Conversion of Context-Free Grammar to Pushdown Automaton

Here we show how to convert any context-free grammar (CFG) to an equivalent pushdown automaton (PDA); this video is a more up-to-date and higher-quality version of a video already on the channel.

The key idea is to simulate the derivation of some string in the CFG on the stack itself of the PDA. The construction involves building 4 "base" states, and then self loops on the third state for each terminal. Initially push on a $, then the start variable, and pop the $ going to the 4th state. Then, add a series of transitions for every rule, popping the LHS variable, and then pushing on the RHS in reverse order. In this case, we worked with a CFG for the language of strings that are not palindromes (over the alphabet {a, b}), although the particular language/CFG does not matter.

Chapters:
0:00 - Intro
0:26 - Showing CFG is correct
1:32 - Overview of CFG to PDA conversion
6:52 - Start of CFG to PDA conversion
8:04 - Dealing with start variable
8:35 - The q_loop state
10:25 - Handling terminals at top of stack
12:58 - Handling variables at top of stack
20:35 - Verifying correctness of conversion
23:54 - Outro

----------------------------------------------------------------------------------------------------------------

What is a context-free grammar? It is a set of 4 items: a set of "variables," a set of "terminals," a "start variable," and a set of rules. Each rule must involve a single variable on its "left side", and any combination of variables and terminals on its right side. See https://www.youtube.com/watch?v=h1OSmLSacNA&ab_channel=EasyTheory for more details.

What is a pushdown automaton? It is a finite state machine, where on each transition, items can be pushed or popped off of a stack it has, which has unlimited height. See https://www.youtube.com/watch?v=Br44Zxv84-Q&ab_channel=EasyTheory for more details.

----------------------------------------------------------------------------------------------------------------

Easy Theory Website: https://www.easytheory.org
GoFundMe: https://www.gofundme.com/f/easy-theory-video-studio
Patreon: https://www.patreon.com/EasyTheoryYT
Fourthwall: https://easy-theory-llc-shop.fourthwall.com
Problem Solving channel: ​⁠ @easytheoryprobsolve

If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1