = 0;
 bool isFinalState( ) { return isFinal; }
 ~State( ) { isFinal = false; }
};

class State1 : public State {
public:
 State1( State & nextState, bool _isFinal ) : State( nextState, _isFinal ) { }
 State * transition( char in );
};

State * State1::transition( char in ) {
 if( in >= '0' && in <= '9' ) return this->nextState;
 else return NULL;
}

class State2 : public State {
public:
 State2( State & nextState, bool _isFinal ) : State( nextState, _isFinal ) { }
 State * transition( char in );
};

State * State2::transition( char in ) {
 if( in == '*' ) return this->nextState;
 else return NULL;
}

class FSM {
 State1 state1;
 State2 state2;
 State1 state3;
 State2 final;
 State * current;
public:
 FSM( ) : state1( state2, false ), state2( state3, false ), state3( final, false ), final( final,true ), current( &state1 ) { }
 bool run( const char *s );
};

bool FSM::run(const char *s) {
 int len = strlen( s );
 int i = 0;
 do {
  current = current->transition( s[i] );
  if( current && current->isFinalState( ) )
   return true;
  i++;
 } while( NULL != current && i < len );
 
 return false;
}

int main() {
 char s[ ] = "3*4";
 FSM fsm;

 if( fsm.run( s ) ) {
  cout << s << " is a regular expression like \"a*b\" " << endl;
 }

 return 0;
}