CSci 311, Models of Computation Chapter 8 Properties of Context-Free Languages

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8.1 Two Pumping Lemmas . . . . . . . . . . . . . . . . . . . . . . . . 1 8.1.1 Context-Free Languages . . . . . . . . . . . . . . . . . . . 2 8.1.2 Linear Languages . . . . . . . . . . . . . . . . . . . . . . . 2 8.2 Closure Properties and Decision Algorithms for Context-Free Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8.2.1 Closure under Union, Concatenation, and Star-Closure . . 3 8.2.2 Non-Closure under Intersection and Complementation . . 4 8.2.3 Closure under Regular Intersection . . . . . . . . . . . . . 6 8.2.4 Linz Example 8.7 . . . . . . . . . . . . . . . . . . . . . . . 7 8.2.5 Linz Example 8.8 . . . . . . . . . . . . . . . . . . . . . . . 8 8.2.6 Some Decidable Properties of Context Free Languages . . 8 Copyright (C) 2015, H. Conrad Cunningham Acknowledgements: These lecture notes are for use with Chapter 8 of the textbook: Peter Linz. Introduction to Formal Languages and Automata, Fifth Edition, Jones and Bartlett Learning, 2012. The terminology and notation used in these notes are similar to those used in the Linz textbook. This document uses several figures from the Linz textbook. Advisory: The HTML version of this document requires use of a browser that supports the display of MathML. A good choice as of December 2015 seems to be a recent version of Firefox from Mozilla.