Abstract computation over first-order structures. Extras: From programs to decision trees I
本文通过引入程序路径和转换系统来分析BSS RAMs在初等结构上的决策过程，并提供算法枚举有限的程序路径。
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Selected work
Representative Papers
Nonparametric Testing of Spatial Dependence in 2D and 3D Random Fields
This paper addresses the nonparametric testing of spatial dependence in two- and three-dimensional random fields. The proposed method maps spatial grid data onto a one-dimensional sequence via space-filling curves—specifically Hilbert and generalized Gilbert curves—and subsequently applies ordinal pattern-based statistical tests to detect dependence structures. Its key contribution lies in the first integration of locality-preserving space-filling curve mappings with nonparametric ordinal pattern analysis, thereby overcoming dimensional and grid-shape constraints inherent in conventional approaches. The framework supports arbitrary-size regular or irregular grids and extends naturally to higher dimensions. Experimental results demonstrate that the method is robust, computationally efficient, and achieves superior detection accuracy compared to existing spatial ordinal-pattern-based techniques, while maintaining conceptual simplicity and ease of implementation.
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Global Permutation Entropy
Traditional permutation entropy (PE) considers only contiguous subsequences, neglecting non-contiguous patterns and thus inadequately characterizing time-series complexity. To address this limitation, we propose Global Permutation Entropy (GPE), a novel complexity measure for real-valued time series. GPE systematically incorporates *all* length-𝑘 subsequences—regardless of temporal contiguity—thereby capturing the full combinatorial structure of ordinal patterns beyond local continuity constraints. Leveraging an efficient algorithm for extracting the complete permutation spectrum and quantifying it via Shannon entropy, GPE enables unbiased characterization of deep structural dynamics. Extensive evaluation on synthetic benchmarks demonstrates that GPE exhibits markedly enhanced sensitivity to dynamical transitions compared to standard PE. An open-source Julia package implementing GPE is publicly available.
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A Reduction of Input/Output Logics to SAT
This work addresses the challenge of automated reasoning for conditional norms in input/output (I/O) logic. We propose a novel SAT-based reduction framework that, unlike conventional approaches requiring truth assignments to normative statements, systematically encodes I/O conditional inference problems into propositional logic formulas solvable by off-the-shelf SAT solvers. Based on this framework, we implement rio, a prototype symbolic reasoning system supporting multiple I/O logics—including basic, simple-minded, and through variants. Experimental evaluation demonstrates that rio achieves both strong expressive power and competitive computational efficiency, successfully verifying several canonical normative examples. To our knowledge, this is the first scalable, formally verifiable automation framework for non-truth-functional normative reasoning.
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Abstract computation over first-order structures. Part IIb: Moschovakis' operator and other non-determinisms
This paper systematically investigates the impact of three unary nondeterministic mechanisms—branching, numerical, and Moschovakis operator-based—on decidability and computational power within the BSS RAM model. Focusing on decidability questions for the equality relation and finite sets containing zero, one, or two constants, it integrates first-order computability analysis over structures, oracle models with constant restrictions, and semantic methods based on Moschovakis operators. The study uncovers systematic patterns governing the “semidecidable → decidable” transition across distinct nondeterministic semantic levels, along with a hierarchy of influence strengths. Key contributions include: (i) the first hierarchical framework characterizing how four structural properties differentially constrain machine capabilities; (ii) a rigorous proof that all semidecidable sets in this model are in fact decidable; and (iii) a substantial strengthening of theoretical distinctions among nondeterministic variants, clarifying their relative expressive power and semantic boundaries.
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Latest Papers
Abstract computation over first-order structures. Extras: From programs to decision trees I
本文通过引入程序路径和转换系统来分析BSS RAMs在初等结构上的决策过程，并提供算法枚举有限的程序路径。
0 citationsRead paper
Nonparametric Testing of Spatial Dependence in 2D and 3D Random Fields
This paper addresses the nonparametric testing of spatial dependence in two- and three-dimensional random fields. The proposed method maps spatial grid data onto a one-dimensional sequence via space-filling curves—specifically Hilbert and generalized Gilbert curves—and subsequently applies ordinal pattern-based statistical tests to detect dependence structures. Its key contribution lies in the first integration of locality-preserving space-filling curve mappings with nonparametric ordinal pattern analysis, thereby overcoming dimensional and grid-shape constraints inherent in conventional approaches. The framework supports arbitrary-size regular or irregular grids and extends naturally to higher dimensions. Experimental results demonstrate that the method is robust, computationally efficient, and achieves superior detection accuracy compared to existing spatial ordinal-pattern-based techniques, while maintaining conceptual simplicity and ease of implementation.
0 citationsRead paper
Global Permutation Entropy
Traditional permutation entropy (PE) considers only contiguous subsequences, neglecting non-contiguous patterns and thus inadequately characterizing time-series complexity. To address this limitation, we propose Global Permutation Entropy (GPE), a novel complexity measure for real-valued time series. GPE systematically incorporates *all* length-𝑘 subsequences—regardless of temporal contiguity—thereby capturing the full combinatorial structure of ordinal patterns beyond local continuity constraints. Leveraging an efficient algorithm for extracting the complete permutation spectrum and quantifying it via Shannon entropy, GPE enables unbiased characterization of deep structural dynamics. Extensive evaluation on synthetic benchmarks demonstrates that GPE exhibits markedly enhanced sensitivity to dynamical transitions compared to standard PE. An open-source Julia package implementing GPE is publicly available.
0 citationsRead paper
A Reduction of Input/Output Logics to SAT
This work addresses the challenge of automated reasoning for conditional norms in input/output (I/O) logic. We propose a novel SAT-based reduction framework that, unlike conventional approaches requiring truth assignments to normative statements, systematically encodes I/O conditional inference problems into propositional logic formulas solvable by off-the-shelf SAT solvers. Based on this framework, we implement rio, a prototype symbolic reasoning system supporting multiple I/O logics—including basic, simple-minded, and through variants. Experimental evaluation demonstrates that rio achieves both strong expressive power and competitive computational efficiency, successfully verifying several canonical normative examples. To our knowledge, this is the first scalable, formally verifiable automation framework for non-truth-functional normative reasoning.
0 citationsRead paper
Abstract computation over first-order structures. Part IIb: Moschovakis' operator and other non-determinisms
This paper systematically investigates the impact of three unary nondeterministic mechanisms—branching, numerical, and Moschovakis operator-based—on decidability and computational power within the BSS RAM model. Focusing on decidability questions for the equality relation and finite sets containing zero, one, or two constants, it integrates first-order computability analysis over structures, oracle models with constant restrictions, and semantic methods based on Moschovakis operators. The study uncovers systematic patterns governing the “semidecidable → decidable” transition across distinct nondeterministic semantic levels, along with a hierarchy of influence strengths. Key contributions include: (i) the first hierarchical framework characterizing how four structural properties differentially constrain machine capabilities; (ii) a rigorous proof that all semidecidable sets in this model are in fact decidable; and (iii) a substantial strengthening of theoretical distinctions among nondeterministic variants, clarifying their relative expressive power and semantic boundaries.
0 citationsRead paper