In this paper, we show that the lattice of filters of a weakly dicomplemented lattice L can be endowed with a dual weak complementation. Its sublattice of principal filters is shown to be dually isomorphic to the weakly complemented reduct of L. Dense elements and skeletons are revisited. A connection is established between filters of skeletons and certain filters of L.
We propose many-valued logic with internalized meta-judgment (MLIM) and prove its completeness. The syntax of MLIM has a new operator to judge whether the truth value of a formula is a designated value in the original many-valued logic. Using MLIM, designated values are incorporated into its syntax, enabling many-valued logic to be treated as classical logic. The semantics of MLIM is a pair semantics, which determines the validity of formulas by a pair of truth values. The proof theory of MLIM is given as natural deduction obtained by combining the inference rules of classical logic and many-valued logic.
We introduce a novel reduction from the satisfiability problem for a set of propositional signed clauses (Signed SAT) to Mixed Integer Linear Programming (MILP). This reduction provides a scalable and effective approach for solving Signed SAT instances via MILP and can be extended to address a broad class of NP-complete combinatorial decision problems through their reduction to Signed SAT. Furthermore, we present a reduction for a variant of Signed SAT in which each clause is expressed as a disjunction of signed literals rather than as a signed disjunction of literals. Finally, we discuss how these reductions can be adapted for pseudo-Boolean (PB) solving, enabling the use of PB solvers that exploit SAT-based techniques.
This study introduces a human-feasible posture optimization framework that reduces aspiration risk using camera-derived posture information. Joint angles are estimated from sagittal-view images with a body motion link model, aspiration risk is predicted using a machine learning classifier, and posture adjustments are identified through optimization constrained by biomechanical range-of-motion (ROM) limits. In experiments with 68 older adults, constrained optimization reduced predicted aspiration risk by 22.7% while avoiding the anatomically unrealistic postures produced by unconstrained optimization. These findings demonstrate that physiologically grounded constraints are essential for reliable and clinically meaningful posture guidance in aspiration prevention.
The paper presents a discussion of the structure of Haar spectra for ternary bent functions, where the term structure refers to the arrangement of Haar spectral coefficients per packets corresponding to the arrangement of Haar functions used as the kernel of the Haar transform. For a bent function, by considering pairs of 2/3 of Haar coefficients at the same positions in the last two packets in the Haar spectrum, we observe that in the function vector of a bent function, the function values are arranged into triples of adjacent elements of the vector. In construction of bent functions, manipulation the initial bent function over these triples, including re-arrangement of values into new triples, preserve bentness. From each bent function in n variables which has 1/3 zero-valued pairs of Haar coefficients from the last two packets, it can be constructed a set of other bent functions in n variables by referring to the values of bent functions in (n−2) variables.
This paper proposes a method to represent certain maximally asymmetric functions (MAFs) compactly. The proposed method decomposes a MAF into three parts, and represents the three parts using suitable decision diagrams. By decomposing a MAF, we can convert a MAF into a set of monotone increasing functions. The set of monotone increasing functions can be compactly represented by edge-valued multiple-valued decision diagrams (EVMDDs). Experimental results show that the total number of nodes needed in the proposed method for certain MAFs is a few orders of magnitude smaller than that in ordinary EVMDDs for general MAFs. We can generate such compact MAFs quickly.
Non-invasive and quantitative assessment of swallowing function is important for preventing complications such as aspiration pneumonia. We propose a 3D metric estimation method for laryngeal movement using 2D tracking with DeepLabCut and metric depth estimation with Depth Pro. Experimental results showed that the distance from the camera to the larynx can be estimated with an error of approximately 3.7 cm, and the standard deviation of laryngeal movement across different camera distances was 0.29 cm. Using laryngeal movement values from previous studies, the coefficient of variation was estimated at 9–14%, indicating reproducibility across varying distances.
This paper presents an improvement of stochastic encrypted data processing scheme with a new stochastic number generation based on quasi-random sequences. We focus on the accuracy and efficiency of stochastic computing, which are dependent on the Stochastic Number Generator (SNG) producing stochastic numbers with random bit-streams. While conventional SNGs use a pseudo-random number generator (PRNG), such as Linear Feedback Shift Registers (LFSRs), we introduce a new SNG with a quasi-random sequence (i.e., Sobol sequence) generator tailored for stochastic encrypted data processing. The proposed SNG produces stochastic numbers based on Sobol sequences, and makes it possible to achieve arithmetic computations with lower errors compared with the conventional one with PRNG. In other words, the stochastic encrypted data processing having the proposed SNG can achieve a required computational accuracy with a much shorter word length, compared to the conventional SNG. Such a significant reduction of the stochastic number length leads to a substantial decrease in the encrypted computation time. This paper demonstrates the effectiveness of the proposed SNG from experimental evaluations for different n-degree polynomials in the form of 1+x+⋯+xn−1 +xn. We confirm from the evaluation result that, in the case of computing the polynomial 1+x+x2 under a certain accuracy condition, we reduce the required stochastic stream length from 8192 (PRNG)—an 8× reduction—and achieve more than a 90% reduction in runtime, showing the proposed approach can improve the efficiency of stochastic encrypted data processing.
This paper presents an improved Ising model framework for polar codes, termed POLARIS, which reduces the number of binary variables by incorporating rate-1 node structures and embedding elements of successive-cancellation decoding into the Ising formulation. The decoder scales efficiently to block lengths up to N = 64, doubling prior Ising-based limits. POLARIS achieves near-successive-cancellation list performance within 0.4 dB while reducing QUBO dimensionality from 192 to 126 variables. These advancements bring Ising-based polar decoding closer to practical realization, offering improved efficiency for implementation on both quantum and hybrid CMOS-classical annealing hardware.
This paper presents an approach for minimizing reversible logic circuits composed of Toffoli gates, employing the A* with Lookahead (AL*) algorithm. Previous A*-based optimization methods have suffered from excessive memory requirements, which limit the size of circuits that can be handled. To overcome this issue, we employ AL*, an algorithm that incorporates the advantages of depth-first search (DFS) into A*. By predicting the expansion priority of each node through a DFS-based lookahead, the proposed method achieves a significant reduction in memory usage. Consequently, our approach optimizes larger circuits that previous A* methods could not handle due to memory overflow, and we present comparative results in this paper.
The generalization ability of a machine learning based system such as ANN directly depends on the quality of the structure and the quality of the training dataset. However, even with a well-designed dataset there are classes of functions such as arithmetic, compound or modulo-based functions that remain difficult to learn. In order to understand the difficulty in learning certain classes we study the inverse problem: given an algebraic ring, how can we construct a dataset that induces a specific learning effort on a chosen machine learning model? For this purpose, we study the learnability of ternary functions under variable structural constraints. We start by a classification approach: we use a group theoretic method and represent each target ternary function class through its corresponding NPN equivalence groups. Using these groups, we generate new datasets that preserve the structural properties of the original function classes (their relative position and distances within the set of all ternary logic functions), while changing the individual functions within the NPN groups. We shift these function groups on the set of existing logic functions and analyze how the difficulty of the resulting dataset changes. We show that when a fixed set of NPN classes is preserved along with their relative ordering, the difficulty of learning the corresponding labels remains stable. These results highlight the critical role of label structure and confirm that machine learning models strongly exploit the inherent organization of the labels during training.
A nonvolatile flip-flop using magnetic tunnel junction (MTJ) devices is an essential building block circuit in nonvolatile logic for realizing ultra-low-power edge devices, because it is responsible for retaining state during power off. However, an area overhead caused by the write circuit that generates the switching current required to back up data into the MTJ devices remains a key issue. In this paper, focusing on several write circuit configurations, we systematically compare and evaluate how device parameters such as MTJ resistance and switching current relate to the area of the write circuit. Based on the results and discussion, we propose a novel area-efficient write circuit with low sensitivity to device parameter variations. Simulation results based on a 55 nm MTJ/MOS-hybrid process technology demonstrate that the proposed circuit achieves up to about one-sixth of the area of conventional configurations and operates stably over a wide range of parameter variations.
Gentzen-style sequent calculi are introduced for certain alternative first-order constructive logics that feature both intuitionistic and paraconsistent negations. These first-order constructive logics were developed by Niki and Omori to enhance Nelson’s constructive paraconsistent four-valued logic N4 and Wansing’s constructive connexive four-valued logic C. For the proposed Gentzen-style sequent calculi, theorems on embedding, cut-elimination, Craig interpolation, and Kripke completeness are established. Additionally, some constructive properties, such as the disjunction property and the constructible falsity property, are derived from these calculi.
This paper presents an edge-mapped QUBO formulation for solving the Traveling Salesman Problem (TSP) using simulated quantum annealing (SQA). Each possible city-to-city edge is represented by a single spin variable, cutting spin count and coupling density versus path-mapped encodings. We further propose an iterative Hamiltonian update: after an initial anneal produces subtours, we reuse the spin configuration and add bridging constraints that force components to connect, gradually reshaping the Hamiltonian toward a valid tour. This combination of edge mapping (fewer spins/faster convergence) and iterative Hamiltonian updating (easier to reach high-quality solutions) delivers 3–5x faster convergence and improved tour quality over a clustering-based annealing baseline on TSPLIB benchmarks.
We generalize the analysis of Miller and Osherson (2009) of distance-based judgment aggregation to a many-valued setting. Solution methods based on median and average aggregation, respectively, are defined for various classes of metrics and are compared and evaluated with respect to two important characteristics.
Multi-level signaling techniques are being increasingly implemented in high-speed digital communication systems, as they can limit the required symbol rate and mitigate the noise effects caused by high-frequency components. In this study, we present a multi-level signaling scheme that suppresses symbol transition-dependent inter-symbol interference (ISI) using a two-dimensional (2D) symbol map and an intermediate level–inserted multi-level representation. We propose a PAM-5 signaling scheme that introduces a new intermediate level to reduce transition amplitudes, thereby mitigating ISI sensitivity and enhancing robustness against sampling timing variations. Furthermore, for transitions that remain difficult to decode, the selected symbols are considered as one-bit erasures even at the intermediate level. The simulation results obtained for the measured characteristics of a two-meter microstrip line indicate that the proposed PAM-5 scheme suppresses cluster spreading in the 2D symbol map and reduces distortion when compared with PAM-4.
Improving the quality of nursing care is essential to enhancing medical services. Therefore, a Web-based system for evaluating and improving nursing care quality has been developed. In this system, nursing experts assess the quality of nursing care, but the evaluation is time-consuming. Consequently, a system that supports evaluators using artificial intelligence technology is being developed. In this study, we performed text classification using features extracted from the evaluation text and prompts generated using genetic algorithms. As a result, the average classification accuracy improved by 1.0%, and that for Q425 increased by 4.0%.
This paper describes the concept of Observability Don’t Cares (ODCs) of nets in digital logic circuits within an algebraic geometry framework. The targeted application is the optimization of (modulo) arithmetic circuits. Our approach models the circuit by way of an ideal in a polynomial ring, with coefficients from an appropriate field. Using an ideal membership formulation, we describe how ODCs correspond to variety subsets of these ideals. The (extended) Gröbner basis algorithm is then employed to compute the ideals corresponding to the ODCs. These ideals can then be translated into corresponding Boolean functions for use with conventional logic optimization tools. We show that our approach computes the ODC-set for a net corresponding to its unobservability at all outputs. Experiments are performed to iteratively compute ODCs at internal nets of various non-linear arithmetic architectures. Logic optimization of these arithmetic circuits is performed using the computed ODCs. Results are compared against conventional logic synthesis techniques that utilize either BDDs or SAT/Craig interpolation for ODC computation and logic optimization. The results demonstrate that, for arithmetic circuits, conventional logic synthesis tools are able to better utilize the ODCs computed by our algebraic approach – as it leads to more area-efficient implementations as compared with contemporary methods.
In this work we introduce a new class of ideals and filters in double Boolean algebras and call it ⊓-ideal (resp. ⊔-filter). We show that ⊓-ideals (resp. ⊔-filters) generalize ideals (resp. filters), and that the set of ⊓-ideals (resp. ⊔-filters) forms an algebraic, and residuated lattice that is actually a Heyting algebra.
Let Ek = {0,1,…,k−1}, k > 2, and Wk be the set of triples in $E_k^3$ with mutually distinct components. A majority function f defined on Ek is called 2valued if it is 2-valued or a constant on Wk. Let the range of f on Wk be a subset of {0,1}.We study some basic properties of such functions f and, concerning {0,1,a} for a ∈ Ek\{0,1}, present the invariants shared by functions contained in the clone generated by f.In addition, a group of minimal functions on Ek is given which are 2-valued majority functions.
