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Questions tagged [finite-automata]

Questions about finite-state automata, an elementary computational model. When interpreting its semantics w.r.t finite words, then it captures the class of regular languages.

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How to convert finite automata to regular expressions?

Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms, e.g. Thompson's algorithm. The other direction seems to be more tedious, though, and sometimes the resulting expressions are…
Raphael
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Difference between a turing machine and a finite state machine?

I am doing a presentation about Turing machines and I wanted to give some background on FSM's before introducing Turing Machines. Problem is, I really don't know what is VERY different from one another. Here's what I know it's different: FSM has…
Julio Garcia
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Are there any non-finite automata?

In automata theory, we all read automata as finite automata, from the very beginning. What I want to know is, why are automata finite? To be clear, what is it in an automaton that is finite - the alphabet, language, strings made with regular…
parvin
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Planar regular languages

In my class a student asked whether all finite automata could be drawn without crossing edges (it seems all my examples did). Of course the answer is negative, the obvious automaton for the language $\{\; x\in\{a,b\}^* \mid \#_a(x)+2\#_b(x) \equiv 0…
Hendrik Jan
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How to simulate backreferences, lookaheads, and lookbehinds in finite state automata?

I created a simple regular expression lexer and parser to take a regular expression and generate its parse tree. Creating a non-deterministic finite state automaton from this parse tree is relatively simple for basic regular expressions. However I…
Aadit M Shah
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How to show that a "reversed" regular language is regular

I'm stuck on the following question: "Regular languages are precisely those accepted by finite automata. Given this fact, show that if the language $L$ is accepted by some finite automaton, then $L^{R}$ is also accepted by some finite; $L^{R}$…
Cat
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Why is a regular language called 'regular'?

I have just completed the first chapter of the Introduction to the Theory of Computation by Michael Sipser which explains the basics of finite automata. He defines a regular language as anything that can be described by a finite automata. But I…
Phil Wright
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What are the conditions for a NFA for its equivalent DFA to be maximal in size?

We know that DFAs are equivalent to NFAs in expressiveness power; there is also a known algorithm for converting NFAs to DFAs (unfortunately I do now know the inventor of that algorithm), which in worst case gives us $2^S$ states, if our NFA had $S$…
Daniil
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Why is English not a regular language?

Surely any language with a finite longest word can be made regular by having an automaton with paths to 26 states for all letters and then having each of those states go to another 26 states, etc., with states going to a looping non-final state…
Alex S
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How to prove that DFAs from NFAs can have exponential number of states?

All non-deterministic finite automata can be turned into equivalent deterministic finite automata. However, a deterministic finite automata only allows a single arrow per symbol pointing from a state. Therefore, its states should be members of the…
John Hoffman
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What is the difference between finite automata and finite state machines?

I have used FSM in Digital sequential Circuit designs. But I am unfamiliar with Finite Automata. Can somebody help me in understanding 'basic' difference between the two ?
gpuguy
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How do I write a proof using induction on the length of the input string?

In my Computing Theory course, a lot of our problems involve using induction on the length of the input string to prove statements about finite automata. I understand mathematical induction, however when strings come into play I get real tripped…
tcdowney
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Intersection of context free with regular languages

The intersection of a context free language L with a regular language M, is said to be always context free. I understood the cross product construction proof, but I still don't get why it is context free but not regular. The language generated by…
sanjeev mk
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Is this language defined using twin primes regular?

Let $\qquad L = \{a^n \mid \exists_{p \geq n}\ p\,,\ p+2 \text{ are prime}\}.$ Is $L$ regular? This question looked suspicious at the first glance and I've realized that it is connected with the twin prime conjecture. My problem is that the…
Daniil
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Exponential separation between NFAs and DFAs in the presence of unions

For a regular language $L$, its DFA complexity is the size of the minimal DFA accepting it, and its NFA complexity is the size of the minimal NFA accepting it. It is well-known that there is an exponential separation between the two complexities, at…
Yuval Filmus
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