Linked Questions

104 votes
15 answers
11k views

A simple decision problem whose decidability is not known

I am preparing for a talk aimed at undergraduate math majors, and as part of it, I am considering discussing the concept of decidability. I want to give an example of a problem that we do not ...
Lev Reyzin's user avatar
  • 12k
55 votes
7 answers
5k views

For which problems in P is it easier to verify the result than to find it?

For (search versions) of NP-complete problems, verifying a solution is clearly easier than finding it, since the verification can be done in polynomial time, while finding a witness takes (probably) ...
Andras Farago's user avatar
26 votes
4 answers
2k views

Separating Logspace from Polynomial time

It is clear that any problem that is decidable in deterministic logspace ($L$) runs in at most polynomial time ($P$). There is a wealth of complexity classes between $L$ and $P$. Examples include $NL$,...
Shiva Kintali's user avatar
27 votes
1 answer
2k views

Deciding emptiness of intersection of regular languages in subquadratic time

Let $L_1,L_2$ be two regular languages given by NFAs $M_1,M_2$ as input. Assume we would like to check whether $L_1\cap L_2\neq \emptyset$. This can clearly be done by a quadratic algorithm which ...
R B's user avatar
  • 9,478
20 votes
1 answer
3k 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,...
Janoma's user avatar
  • 1,406
29 votes
2 answers
2k views

How many DFAs accept two given strings?

Fix an integer $n$ and alphabet $\Sigma=\{0,1\}$. Define $DFA(n)$ to be the collection of all finite-state automata on $n$ states with starting state 1. We are considering all DFAs (not just connected,...
Aryeh's user avatar
  • 10.6k
11 votes
2 answers
355 views

Separating lists of words

There is an open problem in formal languages known as the Separating Problem; which is briefly stated as given two distinct strings of length $n$, how large of a DFA is required to "separate"...
MRC's user avatar
  • 399
18 votes
2 answers
507 views

Separating words with random DFAs

One of the interesting open problems about DFAs listed in Are there any open problems left about DFAs? is the size of a DFA required to separate two strings of length $n$. I am curious if there any ...
Geoffrey Irving's user avatar
9 votes
1 answer
494 views

Formalizing the "no formula for primes" intuition

I was trying to formalize the intuition is that there is no formula for primes, and this is my best attempt: Conjecture: There is no $O(n^2)$ expected time randomized algorithm to generate $\ge n$-...
Geoffrey Irving's user avatar
8 votes
1 answer
329 views

Two DFA intersection emptiness connections to SETH & L vs P

(re "fine grained complexity") Wehar has proved that Two DFA intersection emptiness in $O(n^{2-\epsilon})$ time → SETH false. does anyone see any particular key proof difficulty, challenge, ...
vzn's user avatar
  • 11.1k
-2 votes
1 answer
320 views

Finding research problem for PhD(TCS)? [closed]

I am a theoratical computer science PhD student. I am wanted some suggestion in how to find research problem for PhD research. I have supervisor and he has given me first problem. We had get progress ...
msingh's user avatar
  • 17
6 votes
1 answer
191 views

Separating words and graph isomorphism

I wonder if there are any known implications of Babai's recent quasi-polynomial time algorithm for Graph Isomorphism to separating words by DFA's. In both cases the ultimate goal is to differentiate ...
domotorp's user avatar
  • 14.1k