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Randomized separations in black-box TFNP

T0 review · 0 major / 1 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read A general technique proves that deterministic and randomized black-box reductions from complete TFNP problems are equivalent.

desk verdict The paper gives a general technique showing deterministic black-box reductions from TFNP complete problems are equivalent to randomized ones, strengthening existing separations. read the letter →

arxiv 2606.04697 v1 pith:NHL3VJVT submitted 2026-06-03 cs.CC

Fedor Kiselev This is my paper · ORCID
classification cs.CC
keywords TFNPblack-boxreductionsrandomizedPPPPPADPPAt-PPPseparations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper develops a general technique showing equivalence between deterministic and randomized black-box reducibility from specific TFNP problems to any TFNP problem. This equivalence is established in particular for reductions from the complete problems in PPP, PPAD, PPA, and t-PPP. As a direct result, every previously known black-box separation originating from these classes extends to randomized reductions as well. A reader would care because TFNP problems model total search tasks whose hardness under reductions determines the structure of many computational classes.

What carries the argument

A general technique that equates deterministic and randomized black-box reducibility from complete problems in PPP, PPAD, PPA, and t-PPP to arbitrary TFNP problems.

What would settle it

An explicit TFNP problem together with a deterministic black-box reduction from a PPP-complete problem that admits no corresponding randomized black-box reduction, or vice versa.

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Extended reading notes

Core claim

Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and t-PPP. In turn, it strengthens all known black-box separations, originating from these classes, to randomized separations.

Load-bearing premise

The equivalence technique applies to reductions from the complete problems using only the standard definitions of the classes and black-box reducibility, without extra structural assumptions.

Editorial extensions

If this is right

  • Every known black-box separation from PPP, PPAD, PPA, or t-PPP becomes a randomized separation.
  • Reductions from the complete problems in these classes to any TFNP problem are equivalent whether or not randomness is allowed.
  • The technique requires no additional assumptions beyond the ordinary definitions of the classes and black-box reducibility.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Randomness confers no extra power for black-box reductions originating from these four classes.
  • Future separation proofs for TFNP can be carried out entirely in the deterministic setting and then automatically inherit the randomized version.
  • Similar equivalence techniques might apply to other total-search classes whose complete problems admit certain syntactic properties.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 1 minor

Summary. The manuscript studies deterministic versus randomized black-box reducibility within TFNP. Its central claim is a general technique proving that, for reductions from the complete problems of PPP, PPAD, PPA, and t-PPP to an arbitrary TFNP problem, the existence of a deterministic black-box reduction is equivalent to the existence of a randomized one; the technique is then applied to convert all previously known black-box separations originating from these classes into randomized separations.

Significance. If the equivalence technique holds, the result is significant: it strengthens every known black-box separation from the listed classes to a randomized separation while relying only on the standard definitions of the classes and of black-box reducibility, without additional structural assumptions on the target TFNP problem or on oracle behavior. The generality of the technique (applicable to any TFNP target) is a clear strength.

minor comments (1)
  1. [Abstract] The abstract and introduction would benefit from a one-sentence sketch of the key idea underlying the general equivalence technique (e.g., how totality is preserved under randomization).

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive recommendation to accept and for confirming the significance of the general equivalence technique between deterministic and randomized black-box reductions from the complete problems in PPP, PPAD, PPA, and t-PPP.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation relies on standard definitions

full rationale

The paper introduces a general technique establishing equivalence between deterministic and randomized black-box reducibility from complete problems in PPP, PPAD, PPA, and t-PPP to arbitrary TFNP problems. This equivalence is presented as following directly from the standard definitions of the classes and black-box reducibility notions, without any self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations. The strengthening of existing separations is a consequence of this equivalence applied to the standard definitions.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Abstract-only review provides no details on free parameters, specific axioms, or invented entities; standard complexity-theoretic definitions of TFNP and black-box reductions are presupposed.

assumptions (1)
  • domain assumption Standard definitions and properties of TFNP, PPP, PPAD, PPA, t-PPP, and black-box reducibility hold.
    The result relies on these foundational notions from complexity theory.

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Cite this review

Pith. "Pith review of Randomized separations in black-box TFNP." pith.science (2026). https://pith.science/paper/NHL3VJVT

@misc{pith2026260604697,
  author       = {Pith},
  title        = {Pith review of: Randomized separations in black-box TFNP},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NHL3VJVT}},
  note         = {Machine review of arXiv:2606.04697}
}
abstract

We study the relationship between deterministic and randomized black-box reducibility between problems in TFNP. Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and $t$-PPP. In turn, it strengthens all known black-box separations, originating from these classes, to randomized separations.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

22 extracted references · 17 canonical work pages

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Reviewed June 28, 2026 · model on record in the stance chip above.