1 / 6

Nonclosure Properties in CFLs: Set Intersection & Complement

Exploring CFLs not closed under set intersection & complement operations, counterexamples, and proof techniques in formal language theory. Understanding closure properties and language hierarchy.

wade-carson
Download Presentation

Nonclosure Properties in CFLs: Set Intersection & Complement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 38 • Showing CFL’s not closed under set intersection and set complement

  2. Nonclosure Properties for CFL’s

  3. CFL’s not closed under set intersection • How do we prove that CFL’s are not closed under set intersection? • State closure property as IF-THEN statement • If L1 and L2 are CFL’s, then L1 intersect L2 is a CFL • Proof is by counterexample • Find 2 CFL’s L1 and L2 such that L1 intersect L2 is NOT a CFL

  4. Counterexample • What is a possible L1 intersect L2? • What non-CFL languages do we know? • What could L1 and L2 be? • L1 = • L2 = • How can we prove that L1 and L2 are context-free?

  5. CFL’s not closed under complement • How can we prove that CFL’s are not closed under complement? • We could do the same thing, find a counterexample • Another way • Use fact that any language class which is closed under union and complement must also be closed under intersection

  6. H Equal Equal-3 CFL REC RE All languages over alphabet S H Language class hierarchy REG

More Related