Course overview
State machines — the fundamental concept used today in many practical applications, starting from UI programming in 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.
See also: Essentials of Garbage Collectors class devoted to automatic memory management.
How to?
You can watch preview lectures, and also enroll to the full course, covering the aspects of Automata Theory and regular expressions in the animated and liveannotated format. See also details below what is in the course.
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Why to take this class?
It’s not a secret, 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 techrecruiting: 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 “daytoday” job.
In this class we take this approach. To study Automata “Theory” we make it more practical: we take one of its widelyused 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 our usage of RegExp 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 selfcontained, concise, and describes information directly related to the topic, not distracting on unrelated materials or talks.
 Animated presentation combined with liveediting 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 subtopics 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 difference between NFA, εNFA, and DFA.
 Pioneers of formal grammars and regexp
 Stephen Kleene, Noam Chomsky, Ken Thompson
 Kleeneclosure
 Regular grammars: Type 3
 Finite automata (State machines)
 NFA, DFA

Lecture 2: Regular grammars
 Symbols, alphabets, languages
 Formal grammars: G = (N, T, P, S)
 Regular grammars: Type 3
 BNF notation vs. RegExp notation
 Rightlinear grammars
 Nesting vs. Recursion
 Balanced parenthesis example
 Contextfree grammars

Lecture 3: Finite Automata
 From Regular grammars to State machines
 NFA, εNFA, DFA
 Epsilontransitions
 Formal FA definition: (Q, Σ, Δ, q0, F)
 FA state implementation assignment
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.
 NFA
 Single character fragment
 Epsilon fragment: “the empty string”

Lecture 5: Concatenation pattern: AB
 Concatenation RegExp pattern: AB
 Machine as a Blackbox
 Epsilon transition: attachment mechanism

Lecture 6: Union pattern: A  B
 Union (aka Disjunction) pattern: A  B
 Epsilon transition: enter both machines
 Graph traversal

Lecture 7: Kleene closure: A*
 Kleeneclosure pattern: A*
 Repeat “zero or more” times
 5 basic machines summary

Lecture 8: Complex machines
 Patterns composition and decomposition
 Operator precedence
 Abstract syntax tree (AST)
 Recursivedescent interpreter
 Compound state machine

Lecture 9: Syntactic sugar
 New syntax, same semantics
 Semantic rewrite to equivalent patterns
 A+, A?, Character classes
 NFA optimizations

Lecture 10: NFA optimizations
 Preserve semantics, optimize implementation
 Optimized A* machine
 Specific A+ machine
 Specific A? machine
 Specific character class machine
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.

Lecture 11: NFA acceptor
 NFA graph traversal
 Delegate implementation from machine to a state
 Epsilontransitions: avoid infinite loops!
 RegExp
test
method implementation on NFAs 
Lecture 12: NFA table
 NFA graph to NFA table conversion
 Rows: states, Columns: alphabet
 Calculation of the Epsilon closure
 RegExp analysis toolkit
 Parser API: obtain a RegExp AST
 NFA and DFA tables
 Optimizer module
 Transformation module

Lecture 14: DFA table
 NFA to DFA conversion
 Subset Construction algorithm
 Multiple accepting states
 Epsilon closure: eliminate εtransition

Lecture 15: DFA minimization
 DFA graph
 States equivalence algorithm
 0N equivalence
 Merging states
 Minimal DFA graph

Lecture 16: RegExp match
 RegExp pipeline
 RegExp
test
function implementation  RegExp compilation: obtaining transition table
 Course overview
 Final notes
I hope you’ll enjoy the class, and will be glad to discuss any questions and suggestion in comments.