A plausible breakthrough towards P ⊂ PSPACE
https://www.quantamagazine.org/for-algorithms-a-little-memory-outweighs-a-lot-of-time-20250521/
#TheoreticalComputerScience #ComplexityTheory

People say it's a misconception that quantum computers can evaluate a function on all its possible inputs in parallel. But actually a lot of quantum algorithms do begin by applying a function to a superposition of all possible inputs. It's just that after that point you need to do some difficult linear algebra and you can't always extract the information you want.

In fact, you can define a lot of important complexity classes in this way. The set of problems solvable in polynomial time with an oracle that evaluates a given circuit on all its possible inputs and tells you …

P: … nothing.
BPP: … a randomly chosen output.
PP: … a majority output.
NP: … if any of the outputs is nonzero.
co-NP: … if all of the outputs are nonzero.
PSPACE: … a fixed point.

#Math #Maths #Mathematics #ComputerScience #TheoreticalComputerScience #Quantum #QuantumComputing

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

Just because its turin complete and computable and can define bool/if-else, currying recursion, church numerals and exprs reduce correctly shouldnt mean that it can attribute a computational meaning to an otherwise absurd #math expression
Or should it?
My question is computational meaning even a thing ? If yes , how does that even relate to meaning applied math
I mean the count of 1 , 2, 3 can always be attributed to something g physically measurable
#theoreticalcomputerscience
-- noob

Is there a meaningful way to characterize some "fastest growing function", subject to particular computational limitations? (I answered a question today that asked if all computable functions have polynomial bounds, which they obviously don't.)

We can't ask for the fastest-growing function in FP, because the composition of polynomial runtimes is polynomial. So if f(x) is in FP, so is the faster-growing f(f(x)).

Could we identify the fastest-growing function (using binary) in DTIME(n^2)? It seems like it would be something like "given an n-bit input, write n^2 1's after the input". So if the input was 2^a, we'd get 2^a * 2^(a^2) + (2^(a^2+1) - 1) as output.

But, strictly speaking, there would be a little bit of overhead meaning we couldn't do quite that well. The algorithm above is in DTIME(O(n^2)) but not DTIME(n^2). So it feels like there is a sequence of functions that converges on this one, but there might not be any best possible. And if we permit O(n^2) we're back to not having any fastest-growing function again because we can just slap bigger multiples on our allowed runtime.

So, is there a nontrivial class of computable functions that has an unambiguously fastest-growing member?

#TheoreticalComputerScience

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

This Karp Distinguished Lecture at at the Simons Institute by Rocco Servedio on July 10 on "New Directions in Property Testing" looks exciting! Rocco is a fantastic speaker.
https://simons.berkeley.edu/events/new-directions-property-testing-richard-m-karp-distinguished-lecture

The Karp Lectures are public lectures, meant for a broad, general #TheoreticalComputerScience audience. Registration is free, in person or online.

To check your time zone: https://timeanddate.com/worldclock/converter.html?iso=20240710T223000&p1=tz_pt&p2=240&p3=195&p4=179&p5=438&p6=236

Call for papers for the LearnAut (#Learning and #Automata) 2024 workshop co-located with ICALP/LICS/FSCD!

Please consider submitting your work. 😊

"The aim of this workshop is to bring together experts on #FormalLanguageTheory that could benefit from #GrammaticalInference tools, and researchers in grammatical inference who could find new insights for their methods in #TheoreticalComputerScience. [...] We do accept submissions of work recently published, currently under review or work-in-progress."

https://learnaut24.github.io/

📢 Next week (Wed 12/13) on TCS+: at 10am PT/1pm ET, Aaron Bernstein from Rutgers University will speak on "Negative-Weight Single-Source Shortest Paths in Near-linear Time." Join us for the last TCS+ talk of 2023! #Algorithms #TheoreticalComputerScience

Details: https://tcsplus.wordpress.com/2023/12/06/tcs-talk-wednesday-december-13-aaron-bernstein-rutgers-university/

Register (optional): https://docs.google.com/forms/d/e/1FAIpQLSdSrnuZ2jH8KGepSEJ0uz_iCRr7mJtMntIu6ZBsXIhhKovI6A/viewform

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,

#3SAT,

#3Partition,

#subquadratic,

#subcubic,

#Finegrained,

#HardnessExploration,

#NP,

#PSPACE,

#NPComplete,

#LogSpace,

#ExponentialComplexity,

#ParallelComputation,

#PvsNP,

#NPSPACE,

#NonDeterministicSpace, hashtag

#SavitchTheorem,

#ComplexityClasses,

#Reductions,

#ImportantProblems,

#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/

📢 Next week (Wed 9/27) at 10:00am PT, Hanlin Ren from Oxford will give the first TCS+ talk of the season, on "Polynomial-Time Pseudodeterministic Construction of Primes." #TheoreticalComputerScience

Details: https://tcsplus.wordpress.com/2023/09/20/tcs-talk-wednesday-september-27-hanlin-ren-university-of-oxford/

Register (optional): https://docs.google.com/forms/d/e/1FAIpQLScenFfBzn6Kl45Y1reJAB08D1V4Sd_z0eQTgG76XsG4lpPV1w/viewform

Here's a really interesting (long) paper on what a theory of computing based on arbitrary physical substrates might look like: http://arxiv.org/abs/2307.15408

"Toward a formal theory for computing machines made out of whatever physics offers: extended version"

Herbert Jaeger, Beatriz Noheda, Wilfred G. van der Wiel (2023)

@bnoheda

#NewPaper #TheoreticalComputerScience #neuromorphic #CogSci #CognitiveScience #VSA #VectorSymbolicArchitecture #HDC #HyperdimensionalComputing #AnalogComputing

Collective #math / #TheoreticalComputerScience memory question: Sometime in the last couple of months I followed a link from Masto to a blog post about computing (in the most general sense) defined as continuous rather than discrete mathematics. This blog post mentioned (with references) that having *partial* functions was essential for computation.

Now I can't find the blog post or references. Any pointers to works explaining why partial functions are essential to computation (or refutation) would be greatly appreciated.

ChatGPT introduces me a branch of #theoreticalComputerScience called "#gameSemantics" today!

#gameTheory

@Jose_A_Alonso #ComputationalComplexity #theoreticalComputerScience #TCS #phdPosition

Very nice and clear article by @benbenbrubaker on @QuantaMagazine, describing the meaning and implications of the latest advances regarding random #quantum circuit sampling:
https://www.quantamagazine.org/new-algorithm-closes-quantum-supremacy-window-20230109/

Heck, I felt I understood something! #TheoreticalComputerScience #TCS #ComputationalComplexity

ICYMI, there's been a series of online talks on "adversarially robust streaming #algorithms" on the Foundations of #DataScience virtual seminar series. The first 3 recordings are available:
https://sites.google.com/view/dstheory/past-talks_1

David Woodruff on "Adversarially Robust Streaming Algorithms"

Edith Cohen "On Robustness to Adaptive Inputs: A Case Study of CountSketch"

Omri Ben-Eliezer on "Robust sampling and online learning"

(one or two more to come this semester!) #TheoreticalComputerScience #TCS #talks

Hey, that seems cool!* Zero-Knowledge proofs in the streaming setting (verifier has limited working memory, gets one pass over the input).
https://arxiv.org/abs/2301.02161
By Cormode, Dall’Agnol, @tomgur, and Hickey. #TCS #arXiv #TheoreticalComputerScience

* Except for the default bright green color of the links, that is :)

Oh, polynomial3sat.org is down and the respective code on GitHub is removed. The corresponding paper on arXiv is still accessible. Does anyone know more about what happened?

https://arxiv.org/abs/1903.10081

#satsolving #complexitytheory #PequalsNP #compsci #theoreticalcomputerscience

I have been making an online #weaeklyquiz 📊 in #TheoreticalComputerScience and #maths for more than 3 years now: first on Twitter weekly, now fortnightly both there and here on Mastodon. If you're interested, all the #quiz threads and their answers are listed here:
https://ccanonne.github.io/weeklyquiz.html