搜索结果：deterministic

We present a deterministic parallel multilevel algorithm for balanced hypergraph partitioning that matches the state of the art for non-deterministic algorithms. Deterministic parallel algorithms produce the same result in each invocation, which is crucial for reproducibility. Moreover, determinism is highly desirable in application areas such as VLSI design. While there has been tremendous progress in parallel hypergraph partitioning algorithms recently, deterministic counterparts for high-quality local search techniques are missing. Consequently, solution quality is severely lacking in comparison to the non-deterministic algorithms. In this work we close this gap. First, we present a generalization of the recently proposed Jet refinement algorithm. While Jet is naturally amenable to determinism, significant changes are necessary to achieve competitive performance on hypergraphs. We also propose an improved deterministic rebalancing algorithm for Jet. Moreover, we consider the powerful but slower flow-based refinement and introduce a scheme that enables deterministic results while building upon a non-deterministic maximum flow algorithm. As demonstrated in our thorough experimenta

Empiric antibiotic prescribing in high-risk clinical contexts often requires decision making under conditions of incomplete information, where inappropriate coverage or unjustified escalation may compromise safety and antimicrobial stewardship. While clinical decision-support systems have been proposed to assist in this process, many approaches lack explicit governance and evaluation mechanisms defining scope, abstention conditions, recommendation permissibility, and expected system behavior. This work specifies a governance and evaluation framework for deterministic clinical decision-support systems operating under explicitly constrained scope. Deterministic behavior is adopted to ensure that identical inputs yield identical outputs, supporting transparency, auditability, and conservative decision support in high-risk prescribing contexts. The framework treats governance as a first-class design component, separating clinical decision logic from rule-based mechanisms that determine whether a recommendation may be issued. Explicit abstention, deterministic stewardship constraints, and exclusion rules are formalized as core constructs. The framework defines an evaluation methodology

We introduce a deterministic sparse Fourier transform framework based on a keyed multi-view gating mechanism that leverages 2-of-3 Chinese Remainder Theorem (CRT) agreement to reduce candidate frequency pairs from $O(k^2)$ to $Θ(k)$ under sparse-regime assumptions. Unlike prior approaches that rely on randomized bucketization for candidate formation, the proposed method provides deterministic structure with probabilistic guarantees arising only from assumptions on frequency placement and independence of affine hashing across views. The algorithm is realized through a peeling-based recovery procedure that extracts frequencies directly from singleton bins without explicit pair enumeration. A recursive self-reduction eliminates the $O(\sqrt{N} \log N)$ preprocessing floor, yielding $O(\sqrt{N} \log k)$ expected identification time while maintaining an $O(N \log N)$ worst-case bound via deterministic dense-FFT fallback. A multi-view verification framework combining Parseval energy consistency and bin-wise residual checks ensures bounded failure probability and no false negatives under correct verification. This establishes a framework combining deterministic candidate reduction, sublin

As autonomous research agents and AI co-scientist systems push large language models (LLMs) from drafting toward end-to-end manuscript production, the bottleneck shifts from generation to verification. Fluent LLM output can hide fabricated citations, numbers that drift from source tables, and unmet reporting-guideline items; existing tools generate without verifying, and self-critique inherits the blind spots that produce confident fabrication. We describe an architecture pairing generation with verification, resting on three principles: decompose the workflow into self-contained skills, gate every stage transition with halt-on-failure, and resolve each integrity question with the cheapest sufficient mechanism, a deterministic, re-executable check where one suffices and a prose-level probe only where interpretation is unavoidable. This determinism-where-possible split, organized as an integrity-gate taxonomy, is the core contribution. It is realized as MedSci Skills, an open-source toolkit of 43 skills with a 21-detector deterministic tier, evaluated on three public-dataset pipelines (STARD, PRISMA, STROBE) and a seeded-defect ablation. Across the three pipelines every content-hash

We define a bounded local generator class (BLGC) for deterministic state evolution on graph-indexed systems. The construction consists of finite-range generators operating on bounded local state under deterministic composition. Each update acts only on a bounded-radius neighborhood and applies a bounded local transformation with projection onto a compact state domain. Under the BLGC constraints, per-step operator work remains independent of total system size M. Specifically, incremental update cost satisfies $W_t = O(1)$ with respect to $M \to \infty$ for fixed interaction radius $r$. The framework admits a Hilbert-space embedding in $\ell^2(V)\otimes \mathbb{R}^d$ and yields bounded operators under composition on admissible subspaces. The result establishes a structural decoupling between global state capacity and incremental computational work. The claims apply specifically to the bounded local generator class defined in this paper.

We study the parametric subfamily $p = 3m(m+1) + 1$ with $m = 2^a 3^b - 1$, $a,b \in \mathbb{N}^*$, a 3-smooth slice of the centred hexagonal numbers $3m^2 + 3m + 1 = (m+1)^3 - m^3,$ from the point of view of unconditional primality certification via the Pocklington-Lehmer criterion. The 3-smoothness of $m+1 = 2^a 3^b$ yields, for every $(a,b)$, a fully factored divisor $F = 2^a 3^(b+1)$ of $p-1$ satisfying $F > \sqrt(p)$ unconditionally, reducing the certificate to two witnesses, for $q = 2$ and $q = 3$. Our main new contribution is a complete, deterministic characterisation of the two canonical witnesses. We prove that $w_2 = 5$ is a valid witness if and only if $a - b$ = 1, 2 (mod 4), by quadratic reciprocity; and that $w_3 = 7$ is a valid witness if and only if $m$ is not congruent to 2 (mod 7), by cubic reciprocity in $\mathbb{Z}[omega]$ using the explicit Eisenstein factorisation $p = ((1+m) - m ω)((1+m) - m ω^2)$. These two results turn the heuristic "5 and 7 always work" (which is in fact false) into exact congruence conditions, and yield a deterministic witness-selection rule. Alongside, three elementary arithmetic filters (mod 6, a (-3) quadratic-residue sieve, and a m

A nondeterministic automaton is semantically deterministic (SD) if different nondeterministic choices in the automaton lead to equivalent states. Semantic determinism is interesting as it is a natural relaxation of determinism, and as some applications of deterministic automata in formal methods can actually use automata with some level of nondeterminism, tightly related to semantic determinism. In the context of finite words, semantic determinism coincides with determinism, in the sense that every pruning of an SD automaton to a deterministic one results in an equivalent automaton. We study SD automata on infinite words, focusing on Büchi, co-Büchi, and weak automata. We show that there, while semantic determinism does not increase the expressive power, the combinatorial and computational properties of SD automata are very different from these of deterministic automata. In particular, SD Büchi and co-Büchi automata are exponentially more succinct than deterministic ones (in fact, also exponentially more succinct than history-deterministic automata), their complementation involves an exponential blow up, and decision procedures for them like universality and minimization are PSPACE

The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P = NP by introducing a universal, graph-based deterministic framework applicable to all NP problems without requiring reduction to an NP-complete problem. We model computational transitions as edges within a unified graph structure, where edges correspond to the steps of a deterministic verifier Turing machine for all possible certificates. Due to the overlap of edges among computation paths, the total cardinality of the edge set remains polynomially bounded. A key feature of our approach is that each extension step enforces global consistency via a local infeasibility trimming tool. This mechanism systematically preserves valid NP paths that lead to the target edge under polynomial verification, ensuring the graph remains globally feasible at every stage without explicit enumeration. This represents a paradigm shift from searching over exponential certificates to the incremental extension of verified edges. Since our construction decides NP problems in deterministic polynomial time, it provides

Various variants of Parikh automata on infinite words have recently been introduced in the literature. However, with some exceptions only their non-deterministic versions have been considered. In this paper we study the deterministic versions of all variants of Parikh automata on infinite words that have not yet been studied. We compare the expressiveness of the deterministic models and investigate their closure properties and decision problems with applications to model checking. The model of deterministic limit Parikh automata turns out to be most interesting, as it is the only deterministic Parikh model generalizing the $ω$-regular languages, the only deterministic Parikh model closed under the Boolean operations and the only deterministic Parikh model for which all common decision problems are decidable.

In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential

Unmanned Aerial Vehicle (UAV) mounted Base Stations (UAV-BSs) provide flexible coverage for temporary hotspot scenarios; however, efficiently optimizing 3D deployment to satisfy heterogeneous user distributions remains a significant challenge. While Deep Reinforcement Learning (DRL) approaches have shown promise, they often suffer from prohibitive training overhead and poor generalization in cold-start scenarios where the user topology is unknown a priori. To address these limitations, this paper proposes Satisfaction-driven Coverage Optimization via Perimeter Extraction (SCOPE), which is a deterministic and training-free 3D deployment framework. Unlike existing heuristics that rely on fixed-altitude assumptions, SCOPE integrates a perimeter-based peeling strategy with the Welzl Smallest Enclosing Circle (SEC) algorithm to dynamically optimize 3D positions. Theoretically, we provide a rigorous convergence proof and derive a polynomial time complexity of $O(N^2 \log N)$, ensuring predictable execution for real-time applications. Experimentally, we evaluate SCOPE in unpredictable hotspot environments against both traditional heuristics and state-of-the-art DRL baselines under a match

We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state transitions driven by weakly chaotic dynamics. It serves as a direct replacement for the stochastic denoising process, without requiring retraining or continuous state embeddings. We demonstrate consistent improvements in both efficiency and sample quality on text and image generation tasks. In addition, the proposed algorithm yields improved solutions for diffusion-based combinatorial optimization. Thus, herding-based denoising is a simple yet promising approach for enhancing the generative process of discrete diffusion models. Furthermore, our results reveal that deterministic reverse processes, well established in continuous diffusion, can also be effective in discrete state spaces.

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially observable Markov decision processes, and conditional planning. We present a logic programming framework called non deterministic logic programs, along with a declarative semantics and fixpoint semantics, to allow representing and reasoning about inherently non deterministic real-world applications. The language of non deterministic logic programs framework is extended with non-monotonic negation, and two alternative semantics are defined: the stable non deterministic model semantics and the well-founded non deterministic model semantics as well as their relationship is studied. These semantics subsume the deterministic stable model semantics and the deterministic well-founded semantics of deterministic normal logic programs, and they reduce to the semantics of deterministic definite logic programs without negation. We show the application of the non deterministic logic programs framework to a conditional planning problem.

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density $π$ given only its score $ abla \log π$. Our method approximates the Wasserstein gradient flow on $\mathrm{KL}(f_t\|π)$ by learning the time-varying score $ abla \log f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

In binary ($0/1$) online classification with apple tasting feedback, the learner receives feedback only when predicting $1$. Besides some degenerate learning tasks, all previously known learning algorithms for this model are randomized. Consequently, prior to this work it was unknown whether deterministic apple tasting is generally feasible. In this work, we provide the first widely-applicable deterministic apple tasting learner, and show that in the realizable case, a hypothesis class is learnable if and only if it is deterministically learnable, confirming a conjecture of [Raman, Subedi, Raman, Tewari-24]. Quantitatively, we show that every class $\mathcal{H}$ is learnable with mistake bound $O \left(\sqrt{\mathtt{L}(\mathcal{H}) T \log T} \right)$ (where $\mathtt{L}(\mathcal{H})$ is the Littlestone dimension of $\mathcal{H}$), and that this is tight for some classes. We further study the agnostic case, in which the best hypothesis makes at most $k$ many mistakes, and prove a trichotomy stating that every class $\mathcal{H}$ must be either easy, hard, or unlearnable. Easy classes have (both randomized and deterministic) mistake bound $Θ_{\mathcal{H}}(k)$. Hard classes have random

A regular language is $k$-lookahead deterministic (resp. $k$-block deterministic) if it is specified by a $k$-lookahead deterministic (resp. $k$-block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood ($k$-lookahead determinism) and by Giammarresi et al. ($k$-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Brüggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each $k$-block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a $k$-block deterministic regular language to a $k$-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in $k$-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in $k$-block deterministic regular languages. We also prove that there is a proper hierarchy in $k$-lookahead deterministic regu

This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational equivalence to abstract mathematical descriptions. The second results are stronger because they show observational equivalence between deterministic and indeterministic descriptions found in science. Here I also discuss Kolmogorov's contribution. For the third results I introduce two new meanings of `observational equivalence at every observation level'. Then I show the even stronger result of observational equivalence at every (and not just some) observation level between deterministic and indeterministic descriptions found in science. These results imply the following. Suppose one wants to find out whether a phenomenon is best modeled as deterministic or indeterministic. Then one cannot appeal to differences in the probability distributions of deterministic and indeterministic descriptions found in science to argue that one of the descriptions is preferable because there is no such difference. Finally, I criticise the extant claims of philosophers and

In this article, we focus on computing the quantiles of a random variable $f(X)$, where $X$ is a $[0,1]^d$-valued random variable, $d \in \mathbb{N}^{\ast}$, and $f:[0,1]^d\to \mathbb{R}$ is a deterministic Lipschitz function. We are particularly interested in scenarios where the cost of a single function evaluation is high, while the law of $X$ is assumed to be known. In this context, we propose a deterministic algorithm to compute deterministic lower and upper bounds for the quantile of $f(X)$ at a given level $α\in (0,1)$. With a fixed budget of $N$ function calls, we demonstrate that our algorithm achieves an exponential deterministic convergence rate for $d=1$ ($\mathcal{O}( ρ^N)$ with $ρ\in (0,1)$) and a polynomial deterministic convergence rate for $d>1$ ($\mathcal{O}(N^{-\frac{1}{d-1}})$) and show the optimality of those rates. Furthermore, we design two algorithms, depending on whether the Lipschitz constant of $f$ is known or unknown.

Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.