44 research outputs found
What Does it Mean that PRIMES is in P: Popularization and Distortion Revisited
In August 2002, three Indian computer scientists published a paper, ‘PRIMES is in P’, online. It presents a ‘deterministic algorithm’ which determines in ‘polynomial time’ if a given number is a prime number. The story was quickly picked up by the general press, and by this means spread through the scientific community of complexity theorists, where it was hailed as a major theoretical breakthrough. This is although scientists regarded the media reports as vulgar popularizations. When the paper was published in a peer-reviewed journal only two years later, the three scientists had already received wide recognition for their accomplishment.
Current sociological theory challenges the ability to clearly distinguish on independent epistemic grounds between distorted and non-distorted scientific knowledge. It views the demarcation lines between such forms of presentation as contextual and unstable. In my paper, I challenge this
view. By systematically surveying the popular press coverage of the ‘PRIMES is in P’ affair, I argue--against the prevailing new orthodoxy--that distorted simplifications of scientific knowledge are distinguishable from non-distorted simplifications on independent epistemic grounds. I argue
that in the ‘PRIMES is in P’ affair, the three scientists could ride on the wave of the general press-distorted coverage of their algorithm, while counting on their colleagues’ ability to distinguish genuine accounts from distorted ones. Thus, their scientific reputation was unharmed. This suggests that the possibility of the existence of independent epistemic standards must be incorporated into the new SSK model of popularization
Consistency of circuit lower bounds with bounded theories
Proving that there are problems in that require
boolean circuits of super-linear size is a major frontier in complexity theory.
While such lower bounds are known for larger complexity classes, existing
results only show that the corresponding problems are hard on infinitely many
input lengths. For instance, proving almost-everywhere circuit lower bounds is
open even for problems in . Giving the notorious difficulty of
proving lower bounds that hold for all large input lengths, we ask the
following question: Can we show that a large set of techniques cannot prove
that is easy infinitely often? Motivated by this and related
questions about the interaction between mathematical proofs and computations,
we investigate circuit complexity from the perspective of logic.
Among other results, we prove that for any parameter it is
consistent with theory that computational class , where is one of
the pairs: and , and , and
. In other words, these theories cannot establish
infinitely often circuit upper bounds for the corresponding problems. This is
of interest because the weaker theory already formalizes
sophisticated arguments, such as a proof of the PCP Theorem. These consistency
statements are unconditional and improve on earlier theorems of [KO17] and
[BM18] on the consistency of lower bounds with