# Questions tagged [proofs]

Used for questions about existing or possible proofs of a specific theorem or conjecture

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### What's wrong with this $P \neq BPP$ proof?

I developed this simple argument while learning about the $BP$ operator and McCreight and Meyer's Union Theorem, however I cannot pinpoint where my error is. By the Union Theorem, there exists a total ...
153 views

### If I want to end math, where should I start?

I'm a PhD in math, but I'm not good. I'm familiar with Riemannian geometry, a little partial differential equations, and a little algebraic topology. And the other undergraduate courses of math (I ...
48 views

### Is this variant of Facilities location problem a NP-hard problem?

Given a set of locations $P=\{p_1,p_2,\dots\}$ and a set of facilities $F=\{f_1,f_2,\dots\}，|F|\ge k$ on a plane. We want to partition the facilities into $k$ disjoint subsets (each subset has at ...
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### Proving the Equivalence of REGEX r^n and r^{..n} when r Is Nullable

Im seeking clarification and a rigorous proof regarding the equivalence of r^n and r^{..n} in the context of formal languages, particularly when r is nullable. To clarify the terminology: r denotes ...
1 vote
36 views

### Overlap operator for simple ( regex-like ) Patterns

( Introduction ) Some Notation lower case letters, $a, b, c$ will be used to denote single symbols Upper case letters, $P, Q, R$ will be used to denote string of symbols $a\!:\!S$ means a string ...
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### Combining different length epsilon-ADU hash function families

For context, an $\epsilon$-almost delta universal ($\epsilon$-ADU) hash function family $\mathcal{H} = \{h : M \to D\}$ hashes inputs from $M$ to digests in $D$ such that for any distinct $m, m' \in M$...
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### Conversion between NP certificates

This might be a well-known fact, but I can't convince myself of whether this is true. Suppose I have some NP language and two different verifying procedures V and V' for L. For any x in L, is it the ...
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### What's the difference between "modular" and "compositional"?

When talking about reducing complexity in a software system, we often talk about making it "modular" by breaking it up into multiple modules that are all linked together to form the overall ...
239 views

### Halting problem proofs that do not utilise self-reference or diagonalization

Are there any proofs of the Halting problem that do not involve any self-reference, and diagonalization (or any diagonal argument) whatsoever? All the duplicate questions I have come across end up ...
157 views

### Sources that prove solving 2-SAT with DP takes linear time

Would anyone have any sources that describe/an explanation of how solving 2-SAT using dynamic programming takes a linear amount of time? Can't seem to find a text that proves it in detail/formality. ...
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### Examples of the value of proofs for algorithms

In teaching Intro. Algorithms to undergrads, one of the most difficult tasks is to motivate why they need to know how to prove things about algorithms. (For many students, at least in many US ...
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### Document references describing weaknesses for cutting planes and algebraic proof system?

Here, Fortnow says (section 4.3): Since then complexity theorists have shown similar weaknesses in a number of other proof systems including cutting planes, algebraic proof systems based on ...
1 vote
214 views

### Uniqueness of the distribution maximizing the channel capacity

Setting: We look at a discrete memoryless channel which takes an input probability distribution acting over symbols in $\mathcal{X}$ to an output probability distribution over symbols in $\mathcal{Y}$....
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### Formally prove that the loops of this sorting algorithm will terminate [closed]

Given is the sorting algorithm Bubblesort ...
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1 vote
327 views

### EXPSPACE proof and its implications

I'm dealing with the min-max regret 0-1 Integer Linear Programming problem (MMR-ILP, for short), which is formulated as below. \label{eq:nip_obj} \min_{x \in \Phi} \sum_{i = 1}^n ...
702 views

### Possible to do Complexity theory with only counting and Pigeonhole

Most of the proofs in the book Computational complexity by Barak and Arora seem to be Pigeonhole in disguise. What are some places in Complexity theory where counting and Pigeonhole was insufficient ...
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### How would proof of the Lindelöf hypothesis improve our understanding of computational complexity classes?

A recent press release from the Viterbi School of Engineering at USC discussed the proof of the Lindelöf hypothesis by Athanassios Fokas, a visiting professor from the Department of Applied ...
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1 vote
141 views

### Proof of Sipser-Lautmann Theorem

I have written the following answer as an attempt to prove a variation of Sispser-Lautmann theorem, but it was rejected without any comments. I would appreciate if anyone can find the flaws in this ...
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1k views

### Examples of algorithms and proofs that seem correct, but aren't

In my intro to programming course, we're learning about the Initialization-Maintenance-Termination method of proving an algorithm does what we expect it to. But we've only had to prove that an ...
• 153
5k views

### What's the status of Babai's Graph isomorphism result?

It's been over a year since his January 2017 retraction and correction. Is there news? If not is this normal for validation to take this long? I would expect it would get plenty of attention. Has ...
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### Formally proving no algorithm exists [closed]

Are there standard techniques to show that no algorithms exist for given complexity constraints? For example, consider the following problem. The input is a list of items with exactly one duplicate, ...
217 views

### Graph optimization problem with multiple objectives/constraints

Let's assume that we have a directed acyclic graph $G = (V, E)$, non-negative vertex weight functions $w_a(v)$ and $w_b(v)$, and a non-negative edge weight function $t(u,v)$. We can divide vertices in ...
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