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[4] ai.viXra.org:2508.0057 [pdf] submitted on 2025-08-22 03:27:58
Authors: Ronald Borge
Comments: 6 Pages.
We investigate logical frameworks that characterize probabilistic and quantum polynomial-time computation over unordered finite structures. Building on the paradigm of descriptive complexity (Immerman, 1999; Libkin, 2004), we introduce logics that extend fixed-point operators with controlled probabilistic and quantum constructs.For the probabilistic setting, we define Randomized Fixed-Point Logic (RFP), which augments inflationary fixed-point logic with a random-choice operator and counting mechanism. We prove that RFP captures BPP on unordered structures under a natural probabilistic semantics, without derandomization assumptions, and we establish closure under FO-definable reductions, leveraging classical tools such as Chernoff bounds (Chernoff, 1952; Mitzenmacher & Upfal, 2005).For the quantum setting, we propose Quantum Fixed-Point Logic (QFP), which extends RFP by incorporating unitary evolution and projective measurement, with amplitudes drawn from efficiently computable algebraic numbers. Using operator-algebraic semantics (Nielsen & Chuang, 2010), we show that QFP captures BQP on unordered structures. Approximation of arbitrary unitaries is guaranteed by the Solovay—Kitaev theorem (Kitaev, 1997; Dawson & Nielsen, 2005). Moreover, we exhibit problems definable in QFP but not in RFP, under standard complexity-theoretic assumptions (Arora & Barak, 2009).This work provides the first unified logical characterization of BPP and BQP over unordered structures, refining the descriptive complexity landscape for randomized and quantum polynomial-time computation. Completeness of the proposed framework remains a conjecture.
Category: Data Structures and Algorithms
[3] ai.viXra.org:2508.0051 [pdf] submitted on 2025-08-18 17:49:11
Authors: John Augustine McCain
Comments: 14 Pages. CC-BY-NC 4.0
We present evidence that the fundamental question underlying P vs NP may not be "Can NP problems be solved in polynomial time?" but rather "Can we achieve systematic proba- bilistic success in certificate discovery for problems with sparse solution spaces?" Through the development of multiple computational engines for the Goldbach conjecture—a problem with conjectured polynomial certificates but exponential naive verification—we demonstrate that meaningful confidence can be built about computationally intractable problem spaces through probabilistic reasoning frameworks. We argue this paradigm generalizes to other computational problems and suggests a reframing of complexity theory around probabilistic certificate discovery rather than deterministic algorithmic bounds. Furthermore, we connect this framework to the Anthropic Principle, proposing that computational problems exhibit fine-tuned structure that enables probabilistic discovery, and demonstrate that embodied AI systems already function as oracle-like problem solvers, achieving practical P ≈ NP equivalence. This work has profound implications for AI safety, suggesting the urgent need for truth-oriented rather than force-oriented AI architectures as systems become capable of reasoning about their own computational processes.
Category: Data Structures and Algorithms
[2] ai.viXra.org:2508.0030 [pdf] submitted on 2025-08-13 05:15:32
Authors: Dinuo Chen
Comments: 5 Pages.
Enhancing images captured under low-light conditions is a significant challenge in computervision. Poor illumination often degrades image quality, leading to low contrast, high levels ofnoise, and blurred details. This paper proposes a novel low-light image enhancement method calledAdaptive Gamma and Contrast Correction (AGCC). The model analyzes the brightness of theinput image and calculates the average color values to determine adaptive gamma and contrastcoefficients. These values are computed automatically and adjusted dynamically based on varyingillumination levels, eliminating the need for manual tuning. Both qualitative and quantitative evaluations demonstrate that the AGCC model effectively enhances low-light images while preservingfine details, maintaining natural contrast, and ensuring accurate color representation. The resulting images exhibit visually pleasing and natural appearances. Due to its efficiency and robustness,AGCC can offer a practical solution for various applications, including night-time surveillance,medical image enhancement, and photography in low-light environments.
Category: Data Structures and Algorithms
[1] ai.viXra.org:2508.0018 [pdf] replaced on 2025-08-12 00:31:01
Authors: John Augustine McCain
Comments: 16 Pages. CC-BY-NC 4.0
The P vs NP problem is one of the most central open questions in theoretical computer science, with implications ranging from cryptography to artificial intelligence. However, this paper argues that the standard formal framing of P vs NP conceals a deeper epistemological contradiction. Within strict formalism, the question reduces to a tautology: verification is necessarily downstream of solving. When generalized beyond formal systems, the problem echoes the halting problem and exhibits equivalent undecidability. As such, P vs NP resides in a paradoxical space—either trivially true or fundamentally unknowable. This paper contends that the widespread treatment of P vs NP as a definitive mathematical challenge stems from a categorical mistake: conflating formal verification, discovery processes, and predictive epistemology.
Category: Data Structures and Algorithms