# All Questions

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### Inspirational talk for final year high school pupils

I am often asked by my department to give talks to final year high school pupils about the more mathematical elements of computer science. I do my best to pick topics from TCS which might inspire ...
6k views

### Applicability of Church-Turing thesis to interactive models of computation

Paul Wegner and Dina Goldin have for over a decade been publishing papers and books arguing primarily that the Church-Turing thesis is often misrepresented in the CS Theory community and elsewhere. ...
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### Why go to theoretical computer science/research?

I'm currently starting on the university [computer science] and there we have lot of opportunities to begin with researching. Before finding this website, I had no intention to go on this way [I ...
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### Many-one reductions vs. Turing reductions to define NPC

Why do most people prefer to use many-one reductions to define NP-completeness instead of, for instance, Turing reductions?
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### What do we know about provably correct programs?

The ever increasing complexity of computer programs and the increasingly crucial position computers have in our society leaves me wondering why we still don't collectively use programming languages in ...
3k views

### Optimal greedy algorithms for NP-hard problems

Greed, for lack of a better word, is good. One of the first algorithmic paradigms taught in introductory algorithms course is the greedy approach. Greedy approach results in simple and intuitive ...
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### Regular expressions aren't

Ask even someone with a background in computer science what a regular expression is, and the answer is likely to go beyond the constraint of being within reach of a finite-state automaton. For ...
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### Is optimally solving the n×n×n Rubik's Cube NP-hard?

Consider the obvious $n\times n\times n$ generalization of the Rubik's Cube. Is it NP-hard to compute the shortest sequence of moves that solves a given scrambled cube, or is there a polynomial-time ...
2k views

### Prerequisite for learning GCT

It seems that Geometric Complexity Theory requires much knowledge of pure maths such as algebraic geometry, representation theory. While I am a CS student and do NOT have classes of very abstract ...
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### Mulmuley's GCT program

It is sometimes claimed that Ketan Mulmuley's Geometric Complexity Theory is the only plausible program for settling the open questions of complexity theory like P vs. NP question. There has been ...
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### Han's $O(n \log\log n)$ time, linear space, integer sorting algorithm

Is anyone familiar with Yijie Han's $O(n \log\log n)$, linear space, integer sorting algorithm? This result appears in a fairly short paper (Deterministic sorting in $O(n \log\log n)$ time and linear ...
7k views

### Everyday encounters with NP-complete problems

Mark Dominus collected a few examples of polynomial-time reductions from various NP-hard problems to “regular expression” matching. Envisioning polynomial-time verifications isn't an enormous leap. ...
2k views

### Geometric problems that are NP-complete in $R^3$ but tractable in $R^2$?

A number of geometric problems are easy when considered in $R^1$, but are NP-complete in $R^d$ for $d\geq2$ (including one of my favourite problems, unit disk cover). Does anyone know of a problem ...
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### Most important new papers in computational complexity

We often hear about classic research and publications in the field of computational complexity (Turing, Cook, Karp, Hartmanis, Razborov etc). I was wondering if there are recently published papers ...
2k views

### Surprising Results in Complexity (Not on the Complexity Blog List)

What were the most surprising results in complexity? I think it would be useful to have a list of unexpected/surprising results. This includes both results that were surprising and came out of ...
2k views

### Higher-order algorithms

Most of the well-known algorithms are first-order, in the sense that their input and output are "plain" data. Some are second-order in a trivial way, for example sorting, hashtables or the map and ...
1k views

### Interactive proofs for levels of the polynomial hierarchy

We know that if you have a PSPACE machine, it's powerful enough to give an interactive proof of any level the polynomial hierarchy. (And if I remember right, all you need is #P.) But suppose you want ...
2k views

### Integer multiplication when one integer is fixed

Let $A$ be a fixed positive integer of size $n$ bits. One is allowed to pre-process this integer as appropriate. Given another positive integer $B$ of size $m$ bits, what is the complexity of ...