Typically this type of automaton is called a Finite State Machine (FSM) rather than a DFA. The AI for Pac-Man uses a four-state automaton: DFAs are also easier to reason about and easier to implement.
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You can write a full program, but a DFA is often enough to do the job. If you ever design your own programming language, this will be one of the first things you will write.Ībove: Lexer description for JSON numbers, like -3.05 DFAs for artificial intelligenceĪnother application of finite automata is programming simple agents to respond to inputs and produce actions in some way. The lexer uses a DFA to go through the source file, one character at a time, and emit tokens. For example, if you have this line in C++: The lexer reads in a file of your favorite programming language, and produces a sequence of tokens. In every programming language, the first step in the compiler or interpreter is the lexer. Some programmers may try to use regular expressions to parse HTML, but if you’ve seen the Pumping Lemma, you will understand why this is fundamentally impossible. You don’t need to understand the internals of this in order to use regular expressions, but it’s useful to know some theory so you understand its limitations. If you wanted to check if a string is a valid email address, you might write something the scenes, this regular expression gets converted into an NFA, which can be quickly evaluated to produce an answer. Regular expressions are a useful tool that every programmer should know. This explains why theorists care about regular languages - but what are some real world applications? DFAs and regular expressions No matter how long the input is, a DFA only keeps track of what state it’s currently in, so it only requires a constant amount of memory.īy studying properties of regular languages, we gain a better understanding of what is and what isn’t possible with computers with very little memory. In a similar vein, regular languages describe what is possible to do with a computer with very little memory. You might have heard of Turing machines, which abstracts the idea of a “computer”. I’ve done some theoretical research on formal language theory and DFAs, so my immediate response was why DFAs are important to theorists.Ībove: A DFA requires O(1) memory, regardless of the length of the input. “So… how is this useful in real life?” DFAs as a model of computation Inevitably, a student asked the one question you should never ask a theorist: I could practically feel my students falling asleep in their seats. I began by writing down the definition of a DFA:Ī deterministic finite automaton (DFA) is a 5-tuple where: is a finite set of states… This term, I was teaching a course on intro to theory of computation, and one of the topics was finite automatons - DFAs, NFAs, and the like.
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