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The oracle problem refers to the inability of an agent to know if the information coming from an oracle is authentic and unbiased. In ancient times, philosophers and historians debated on how to evaluate, increase, and secure the reliability of oracle predictions, particularly those from Delphi, which pertained to matters of state. Today, we refer to data carriers for automatic machines as oracles, but establishing a secure channel between these oracles and the real world still represents a challenge. Despite numerous efforts, this problem remains mostly unsolved, and the recent advent of blockchain oracles has added a layer of complexity because of the decentralization of blockchains. This paper conceptually connects Delphic and modern blockchain oracles, developing a comparative framework. Leveraging blockchain oracle taxonomy, lexical analysis is also performed on 167 Delphic queries to shed light on the relationship between oracle answer quality and question type. The presented framework aims first at revealing commonalities between classical and computational oracles and then at enriching the oracle analysis within each field. This study contributes to the computer science lit

In recent years, the quantum oracle model introduced by Aaronson and Kuperberg (2007) has found a lot of use in showing oracle separations between complexity classes and cryptographic primitives. It is generally assumed that proof techniques that do not relativize with respect to quantum oracles will also not relativize with respect to classical oracles. Aaronson (2009) showed that this is not the case by showing a complexity class containment that relativizes with respect to classical oracles but not with quantum oracles. However, their result only works for zero-error quantum complexity classes and they leave open the problem for bounded-error complexity classes. We show that there is a quantum oracle problem that is contained in the class QMA, but not in a class we call polyQCPH. However, with respect to classical oracles, QMA is contained in polyQCPH, because polyQCPH is equal to PSPACE with respect to classical oracles. Our result works for polyQCPH, which is a bounded-error complexity class, thus it resolves the open problem from Aaronson (2009). We also show that the same separation holds relative to a distributional oracle, which is a model introduced by Natarajan and Nirkh

The effectiveness of testing in uncovering software defects depends not only on the characteristics of the test inputs and how thoroughly they exercise the software, but also on the quality of the oracles used to determine whether the software behaves as expected. Therefore, assessing the quality of oracles is crucial to improve the overall effectiveness of the testing process. Existing metrics have been used for this purpose, but they either fail to provide a comprehensive basis for guiding oracle improvement, or they are tailored to specific types of oracles, thus limiting their generality. In this paper, we introduce state field coverage, a novel metric for assessing oracle quality. This metric measures the proportion of an object's state, as statically defined by its class fields, that an oracle may access during test execution. The main intuition of our metric is that oracles with a higher state field coverage are more likely to detect faults in the software under analysis, as they inspect a larger portion of the object states to determine whether tests pass or not. We implement a mechanism to statically compute the state field coverage metric. Being statically computed, the m

Deciphering oracle bone scripts plays an important role in Chinese archaeology and philology. However, a significant challenge remains due to the scarcity of oracle character images. To overcome this issue, we propose Diff-Oracle, a novel approach based on diffusion models to generate a diverse range of controllable oracle characters. Unlike traditional diffusion models that operate primarily on text prompts, Diff-Oracle incorporates a style encoder that utilizes style reference images to control the generation style. This encoder extracts style prompts from existing oracle character images, where style details are converted into a text embedding format via a pretrained language-vision model. On the other hand, a content encoder is integrated within Diff-Oracle to capture specific content details from content reference images, ensuring that the generated characters accurately represent the intended glyphs. To effectively train Diff-Oracle, we pre-generate pixel-level paired oracle character images (i.e., style and content images) by an image-to-image translation model. Extensive qualitative and quantitative experiments are conducted on datasets Oracle-241 and OBC306. While signific

Suppose we have a two-party communication protocol for $f$ which allows the parties to make queries to an oracle computing $g$; for example, they may query an Equality oracle. To translate this protocol into a randomized protocol, we must replace the oracle with a randomized subroutine for solving $g$. If $q$ queries are made, the standard technique requires that we boost the error of each subroutine down to $O(1/q)$, leading to communication complexity which grows as $q \log q$. For which oracles $g$ can this naive boosting technique be improved? We focus on the oracles which can be computed by constant-cost randomized protocols, and show that the naive boosting strategy can be improved for the Equality oracle but not the 1-Hamming Distance oracle. Two surprising consequences are (1) a new example of a problem where the cost of computing $k$ independent copies grows superlinear in $k$, drastically simplifying the only previous example due to Blais & Brody (CCC 2019); and (2) a new proof that Equality is not complete for the class of constant-cost randomized communication (Harms, Wild, & Zamaraev, STOC 2022; Hambardzumyan, Hatami, & Hatami, Israel Journal of Mathematics

Agent memory is a systems problem for long-horizon agents. Practical deployments require retention of task state across extended conversations, recovery of user-specific facts and preferences across sessions, and accumulation of procedural knowledge from prior outcomes. These requirements extend beyond document retrieval: a memory layer must determine which interactions become durable state, how that state is scoped, how it is retrieved under latency constraints, and how it is revised or removed over time. This report studies Oracle Agent Memory as a database-native memory substrate built on Oracle Database. Three themes organize the discussion: memory as a lifecycle spanning ingestion, extraction, consolidation, retrieval, summarization, and revision or removal; a layered architecture that separates an active memory core from a passive memory-store interface with explicit scope control across users, agents, and threads; and evaluation methodology in which downstream task accuracy is complemented by memory-centric measures such as evidence retrieval, recall, latency, and estimated token use. The report summarizes LongMemEval results, reaching 93.8% accuracy, compares Oracle Agent M

We introduce \emph{TAPO-Structured Description Logic} (TAPO--DL), a formal extension of classical description logic designed to model \emph{information behavior} as a structured, dynamic process. TAPO--DL extends the standard T--Box/A--Box architecture with two additional layers: a \emph{Procedural Box} (P--Box), which supports concept-driven, imperative-style programs such as conditional and iterative actions, and an \emph{Oracle Box} (O--Box), which formalizes controlled interaction with external information sources. While the terminological and assertional components capture static conceptual and factual knowledge, the procedural and oracle-based components enable the explicit representation of information-generating actions and external validation. We provide a unified semantic framework for TAPO--DL based on a co-generative, sheaf-theoretic interpretation, in which local informational states are modeled as sections and informational stability corresponds to the existence of coherent global structures. Within this setting, informational truth is characterized as stability under repeated agentive interaction rather than correspondence to a fixed global state. By integrating desc

By incorporating regret minimization, double oracle methods have demonstrated rapid convergence to Nash Equilibrium (NE) in normal-form games and extensive-form games, through algorithms such as online double oracle (ODO) and extensive-form double oracle (XDO), respectively. In this study, we further examine the theoretical convergence rate and sample complexity of such regret minimization-based double oracle methods, utilizing a unified framework called Regret-Minimizing Double Oracle. Based on this framework, we extend ODO to extensive-form games and determine its sample complexity. Moreover, we demonstrate that the sample complexity of XDO can be exponential in the number of information sets $|S|$, owing to the exponentially decaying stopping threshold of restricted games. To solve this problem, we propose the Periodic Double Oracle (PDO) method, which has the lowest sample complexity among regret minimization-based double oracle methods, being only polynomial in $|S|$. Empirical evaluations on multiple poker and board games show that PDO achieves significantly faster convergence than previous double oracle algorithms and reaches a competitive level with state-of-the-art regret

Language models exhibit remarkable natural language generation capabilities but remain prone to hallucinations, generating factually incorrect information despite producing syntactically coherent responses. This study introduces the Licensing Oracle, an architectural solution designed to stem hallucinations in LMs by enforcing truth constraints through formal validation against structured knowledge graphs. Unlike statistical approaches that rely on data scaling or fine-tuning, the Licensing Oracle embeds a deterministic validation step into the model's generative process, ensuring that only factually accurate claims are made. We evaluated the effectiveness of the Licensing Oracle through experiments comparing it with several state-of-the-art methods, including baseline language model generation, fine-tuning for factual recall, fine-tuning for abstention behavior, and retrieval-augmented generation (RAG). Our results demonstrate that although RAG and fine-tuning improve performance, they fail to eliminate hallucinations. In contrast, the Licensing Oracle achieved perfect abstention precision (AP = 1.0) and zero false answers (FAR-NE = 0.0), ensuring that only valid claims were gener

We give an oracle separation between QMA and QCMA for quantum algorithms that have bounded adaptivity in their oracle queries; that is, the number of rounds of oracle calls is small, though each round may involve polynomially many queries in parallel. Our oracle construction is a simplified version of the construction used recently by Li, Liu, Pelecanos, and Yamakawa (2023), who showed an oracle separation between QMA and QCMA when the quantum algorithms are only allowed to access the oracle classically. To prove our results, we introduce a property of relations called \emph{slipperiness}, which may be useful for getting a fully general classical oracle separation between QMA and QCMA.

The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum states. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We

Bennett and Gill (1981) showed that P^A != NP^A != coNP^A for a random oracle A, with probability 1. We investigate whether this result extends to individual polynomial-time random oracles. We consider two notions of random oracles: p-random oracles in the sense of martingales and resource-bounded measure (Lutz, 1992; Ambos-Spies et al., 1997), and p-betting-game random oracles using the betting games generalization of resource-bounded measure (Buhrman et al., 2000). Every p-betting-game random oracle is also p-random; whether the two notions are equivalent is an open problem. (1) We first show that P^A != NP^A for every oracle A that is p-betting-game random. Ideally, we would extend (1) to p-random oracles. We show that answering this either way would imply an unrelativized complexity class separation: (2) If P^A != NP^A relative to every p-random oracle A, then BPP != EXP. (3) If P^A = NP^A relative to some p-random oracle A, then P != PSPACE. Rossman, Servedio, and Tan (2015) showed that the polynomial-time hierarchy is infinite relative to a random oracle, solving a longstanding open problem. We consider whether we can extend (1) to show that PHA is infinite relative to oracle

Automation of test oracles is one of the most challenging facets of software testing, but remains comparatively less addressed compared to automated test input generation. Test oracles rely on a ground-truth that can distinguish between the correct and buggy behavior to determine whether a test fails (detects a bug) or passes. What makes the oracle problem challenging and undecidable is the assumption that the ground-truth should know the exact expected, correct, or buggy behavior. However, we argue that one can still build an accurate oracle without knowing the exact correct or buggy behavior, but how these two might differ. This paper presents SEER, a learning-based approach that in the absence of test assertions or other types of oracle, can determine whether a unit test passes or fails on a given method under test (MUT). To build the ground-truth, SEER jointly embeds unit tests and the implementation of MUTs into a unified vector space, in such a way that the neural representation of tests are similar to that of MUTs they pass on them, but dissimilar to MUTs they fail on them. The classifier built on top of this vector representation serves as the oracle to generate "fail" labe

In the classical prophet inequality settings, a gambler is given a sequence of $n$ random variables $X_1, \dots, X_n$, taken from known distributions, observes their values in this (potentially adversarial) order, and select one of them, immediately after it is being observed, so that its value is as high as possible. The classical \emph{prophet inequality} shows a strategy that guarantees a value at least half of that an omniscience prophet that picks the maximum, and this ratio is optimal. Here, we generalize the prophet inequality, allowing the gambler some additional information about the future that is otherwise privy only to the prophet. Specifically, at any point in the process, the gambler is allowed to query an oracle $\mathcal{O}$. The oracle responds with a single bit answer: YES if the current realization is greater than the remaining realizations, and NO otherwise. We show that the oracle model with $m$ oracle calls is equivalent to the \textsc{Top-$1$-of-$(m+1)$} model when the objective is maximizing the probability of selecting the maximum. This equivalence fails to hold when the objective is maximizing the competitive ratio, but we still show that any algorithm for

We discuss the problem of learning a deterministic finite automaton (DFA) from a confidence oracle. That is, we are given access to an oracle $Q$ with incomplete knowledge of some target language $L$ over an alphabet $Σ$; the oracle maps a string $x\inΣ^*$ to a score in the interval $[-1,1]$ indicating its confidence that the string is in the language. The interpretation is that the sign of the score signifies whether $x\in L$, while the magnitude $|Q(x)|$ represents the oracle's confidence. Our goal is to learn a DFA representation of the oracle that preserves the information that it is confident in. The learned DFA should closely match the oracle wherever it is highly confident, but it need not do this when the oracle is less sure of itself.

The effectiveness of a test suite in detecting faults highly depends on the correctness and completeness of its test oracles. Large Language Models (LLMs) have already demonstrated remarkable proficiency in tackling diverse software testing tasks, such as automated test generation and program repair. This paper aims to enable discussions on the potential of using LLMs for test oracle automation, along with the challenges that may emerge during the generation of various types of oracles. Additionally, our aim is to initiate discussions on the primary threats that SE researchers must consider when employing LLMs for oracle automation, encompassing concerns regarding oracle deficiencies and data leakages.

We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Distinct characterizations are provided for deterministic and stochastic signaling functions, based on simultaneous posterior matching, partition refinements, and common knowledge components. This study extends the work of Blackwell (1951) to games, and expands the study of Aumann (1976) on common knowledge, along with the companion Part II, which develops a theory of information loops.

This paper investigates the impact of noise in the quantum query model, a fundamental framework for quantum algorithms. We focus on the scenario where the oracle is subject to non-unitary (or irreversible) noise, specifically under the \textit{faulty oracle} model, where the oracle fails with a constant probability and acts as identity. Regev and Schiff (ICALP'08) showed that quantum advantage is lost for the search problem under this noise model. Our main result shows that every quantum query algorithm can be made robust in this noise model with a roughly quadratic blow-up in query complexity, thereby preserving quantum speedup for all problems where the quantum advantage is super-cubic. This is the first non-trivial robustification of quantum query algorithms against an oracle that is noisy.

Before the advent of alternative blockchains such as Ethereum, the future of decentralization was all in the hands of Bitcoin. Together with Nakamoto itself, early developers were trying to leverage Bitcoin potential to decentralize traditionally centralized applications. However, being Bitcoin a decentralized machine, available non-trustless oracles were considered unsuitable. Therefore, strategies had to be elaborated to solve the so-called oracle problem in the newborn scenario. By interviewing early developers and crawling early forums and repositories, this paper aims to retrace and reconstruct the chain of events and contributions that gave birth to oracles on Bitcoin. The evolution of early trust models and approaches to solving the oracle problem is also outlined. Analyzing technical and social barriers to building oracles on Bitcoin, the transition to Ethereum will also be discussed.