Multiple Interfaces modifying contract

I have a problem with my interface-design. I especially ask for help with the overloaded compute-Method.

For a calculator I work with these Interfaces:

public interface ICalculator{
    public double compute(String expression) throws IllegalArgumentException;
}

public interface IParameterizedCalculator extends ICalculator {
    public double setParameter(String parameter, double value) throws IllegalArgumentException;

    public double getParameter(String parameter) throws IllegalArgumentException;

    // IllegalArgumentException when expression is null or malformed
    // IllegalStateException when a parameter in the expression was not set prior to this method
    double compute(String expression) throws IllegalArgumentException, IllegalStateException;
}

public interface IPersistentCalculator extends ICalculator {
    // IllegalStateException when no expression is stored
    double compute() throws IllegalStateException;

    void store(String expression) throws IllegalArgumentException;
}

IParameterizedCalculator adds an Exception to compute. As the previously stateless ICalculator suddenly became stateful I see no way than to add this exception.
IPersistantCalculator doesn't modify the original compute(String), but overloads it with compute(), which also has a state and therefore throws an IllegalStateException (but not necessarily an IllegalArgumentException, as the only way to store an expression is through the store(String)-Method and I don't care if someone hacks my code via reflection or debugger). However this IllegalStateException has a different reason (another "state" if you want).

I have three questions now:

• How do I properly extend the throws-clause to indicate that my derived methods will throw more than their parent?
• How do I communicate this in a class MyCalculator implements IPersistentCalculator, IParameterizedCalculator (which only exposes a single compute(String)-method)?
• How do I communicate that the MyCalculator.compute()-Method may throw IllegalStateException when a parameterized expression has been stored?