Automata Theory: inside a RegExp machine

Deep dive into state machines, Finite automata, and Regular expressions

Course overview

State machines — the fundamental concept used today in many practical applications, starting from UI programming like React, automated reply systems, lexical analysis in parsers and formal language theory — i.e. the RegExp machines, — and up to real life use cases, such as simple traffic lights, vending machines, and others.

The state machines are backed by the larger theoretical field of computer science known as Theory of Computation, and also by its direct theoretical model — the Automata Theory.

In this class we study the Automata Theory on the practical example of implementing a Regular Expressions machine.

Why to take this class?

It’s not a secret, that big tech companies, such as Google, Facebook, etc. organize their recruiting process around generalist engineers, which understand basic fundamental systems, data structures, and algorithms. In fact, it’s a known issue in tech-recruiting: there are a lot of “programmers”, but not so many “engineers”. And what does define an “engineer” in this case? — an ability so solve complex problems, with understanding (and experience) in those generic concepts.

And there is a simple trick how you can gain a great experience with transferable knowledge to other systems. — You take some complex theoretical field, which might not (yet) be related to your main job, and implement it in a language you’re familiar with. And while you build it, you learn all the different data structures and algorithms, which accommodate this system. It should specifically be something generic (for example, State machines), so you can further transfer this knowledge to your “day-to-day” job.

In this class we take this approach. To study Automata “Theory” we make it more practical: we take one of its widely-used applications, the lexical analysis, and pattern matching, and build a RegExp machine.

Not only we’ll completely understand how the Regular Expressions work under the hood (and what will make their usage more professional), but also will be able to apply this knowledge about formal grammars, languages, finite automata — NFAs, DFAs, etc — in other fields of our work.

Who this class is for?

For any curious engineer willing to gain a generic knowledge about Finite Automata and Regular Expressions.

Notice though, that this class is not about how to use regular expressions (you should already know what a regular expression is, and actively use it on practice as a prerequisite for this class), but rather about how to implement the regular expressions — again with the goal to study generic complex system.

In addition, the lexical analysis (NFAs and DFAs specifically) is the basis for the parsers theory. So if you want to understand how parsers work (and more specifically, their Tokenizer or “Lexer” module), you can start here too. The path for a compiler engineer starts exactly from the Finite automata and lexical analyzer.

What are the features of this class?

The main features of these lectures are:

• Concise and straight to the point. Each lecture is self-contained, concise, and describes information directly related to the topic, not distracting on unrelated materials or talks.

• Animated presentation combined with live-editing notes. This makes understanding of the topics easier, and shows how (and when at time) the object structures are connected. Static slides simply don’t work for a complex content!

What is in the course?

The course is divided into three parts, in total of 16 lectures, and many sub-topics in each lecture. Below is the table of contents and curriculum.

Part 1: Formal grammars and Automata

In this part we discuss the history of State machines, and Regular expressions, talk about Formal grammars in Language theory. We also consider different types of Finite automata, understanding the differences between NFA, ε-NFA, and DFA.

Part 2: RegExp NFA fragments

In this part we focus on the main NFA fragments, the basic building blocks used in RegExp automata. We study how by using generic principle of composition, we can obtain very complex machines, and also to optimize them.

Part 3: RegExp machine

Finally, we implement an actual test method of regular expressions which transit from state to state, matching a string. First we understand how an NFA acceptor works by traversing the graph. Then we transform it into an NFA table, and eventually to a DFA table. We also talk and describe in detail DFA minimization algorithm.

I hope you’ll enjoy the class, and will be glad to discuss any questions and suggestion in comments.

Sincerely,

Dmitry Soshnikov