Questions tagged [dfa]

Questions about deterministic finite automata

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59
votes
10answers
7k views

Are there any open problems left about DFAs?

After studying deterministic finite state automata (DFA) in undergrad, I felt they are extremely well understood. My question is whether there is something we still don't understand about them. I don'...
19
votes
1answer
2k views

What is the number of languages accepted by a DFA of size $n$?

The question is simple and direct: For a fixed $n$, how many (different) languages are accepted by a DFA of size $n$ (i.e. $n$ states)? I will formally state this: Define a DFA as $(Q,\Sigma,\delta,...
247
votes
11answers
95k views

What is the enlightenment I'm supposed to attain after studying finite automata?

I've been revising Theory of Computation for fun and this question has been nagging me for a while (funny never thought of it when I learnt Automata Theory in my undergrad). So "why" exactly do we ...
23
votes
1answer
822 views

Finding the smallest DFA that separates two words without using brute force search?

Given two strings x and y, I want to build a minimum size DFA that accepts x and rejects y. One way to do this is brute force search. You enumerate DFA's starting with the smallest. You try each ...
23
votes
1answer
565 views

Languages recognized by polynomial-size DFAs

For a fixed finite alphabet $\Sigma$, a formal language $L$ over $\Sigma$ is regular if there exists a deterministic finite automaton (DFA) over $\Sigma$ which accepts exactly $L$. I am interested in ...
11
votes
1answer
4k views

What algorithms exist for construction a DFA that recognizes the language described by a given regex?

All of my textbooks use the same algorithm for producing a DFA given a regex: First, make an NFA that recognizes the language of the regex, then, using the subset (aka "powerset") construction, ...
4
votes
3answers
437 views

How to minimize a FSM transducer?

In contrast to FSM minimization which is well studied with various algorithms, theorems and has many practical applications, I'm looking for any nontrivial insight, analysis and references to the ...
3
votes
1answer
203 views

Finding self-similar homomorphisms of a FSM transducer

Consider a special case of homomorphisms of FSM transducers (or "generalized sequential machines" in [1]). Let $F$ be a transducer accepting a language $L$, and let $h(x)$ be a homomorphism function ...
12
votes
1answer
710 views

The Cost of an Equivalence Query for DFA

Inspired by this question, I am curious about the following: What is the worst-case complexity of checking whether a given DFA accepts the same language as a given regular expression? Is this ...
10
votes
1answer
215 views

Is it decidable whether the output length of a transducer is bounded by the input length?

The transducers considered here are those Wikipedia calls finite state transducers. The behavior of a transducer $T$, that is, the relation it computes, is written $[T]$: a word $y$ is an output for $...