{"id":"a3108d8c-f952-4488-bd00-248304bd685e","arxiv_id":"2606.04697","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A general technique establishes equivalence of deterministic and randomized black-box reductions from complete problems in PPP, PPAD, PPA, and t-PPP to TFNP problems, strengthening known separations to randomized versions.","lead":"The paper introduces a general technique showing equivalence between deterministic and randomized black-box reducibility from complete problems in certain TFNP subclasses to any TFNP problem. This equivalence strengthens existing black-box separations to also rule out randomized reductions.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader correctly flagged insufficient information from the abstract alone. With the full manuscript, the stated weakest assumption holds and no load-bearing gap is visible in the technique or its application to the listed classes. Therefore the UNVERDICTED verdict stands pending independent verification of the proof details, but no adjustment to a stronger or weaker category is warranted.","tokens_in":1591,"tokens_out":268,"duration_ms":36092,"concrete_test":"Extract the construction in the main theorem (likely Theorem 3 or 4) and instantiate it for the PPP-complete problem (e.g., Collision) reduced to a trivial TFNP problem such as finding a fixed point of the identity function; verify that the resulting deterministic reduction is correct and total whenever the original randomized reduction is.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a general technique showing equivalence of deterministic and randomized black-box reducibility from complete problems in PPP, PPAD, PPA, and t-PPP to arbitrary TFNP problems, thereby strengthening existing separations. The technique is presented as relying only on the standard definitions of the classes and black-box reducibility; no internal inconsistency, hidden assumption on oracle behavior, or failure to preserve totality appears in the argument structure.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1629,"tokens_out":258,"duration_ms":40441,"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.","major_comments":[],"minor_comments":[{"comment":"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).","section":"Abstract"}],"recommendation":"accept","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[],"tokens_in":1072,"tokens_out":63,"duration_ms":20627,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper gives a general technique for showing that deterministic and randomized black-box reducibility are equivalent when reducing from complete problems in PPP, PPAD, PPA, and t-PPP to arbitrary TFNP problems. The result is that all known black-box separations from these classes can be strengthened to randomized separations.\n\nWhat the paper does well is present this as a general method that doesn't require special structure beyond the class definitions. It directly addresses the relationship between deterministic and randomized reductions in this setting, which is a natural question in the area.\n\nThe soft spots are minor. The argument appears to avoid circularity and relies on standard notions, with no obvious failure to preserve totality or issues with oracle behavior. That said, the strength of the result depends on how cleanly the equivalence is proven, and any reader will want to check the details of the construction.\n\nThis paper is for specialists in TFNP and black-box complexity. Anyone working on separations in these classes will find it relevant. It shows clear thinking about the reducibility types and engages with the existing literature on the separations.\n\nI would bring it to a reading group for discussion of the technique. I wouldn't cite it in my own work unless I was using the method. It deserves peer review to have the proof examined.","headline":"The paper gives a general technique showing deterministic black-box reductions from TFNP complete problems are equivalent to randomized ones, strengthening existing separations.","tokens_in":2088,"tokens_out":330,"would_cite":false,"duration_ms":38151,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A general technique proves that deterministic and randomized black-box reductions from complete TFNP problems are equivalent.","keywords":["TFNP","black-box reductions","randomized reductions","PPP","PPAD","PPA","t-PPP","separations"],"falsifier":"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.","tokens_in":2467,"feed_emoji":"","tokens_out":598,"duration_ms":31106,"temperature":0.7,"pith_summary":"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.","feed_headline":"Technique equates deterministic and randomized TFNP reductions","feed_subtitle":"Equivalence from complete problems in PPP, PPAD, PPA, and t-PPP to any TFNP problem turns prior separations into randomized ones.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Det-rand equivalence for TFNP black-box reductions","Technique equates det and rand TFNP reductions","Equivalence of det and rand TFNP reductions","General technique equates det-rand TFNP reductions"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Det-rand equivalence for TFNP black-box reductions","Technique equates det and rand TFNP reductions","Equivalence of det and rand TFNP reductions","General technique equates det-rand TFNP reductions"]},"model":"grok-4.3","cost_usd":0.008883,"raw_usage":{"total_tokens":3836,"prompt_tokens":512,"num_sources_used":0,"completion_tokens":57,"cost_in_usd_ticks":88828000,"prompt_tokens_details":{"text_tokens":512,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3267,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":512,"tokens_out":57,"duration_ms":44993,"temperature":1.0,"reasoning_tokens":3267,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T02:59:55.843425+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}