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Questions tagged [time-complexity]

Time complexity of decision problems or relations among time-bounded complexity classes. (Use [tag:analysis-of-algorithms] for the time taken by particular algorithms.)

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4answers
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What is the “right” definition of upper and lower bounds?

Let $f(n)$ be the worst case running time of a problem on input of size $n$. Let us make the problem a bit weird by fixing $f(n) = n^2$ for $n=2k$ but $f(n) = n$ for $n=2k+1$. So, what is the lower ...
18
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3answers
591 views

Trade off between time and query complexity

Working directly with time complexity or circuit lower bounds is scary. Hence, we develop tools like query complexity (or decision-tree complexity) to get a handle on lower bounds. Since each query ...
43
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7answers
3k views

Using lambda calculus to derive time complexity?

Are there any benefits to calculating the time complexity of an algorithm using lambda calculus? Or is there another system designed for this purpose? Any references would be appreciated.
39
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6answers
11k views

Complexity of Finding the Eigendecomposition of a Matrix

My question is simple: What is the worst-case running time of the best known algorithm for computing an eigendecomposition of an $n \times n$ matrix? Does eigendecomposition reduce to matrix ...
58
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10answers
10k views

One Stack, Two Queues

background Several years ago, when I was an undergraduate, we were given a homework on amortized analysis. I was unable to solve one of the problems. I had asked it in comp.theory, but no ...
22
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2answers
1k views

To what extent can an algorithm predict the time complexity an arbitrary input program?

The Halting problem states that it is impossible to write a program that can determine if another program halts, for all possible input programs. I can, however, certainly write a program that can ...
21
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1answer
2k views

Is there a proof that addition is faster than multiplication?

The best upper bound known on the time complexity of multiplication is Martin Fürer's bound $n\log n2^{O(\log^* n)}$, which is more than linear time complexity of addition. Do we have a proof that ...
6
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2answers
1k views

Do runtimes for P require EXP resources to upper-bound? … are concrete examples known? (answer: yes and yes)

Update #6: Wow, quick service on TCS StackExchange! Emanuele Viola has provided an answer Are runtime bounds in P decidable? Answer: No. Emanuele's answer illuminates (for me) Luca Trevisan's ...
13
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1answer
753 views

Equivalent definitions of time constructibility

We say that a function $f:\mathbb{N}\rightarrow\mathbb{N}$ is time-constructible, if there exists a deterministic multi-tape Turing machine $M$ that on all inputs of length $n$ makes at most $f(n)$ ...
12
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2answers
2k views

Reversing a list using two queues

This question is inspired by an existing question about whether a stack can be simulated using two queues in amortized $O(1)$ time per stack operation. The answer seems to be unknown. Here is a more ...
13
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1answer
661 views

Is Quasi-polynomial time in PSPACE?

I had done some search on this but I was not able to find an answer either way. Huck answered it fully. Thanks :)
13
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1answer
679 views

Distinguishing between two coins

It is well known that the complexity of distinguishing an $\epsilon$ biased coin from a fair one is $\theta(\epsilon^{-2})$. Are there results for distinguishing a $p$ coin from a $p+\epsilon$ coin? I ...
6
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0answers
564 views

Is this permutation-sum problem NP-complete?

A new, tighter tardiness bound has been found for global Earliest-Deadline-First scheduling of jobs on symmetric multiprocessors. But this bound seems to be particularly hard to compute. In particular,...
23
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6answers
1k views

Advanced techniques for determining complexity lower bounds

Some of you may have been following this question, which was closed due to not being research level. So, I'm extracting the part of the question which is at a research level. Beyond the "simpler" ...
14
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3answers
1k views

Lower Bounds for Data Structures

Are results known which rule out the existence of "too-good-to-be-true" data structures? For example: can one add $Split$ and $Join$ functionality to an order maintenance data structure (see Dietz ...
10
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1answer
2k views

Complexity of converting a boolean circuit to a boolean formula

Given a boolean circuit $C$ on $n$ variables (which uses just NOT,AND and OR gates), what is the most efficient way to extract the boolean formula represented by the circuit? Is there a polytime ...
19
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5answers
1k views

Why do relational databases work at all, given the theoretical exponential complexity of answer finding (in the size of the query)?

It seems to be known that to find an answer to a query $Q$ over a relational database $D$, one needs time $|D|^{|Q|}$, and one cannot get rid of the exponent $|Q|$. As $D$ can be very large, we ...
18
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5answers
575 views

What notable automaton models have polynomially-decidable containment?

I'm trying to solve a particular problem, and I thought I might be able to solve it using automata theory. I'm wondering, what models of automata have containment decidable in polynomial time? i.e. if ...
14
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3answers
2k views

Linear time in-place riffle shuffle algorithm

Is there a linear time in-place riffle shuffle algorithm? This is the algorithm that some especially dextrous hands are capable of performing: evenly dividing an even-sized input array, and then ...
4
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0answers
250 views

The problem of whether or not every function computable in time $T(n)$ is computable in time $T(n)^{O(1)}$ and space $T(n)^{o(1)}$ simultaneously

If a function is computable in time $T(n)$, is it computable in time $T(n)^{O(1)}$ and space $T(n)^{o(1)}$ simultaneously? We won't be able to prove it, because it implies the open problems $\text{P} ...
9
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1answer
2k views

Complexity of Finding the Eigendecomposition of a *Symmetric* Matrix

This is a specialized version of a previous question: Complexity of Finding the Eigendecomposition of a Matrix . For NxN symmetric matrices, it is known that O(N^3) time suffices to compute the ...
6
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1answer
335 views

Formalization of proofs and computational complexity paradox?

While reading some articles on formal proofs (see also my previous question on cstheory about the length of ZFC proofs versus human written proofs), I came up with this apparent paradox. Let $M_{...
12
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1answer
437 views

Does Kannan's theorem imply that NEXPTIME^NP ⊄ P/poly?

I was reading a paper of Buhrman and Homer “Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy”. On the bottom of page 2 they remark that the results of Kannan imply that $...
10
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1answer
273 views

Is this language recognizable by a 3 symbols TM in O(n log n)?

I was playing with the very interesting and still open question "Alphabet of single-tape Turing machine" (by Emanuele Viola) and came up with the following language : $L = \{ x \in \{0,1\}^n \text{ s....
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2answers
744 views

What is the initialization time of a link-cut tree?

Link-cut tree is a data structure invented by Sleator and Tarjan, which supports various operations and queries on a $n$-node forest in time $O(\log n)$. (For example, operation link combines two ...
7
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2answers
286 views

Are space and time hierarchies even comparable?

I am wondering if there are any results to what extent the space and time hierarchies "disagree" on which problem is harder. For example, is it known whether there are languages $L_1$ and $L_2$ such ...
11
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3answers
634 views

Can we compute $n$ from the bits of $3^n$ in $O(n)$ time?

I'm seeking an efficient algorithm for the problem: Input: The positive integer $3^n$ (stored as bits) for some integer $n \geq 0$. Output: The number $n$. Question: Can we compute $n$ from ...
8
votes
1answer
320 views

Are there more polynomial time problems with complexity lower bounds?

I'm looking for more problems in $P$ with classical time complexity lower bounds. Some people might wonder how you could prove such a lower bound. See below. Exponential Lower Bounds: Claim: If ...
6
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0answers
86 views

Small universal monotone Turing machines

This paper surveys small universal Turing machines. What are some examples of small universal monotone Turing machines, as described by Schmidhuber? Which of these are efficient (polynomial time) ...
5
votes
0answers
337 views

How are lower bounds for computational complexity proved? [closed]

As the title says, how are lower bounds for computational complexity proved? I'm interested why it is possible to say that a certain algorithm cannot run in faster time than some lower bound. ...
4
votes
0answers
121 views

Real-time countable vs fully time-constructible

Real-time countable functions were used in time hierarchy theorem in the papers of Hartmanis and Stearns (Theorem 9, 9.1 ...) and also of Hennie and Stearns (Theorems 3, 5, 7 ...). Now it is a "...
2
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1answer
305 views

Finding max of two elements in linear time with restriction

I have a matrix in the following form: ...
4
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2answers
165 views

Function with space-depending computation time

Does a function exist which is easily computable for one space capacity and is hard to compute for another? I am looking for a function which can be computed in polytime when available space is at ...
4
votes
0answers
125 views

Deciding transitivity of a directed acyclic graph [duplicate]

Is there any algorithm that decides whether a given directed acyclic graph is transitive or not, in time-complexity asymptotically better than boolean matrix multiplication?