8
$\begingroup$

I've been reading some formal language theory papers, and I've come across a term that I don't understand.

The paper will often refer to a set being "effectively closed under intersection" or other operations. What does "effectively" mean here? How does this differ from normal closure?

For reference, the paper I'm seeing these in is:

M. Daley and I. McQuillan. Formal modelling of viral gene compression. International Journal of Foundations of Computer Science, 16(3):453–469, 2005.

$\endgroup$
13
$\begingroup$

"Effectively closed" means that the family is closed under the operation, and that the closure can be computed by giving an automaton/grammar for it (if the original languages are also given in such an effective representation). E.g., given a finite state automaton, we can actually find an automaton for the complement.

Then it is a natural question, whether there are examples of closure properties that are not effective. I know one right now. For a regular language $R$ and any language $L$ the quotient $R/L$ is again regular. There is no effective way to construct a FSA for that quotient if $L$ is e.g. recursively enumarable.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.