Debate is efficient with your time

• URL: http://arxiv.org/abs/2602.08630v1
• Date: Mon, 09 Feb 2026 13:21:32 GMT
• Title: Debate is efficient with your time
• Abstract summary: We introduce Debate Query Complexity(DQC), the minimum number of bits a verifier must inspect to correctly decide a debate.<n>We find that PSPACE/poly is precisely the class of functions decidable with O(log n) queries.<n>We also establish that functions depending on all their input bits require Omega(log n) queries, and that any function computable by a circuit of size s satisfies DQC(f) = log(s) + 3.
• Score: 26.121215987560635
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: AI safety via debate uses two competing models to help a human judge verify complex computational tasks. Previous work has established what problems debate can solve in principle, but has not analysed the practical cost of human oversight: how many queries must the judge make to the debate transcript? We introduce Debate Query Complexity}(DQC), the minimum number of bits a verifier must inspect to correctly decide a debate. Surprisingly, we find that PSPACE/poly (the class of problems which debate can efficiently decide) is precisely the class of functions decidable with O(log n) queries. This characterisation shows that debate is remarkably query-efficient: even for highly complex problems, logarithmic oversight suffices. We also establish that functions depending on all their input bits require Omega(log n) queries, and that any function computable by a circuit of size s satisfies DQC(f) <= log(s) + 3. Interestingly, this last result implies that proving DQC lower bounds of log(n) + 6 for languages in P would yield new circuit lower bounds, connecting debate query complexity to central questions in circuit complexity.

Related papers

• How Hard is it to Decide if a Fact is Relevant to a Query? [1.6058099298620423]
  Given a database D, a Boolean conjunctive query (CQ) q, and fact f in D, decide whether f is relevant to q wrt.<n>We identify self-joins (multiple atoms with the same relation) as the culprit.<n>Our results thus pinpoint what makes relevance harder than query evaluation and identify natural classes of queries which admit efficient relevance computation.
  arXiv  Detail & Related papers  (2026-04-24T10:29:27Z)
• OrLog: Resolving Complex Queries with LLMs and Probabilistic Reasoning [51.58235452818926]
  We introduce OrLog, a neuro-symbolic retrieval framework that decouples predicate-level plausibility estimation from logical reasoning.<n>A large language model (LLM) provides plausibility scores for atomic predicates in one decoding-free forward pass, from which a probabilistic reasoning engine derives the posterior probability of query satisfaction.
  arXiv  Detail & Related papers  (2026-01-30T15:31:58Z)
• Avoiding Obfuscation with Prover-Estimator Debate [33.14645106993676]
  We propose a protocol for AI debate that guarantees the correctness of human judgements for complex problems.<n>We show that a dishonest debater can use a computationally efficient strategy that forces an honest opponent to solve a computationally intractable problem to win.
  arXiv  Detail & Related papers  (2025-06-16T15:37:33Z)
• Efficient and Scalable Neural Symbolic Search for Knowledge Graph Complex Query Answering [50.1887329564127]
  We propose an efficient and scalable symbolic search framework for complex queries.<n>Our framework reduces the computational load of symbolic methods by 90% while maintaining nearly the same performance.
  arXiv  Detail & Related papers  (2025-05-13T01:24:09Z)
• Critical Thinking: Which Kinds of Complexity Govern Optimal Reasoning Length? [72.70486097967124]
  We formalize a framework using deterministic finite automata (DFAs)<n>We show that there exists an optimal amount of reasoning tokens such that the probability of producing a correct solution is maximized.<n>We then demonstrate an implication of these findings: being able to predict the optimal number of reasoning tokens for new problems and filtering out non-optimal length answers results in consistent accuracy improvements.
  arXiv  Detail & Related papers  (2025-04-02T17:45:58Z)
• Advancing Algorithmic Approaches to Probabilistic Argumentation under the Constellation Approach [0.0]
  We develop an algorithm for the complex task of computing the probability of a set of arguments being a complete extension. An experimental evaluation shows promise of our approach.
  arXiv  Detail & Related papers  (2024-07-06T12:08:38Z)
• On scalable oversight with weak LLMs judging strong LLMs [67.8628575615614]
  We study debate, where two AI's compete to convince a judge; consultancy, where a single AI tries to convince a judge that asks questions. We use large language models (LLMs) as both AI agents and as stand-ins for human judges, taking the judge models to be weaker than agent models.
  arXiv  Detail & Related papers  (2024-07-05T16:29:15Z)
• Exceeding Computational Complexity Trial-and-Error Dynamic Action and Intelligence [0.0]
  Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. In this paper, we try to clarify concepts, and we propose definitions such as unparticularized computing, particularized computing, computing agents, and dynamic search. We also propose and discuss a framework, i.e., trial-and-error + dynamic search.
  arXiv  Detail & Related papers  (2022-12-22T21:23:27Z)
• Successive Prompting for Decomposing Complex Questions [50.00659445976735]
  Recent works leverage the capabilities of large language models (LMs) to perform complex question answering in a few-shot setting. We introduce Successive Prompting'', where we iteratively break down a complex task into a simple task, solve it, and then repeat the process until we get the final solution. Our best model (with successive prompting) achieves an improvement of 5% absolute F1 on a few-shot version of the DROP dataset.
  arXiv  Detail & Related papers  (2022-12-08T06:03:38Z)
• On Theoretical Complexity and Boolean Satisfiability [0.0]
  This thesis introduces some of the most central concepts in the Theory of Computing. We then explore some of its tractable as well as intractable variants such as Horn-SAT and 3-SAT. Finally, we establish reductions from 3-SAT to some of the famous NP-complete graph problems.
  arXiv  Detail & Related papers  (2021-12-22T10:13:34Z)
• A tetrachotomy of ontology-mediated queries with a covering axiom [1.749935196721634]
  Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description and their optimal rewritings to standard database queries. We focus on Boolean conjunctive-mediated queries called disjunctive sirups (or d-sirups) Some d-sirups only have exponential-size resolution features, some only double-exponential-size positive existential existential-rewritings and single-exprecursive datalog rewritings.
  arXiv  Detail & Related papers  (2020-06-07T14:47:07Z)
• From Checking to Inference: Actual Causality Computations as Optimization Problems [79.87179017975235]
  We present a novel approach to formulate different notions of causal reasoning, over binary acyclic models, as optimization problems. We show that both notions are efficiently automated. Using models with more than $8000$ variables, checking is computed in a matter of seconds, with MaxSAT outperforming ILP in many cases.
  arXiv  Detail & Related papers  (2020-06-05T10:56:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.