Theory of automata prerequisites

Question

I'm interested in automata theory to improve my understanding of programming and compiler design (I would like to create some simple syntax's in my own projects , for example; L-Systems, AI, neural net structures and intelligent object-object conversation 'AI dialog') but there are things I need to learn before I go forward.

There are a lot of new symbols and mathematical concepts I need to learn before studying automata theory, I could not copy and paste examples because of the symbols and I don't have the required reputation to post an image so hears a link to a wiki article.

Context-free grammar article on Wikipedia

Under the heading "Proper CFGs" you can see some definitions. I don't understand them. Could someone please tell me what this notation is called so I can Google it. Any other pointers or information would also be helpful but just knowing a few key words will help. Also if anyone knows of a comprehensive resource that can be accessed for free e.g, an IIT Video lecture on the subject of that notation I would be eternally grateful as I can't afford tutoring or even text books at this time.

The resource I'm using at the moment for automata theory(for anyone who is interested) is Theory of Automata IIT Lectures on YouTube.

Answer 1

The symbols ∀ and ∃ are logical quantifiers, respectively meaning "for all" and "there exists".

Typically you are first introduced to them in a discrete mathematics course, though they're a part of predicate logic (also known as first-order logic); in my particular university's CS program, Discrete Math is a pre-requisite for Logic for Computer Science, which in turn is a pre-requisite for Formal Languages and Automata.

The star * symbol in the term (V union Sigma)* there is studied in formal languages/automata theory itself: it is the Kleene star operator. Its input is an alphabet (a set of symbols), and it produces the set of all strings of zero or more symbols over that alphabet.

A useful tool for studying formal languages and automata is JFLAP.

Answer 2

I read many books on the subject of Languages and Automata, including the Dragon books on compilers (and the much more pragmatic Jack Crenshaw's Let's Write a Compiler), but none of it really clicked until I read the classic Finite and Infinite Machines by Marvin Minsky. Being an old book, it does not cover the latest research and developments in the field at all, but he explains the state-of-the-art for the 1960s in Automata, Neural Networks, Turing Machines, Functional Programming and Lambda Calculus, and the oft-neglected third wheel of String-Rewriting Systems. And the writing is exceptionally excellent and engaging. IIRC Minksy even co-authored a robot story with Isaac Asimov, so he has some serious writing credentials.

Like I say, this book will not bring you up-to-date in any of these fields, but it's the best book I've found for explaining everything from the ground up. And it would provide a very firm basis for reading anything more recent. This book is in the bibliography of every book published since.

Answer 3

This topic, at the level that you have referred to in your link, is really only for mathematicians or graduate-level theoretical computer science students. The symbols you are referring to are just symbolic logic. If you are really interested in automata theory, I would recommend trying to find resources that explore the topic from a conceptual level and avoid using complex logical statements. OR, if you really want to dive in, you can teach yourself symbolic logic, some set theory, probably some modern algebra, and then tackle automata theory from there.