Lmst

Taucht ein in die faszinierende Welt der booleschen Satisfiability (SAT) mit Python! 🐍💻
Von einfachen Konzepten bis hin zu komplexen Algorithmen wie DPLL und CDCL – dieser Artikel erklärt, warum SAT-Probleme die Grundlage vieler realer Anwendungen bilden und wie sie mit P vs. NP verbunden sind. Lest mehr über die Herausforderungen und Schönheit der Berechenbarkeit! 🔍 #SAT #Python #Informatik #PvsNP
I Can’t Get No (Boolean) Satisfaction https://shairozsohail.medium.com/i-cant-get-no-boolean-satisfaction-0765a068b3b2

😎

Shortest-possible walking tour to 81,998 bars in South Korea https://www.math.uwaterloo.ca/tsp/korea/index.html #TSP #PvsNP #math

Solving P = NP would be a master key, but for what? #PvsNP #ComplexityTheory #CyberSecurity #AIResearch #Innovation #FutureOfTech #Mathematics #TheoreticalComputerScience #Optimization #DigitalInfrastructure

https://t.co/qgPMixQpt6

This paper addresses the P versus NP problem, one of the most signiﬁcant
open questions in theoretical computer science and mathematics. We present a
novel approach to understanding the relationship between these complexity classes,
examining the structural properties of NP-complete problems and their potential
reducibility to polynomial-time algorithms. We introduce the concept of P = NP as
a potential ”master key” that would unlock eﬃcient solutions to countless problems
previously considered intractable. Our analysis explores both the tremendous bene-
ﬁts this breakthrough would bring to optimization, medicine, artiﬁcial intelligence,
and creative endeavors, alongside the potentially catastrophic implications for cy-
bersecurity and global digital infrastructure. We also examine important caveats,
including the distinction between constructive and non-constructive proofs and the
possibility of high-degree polynomial algorithms that would remain impractical.
The paper further explores philosophical implications, questioning how computa-
tional eﬃciency might transform our understanding of creativity, discovery, and the
nature of diﬃcult problems. This comprehensive examination reveals the profound
paradox at the heart of the P versus NP question—a mathematical discovery that
could simultaneously advance humanity’s capabilities and undermine its security
foundations.

Please DO NOT ask me to comment on this newly published "proof" of P != NP.

https://eprint.iacr.org/2025/445

#PvsNP #Cryptography #computerscience

P=NP, proof by halting problem V2

#OnePolynomial #OneP

#math #theory #pvsnp #pequalnp #pnp #mathematics #cs #computerscience #solution #proof

https://onepolynomial.wordpress.com/2024/10/21/pnp-proof-by-halting-problem-v2/

P=NP, proof by halting problem

#pvsnp #pequalnp #pnp #onepolynomial #oneP #cs #theory #math #mathematics #computerscience #proof

https://onepolynomial.wordpress.com/2024/10/17/pnp-proof-by-halting-problem/

P=NP

https://onepolynomial.wordpress.com/2024/10/16/pnp/

#onepolynomial #pnp #pvsnp #pequalnp #cs #computerscience #theoreticalcomputerscience #math #mathematics #proof #new #discovery #result #results #groundbreaking

@aragubas Get ready for a computer science info dump.

What @crumbcake described in his last reply is the halting problem, which is undecidable. In other words, it's impossible for a computer (as we currently define them) to answer that problem for every possible input. Computerphile did a 6 minute video explaining the halting problem and why it's undecidable if you'd like to know more.

The question of P vs NP is, informally stated, this: If it's easy to check an answer to a problem, is it also easy to find an answer? An example of such a problem is sudoku. It's pretty easy to look over a completed grid for correctness but it seems much harder to find a solution to an incomplete grid. But is it harder under the more rigorous computer science definitions of computational complexity? We actually don't know, and there's a million dollar prize if you can prove it one way or the other.

If you'd like to learn a little more, I'd highly recommend this 11 minute long video about the computational complexity zoo for a relatively approachable introduction to all these concepts. Enjoy. 💙

#ComputerScience #PvsNP #HaltingProblem #ComputationalComplexity

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

In our effort to put courses online, we continue lectures on Algorithmic Lower Bound Course. Now you can watch

Lesson 4-11: Algorithmic Lower Bounds by Mohammad Hajiaghayi - NP-Completeness and Beyond

(FEEL FREE TO SUBSCRIBE TO YOUTUBE @hajiaghayi FOR FUTURE LESSONS Premiering on WEDNESDAYS)

https://youtu.be/VZyffnAb1r0 (Lesson 4: 3-Partition Problem & Proving NP-Hardness)

https://youtu.be/4fCD9_1eQw0 (Lesson 5: Puzzle Problem NP-Hardness & 3-Partition)

https://youtu.be/FIyEj72-UJQ (Lesson 6: 3-SAT Problem & Proving NP-Hardness)

https://youtu.be/tbSJzaKx2pA (Lesson 7: Puzzle Problem NP-Hardness via 3-SAT)

https://youtu.be/voRVebBsh94 (Lesson 8: Fine-grained Subcubic Complexity: Part 1)

https://youtu.be/gRURSM6QARo (Lesson 9: Fine-grained Subcubic Complexity: Part 2)

https://youtu.be/qPw82bTAXkc (Lesson 10: Fine-grained Subquadratic Complexity 1)

https://youtu.be/C6j4avVkI7U (Lesson 11: Fine-grained Subquadratic Complexity 2)

#AlorithmicComplexity,

#HardnessExploration,

#NP,

#PSPACE,

#NPComplete,

#LogSpace,

#ExponentialComplexity,

#ParallelComputation,

#PvsNP,

#NPSPACE,

#NonDeterministicSpace, hashtag

#CommunicationComplexity, hashtag

#GeometricProblems,

#AlgorithmDesign,

#ComputationalComplexity,

#TheoreticalComputerScience,

#AlgorithmicLowerBounds

For comprehensive handwritten lecture notes on this course, visit the instructor's website:

http://www.cs.umd.edu/~hajiagha/
The course textbook "Computational Intractability: A Guide to Algorithmic Lower Bounds" by Demaine, Gasarch, and Hajiaghayi is available for free at:

https://hardness.mit.edu/

#GeorgeWBush #someone #discovered #ou #secret #PvsNP #algorithm #publish #astonished #phdstudent #doctoratestudent #phd #doctorate #motivation #meme #memes #phdmotivation #phdmeme #phdmemes #phdlife #phdstudentlife #phdtroll #doctoratemotivation #doctoratememe #doctoratememes #doctoratelife #doctoratestudentlife #doctoratetroll

Addendum 13

Large Language Model for Science: P vs. NP
https://arxiv.org/abs/2309.05689

* LLM to augment/accel. research on P vs. NP problem: https://en.wikipedia.org/wiki/P_versus_NP_problem
+ unsolved prob., theor. comp. sci.
+ asks wh. every problems quickly verified can also be quickly solved
* in-depth thinking w. LLM for complex problem-solving
* GPT-4 produced proof schema, engaged in rigorous reasoning throughout 97 dialogue turns (Socratic method)
* concluded P ≠ NP in alignment w. Xu & Zhou 2023

#LLM #GPT4 #PvsNP