Search Results - algorithmics. computability. computer arithmetics

Unified Validator Framework for the Collatz Conjecture: Logical, Spectral, and Cryptographic Resolution Protocols

Authors: Forrest M. Anderson, Forrest

Subject Terms: Collatz Conjecture, 3x+1 Problem, Syracuse Problem, Paul Erdős, John Horton Conway, Kurt Gödel, Alan Turing, Stephen Wolfram, Terence Tao, Yuri Matiyasevich, Gregory Chaitin, Harvey Friedman, Scott Aaronson, Proof Complexity, Natural Proofs Barrier, Razborov-Rudich Natural Proofs, P vs NP, Spectral Complexity, Spectral Complexity Operator, Spectral Operator Framework, Meta-mathematics, Arithmetic Dynamics, Discrete Dynamical Systems, Symbolic Dynamics, Integer Sequences, Recursive Functions, Halting Problem, Turing Machines, Turing Complete, Undecidability, Computability, Algorithmic Information Theory, Kolmogorov Complexity, Digital Arithmetic, Mathematical Logic, Formal Logic, Peano Arithmetic, ZFC, Logical Independence, Gödel Incompleteness Theorems, Incompleteness Theorems, Bounded Computation, Complexity Theory, Computational Complexity, Theoretical Computer Science, Discrete Math, Open Problems in Mathematics, Automated Theorem Proving, Formal Proof Systems, Mathematical Induction, Chaos in Arithmetic, Foundations of Mathematics, Arithmetic Functions, Special Sequences, Elementary Number Theory, Number Theory, Models of Computation, Logic in Computer Science, Dynamical Systems, Proof Theory, Decision Problems, Algorithmic Complexity, Computational Models

Retracted

Authors: Fathi, Kevin

Subject Terms: Quantum Gravity, Compact Generation, Spectral Correspondence, Asymptotic Analysis, Supercuspidal Representations, Automorphic representations, Halting Problem, Local Quantum Gradient Descent, Compression Theory, Number Theory, Compression-based unprovability, Mathematical Logic, Canonical Grammars, Canonical Normal Form, Galois Parameters in Mod- ℓ, recursive sequences, Frame Coherence, Symbolic entropy, Moduli Spaces, Trace Functor, Delta-Based Routing, Dark Energy, Riemann Hypothesis, Rational Points on Varieties, Double bind logic, Symbolic Irreducibility, Strategic Ambiguity, Quantum Kolmogorov complexity, Endoscopic Character Identities, sequence coverage, Dynamic Network Relabeling, growth lemma, Quantum complexity theory, Rewrite Grammars, Trace Pairing, Automorphic L-functions, Combinatorial Number Theory, Spectral Trace Rigidity, Constructive logic, Graph Labeling, Millennium Prize Problems, Statistical Mechanics, Vacuum Spectrum, Theoretical computer science, Representation-Theoretic Stability, Trace Operator, k-Local Hamiltonian, Mod- ℓ Transfer Factors, Torsion Sheaves, Scalable Network Protocols, Entropy Saturation, Purity Theorem, Shannon Entropy, Moy–Prasad Filtration, Algorithmic Information Theory, Shimura Varieties, Resolve budget, Information-theoretic logic, Ramsey Theory, Computability Theory, natural number shuffles, Distributed Systems, combinatorics, Boltzmann Entropy, Canonical CNF grammar, Vacuum Structure, Rational Hodge Classes, insertion-deletion systems, Witness Incompressibility Conjecture (WIC), Residue Class Elimination, Trace Formula, Symbolic Entropy, Energy Extraction, Reflective Frame Logic (RFL), Algebraic Cycles, Recursive Geometry, Rational Points, Non-Stoquastic Hamiltonian, Complexity Theory, Extremal Set Theory, Representation Theory over Finite Fields, d-regular expander, Computational Irreversibility, Obstruction Theory, Clause Complexity, Lattice-Confined Deuterium, Spectral Geometry, Frobenius and Inertia Actions, Chaitin's Omega, Recursive grammar, Functoriality, Motives, Diophantine Equations, Thermodynamics, Quantum Computing, Satake Parameters, Topological Energy Fields, Epsilon Factors, Indicator Vectors, S-Duality, Mordell–Weil Rank, Langlands Functoriality, Peano Arithmetic, Zero-Point Energy, Ramified Mod- ℓ Types, Cohomological Realization, Parity constraints, Sieve Methods, Rational points, Monoidal Duality, integer permutation, Navier–Stokes, Shafarevich–Tate Group, Mod- ℓ Representation Theory, Algebraic cycles, Frame coherence, Quantum Control, Clause Saturation, Budget-Incompressibility Conjecture (BIC), Spectral Functor, Combinatorics, Tseitin formulas, Derived Category, Graph Theory, Derived Categories, Arithmetic Geometry, Eigenvalue Symmetry, Canonical Normal Forms, Meta-mathematics, Structural Compression, Extremal Combinatorics, Fine-Structure Constant, Twin Primes, Stable Distributions, Cohomology theory, Unified Physics, Mod- ℓ Langlands, Resolution proof complexity, Symbolic Central Limit Theorem, computational complexity, Physical Computation, Symbolic Irreversibility, Computational complexity, Trace dynamics, Density Bounds, Graceful Tree Conjecture, Recursive Type Arithmetic, Foundations of Mathematics, Landauer's Principle, Cycle Class Map, Hecke Algebras over 𝐹 ℓ, monotonic insertion, Formal grammar, Reductive p-adic Groups, sequence generalization, FOS: Mathematics, Stable Character Identities, p-adic Langlands, Mirror Symmetry, Learning systems, Automorphic Representations, Ergodic Symbolic Processes, Spectral Trace, Irreducibility, Time-Bounded Quantum-to-Classical Principle, Fixpoint Dynamics, Incompressibility, Global Functoriality, combinatorial construction, Entropy-bound derivation, Symbolic Probability, Canonical Functorial Lift, Mass Gap, Local Modularity Lifting, Brane Categories, Quantum Boon-Bind Hierarchy (QBBH), Langlands functoriality, Spectral gap, Canonical rewrite systems, Graceful Labeling, Mod- ℓ Langlands Program, Elementary Methods, Frame Topos Theory (FTT), Condensed Matter Fusion, Langlands Endoscopy, Algorithmic information theory, Kimberling sequence, Trace Stabilization, Pseudo-L-Groups, Prime Constellations, Network Topology Verification, Mathematical Physics, Symbolic compression, Harish-Chandra Expansion, Spectral Gap, Admissible Sets, Asymptotic Enumeration, Dualizability, Trace Rigidity, Curvature Quantization, Roth's Theorem, Gravitational Curvature, Path Trace Encoding, Quantum BindTseitin Hamiltonian, Information-Theoretic Physics, ∞-Categories, Symbolic Dynamics, Symbolic Trace Compression, Probabilistic Limit Theorems, Frame Collapse, Turing reduction, Quantum Field Theory, Additive Combinatorics, Degeneracy, Information theory, Trace Cohomology, Étale Cohomology, Symbolic collapse, Langlands Duality, Recursive Labeling, Quantum Coherence, k-Tuple Conjecture, Temporal Cosmology, Canonical Bijection, Pigeonhole Principle, Frobenius Trace, Discrete Mathematics, Inductive Graph Theory, Positivity of Trace, Computability theory, Galois Parameters, Grammar-Based Inference, Algebraic geometry, Nonlinear Dynamics, P vs NP problem, Tame vs Wild Representations, Epsilon Factors in Mod- ℓ Setting, Mathematical logic, Kolmogorov Complexity, Topos Theory, Wild Ramification, Evolutionary selection, Parity Hamiltonian, Statistical mechanics, Algebraic Geometry, Modular Forms, Quantum Boon-Bind Hierarchy, structural complexity, Non-Gaussian Limit Laws, Hilbert Space Geometry, Trace Operators, Eigenvarieties, Unified symbolic theorem, Wild Supercuspidals, Black Hole Information, Quantum Langlands, Entropy Gradient, Bateson Game, Address Collision Avoidance, Landauer principle, Structural Paradox, P vs NP, Yang–Mills Theory, Sheaf Theory, Analytic rank, Base Change in Mod- ℓ Setting, Prime Distribution, Frobenius and Inertia Types, Arithmetic Progressions, Langlands Classification in Characteristic ℓ, Foundations of Computation, Computational complexity theory, Residue Coverage, rewrite systems, Feynman–Kitaev Hamiltonian, Tame vs Wild Modularity, Modular Obstruction, Elementary Number Theory, Stable Trace Formula, Gauge Theory, Endomorphism Algebra, BindTseitin constraints, Tree-Based Networks, Cohomological Descent, Structural Complexity, Foundational mathematics, Hodge classes, Entropy gradient, Entropy-based inference, Quantum Vacuum, Formal Language Theory, Budget-Incompressibility Conjecture, symbolic dynamics, XOR-SAT, Structural Bounds, Mod- l Local Langlands, Harish-Chandra Characters, proof by contradiction, Elliptic Curves, Unbounded Prime Gaps, Quantum State Coherence, Representation Theory, Parameter Lifting, growth argument, Galois Representations, PDE Curvature, Automorphic Representations mod- ℓ, Busy Beaver Function, CNF formulas, Mod- ℓ Galois Parameter, Batesonian Physics, Proof Theory, Reduction of ℓ-adic Representations, Algorithmic Randomness, Turing Machines, Tannakian Categories, Kolmogorov complexity, Network Addressing, Fusion Reaction Pathways, Twisted D-Modules, Sign Problem, Tseitin transformation, Langlands Correspondence, Selmer group, Local Langlands Correspondence, Structural irreversibility, Spectral Decomposition, History state, Edge Difference Encoding, Quantum Kolmogorov Complexity, Functional Equation, Convergence and fixation, Character Expansion, NP-completeness, Automorphic Sheaves, Edge Difference Uniqueness, Synergy, Meta-logic, Growth Barrier, Wild Inertial Types, CNF Grammar, Orbital Integrals, fixpoint collapse, One-way functions, Variable Progression Length, Formal logic, Universal Equivalence, Energy barriers, Path Integral Methods, Hecke Eigensheaves, Forbidden Configurations, symbolic grammar, L-group homomorphisms, Character Theory, Non-Reductive Groups, coverage theorem, double bind machine, integer sequences, Overlap Gap Property, Quantum Tunneling, Tamagawa Numbers, Regulator, Progression-Free Sets, Beal Conjecture, k-local Hamiltonian, Reductive Groups over Global Fields, Fixpoint Descent, Erdős Problems, natural number permutation, Frame compression barrier, Entropy-Based Convergence, Routing Algorithms, Yang–Mills Mass Gap, Universal Frame Logic (UFL), Mod- ℓ L-functions, Wireless Sensor Networks, Information Theory, Derived Stacks, Birch and Swinnerton-Dyer Conjecture, number theory, Elliptic curves, Frustrated Quantum Systems, Post-ZFC Logic, semantic degeneracy, recursive enumeration, Perverse Sheaves, L-packets and Character Matching, Entropy-based proof, L-packets and Stability, Prime Patterns, Gauge Symmetry, Epistemic foundations of math, Categorical Proof, Recursive Structures, Geometric Langlands, Recursive Type Arithmetic (RTA), Chaitin incompleteness, Geometric Langlands with Torsion Coefficients, Reductive Groups, Character Matching, Symbolic proof systems, Prime Tuples, Edge expansion, Entropy–complexity correspondence, Theoretical Computer Science, logical paradox, Clause Overlap, Ecological Physics, Spectral Kernel, Hodge Theory, Injective Labeling, Mod- ℓ Langlands Correspondence, Recursive Logic, algorithmic information theory, Mod- ℓ Shimura Varietie, Entropy Production, Meta-Coherence Logic (MCL), Motivic Cohomology, Structural paradox, Endoscopic Transfer, Encoding asymmetry, Unified Field Theory, Szemerédi's Theorem, Fixpoint Rigidity, Categorical Trace, Modularity Lifting, Global Fields, symbolic entropy, Entropy Geometry, Entropy Collapse, Label-Delta Matching, L-functions, Depth-Positive Types, Langlands Dual Group, Configuration Entropy, Recursive Frame Theory, Quantum Complexity Theory, Time Emergence, Muon-Catalyzed Fusion, Additive Number Theory, Mod- ℓ Eigenvarieties, Mod- ℓ Trace Formula, Spectral Rigidity, Batesonian Game Theory, Positive Energy, Hodge Conjecture, Behrend Construction, Canonical CNF encoding, Prime Factorization, Constructive Algorithms, constructive proof, elementary proof, Moduli Stacks, Cryptographic hardness, Low-Energy Nuclear Fusion, BQP vs. QMA, one-way function, Modular Representation Theory, Mod- ℓ Local Langlands, Density Threshold, Tree Structures, Depth Stratification, Tunneling Probability, Noncomputability, Entropy collapse, Automorphic L-Functions, Incompleteness theorem, ∞-Categorical Descent, BB(6), Hardy–Littlewood Conjecture, Bit Complexity Optimization, Graph Theory Applications, Proof theory, Derived Moduli Stacks, Langlands Program, Recursive Tension Fields, Szemerédi-Type Theorems, Expander graphs, Frobenius Trace Invariants, Inertial Equivalence, Multicast Routing, Arithmetic Moduli, Millennium Problems

Factorials, Integers, and Factorial Theorems for Computing and Cryptography

Authors: Chinnaraji Annamalai

Source: SSRN Electronic Journal.

Subject Terms: Computability, Chaos-based Image Encryption Techniques, Arithmetic, Discrete mathematics, Computer science, Mathematical analysis, Cryptanalysis, Algorithm, Computational Complexity and Algorithmic Information Theory, Theoretical computer science, Computational Theory and Mathematics, Artificial Intelligence, Factorial, Computer Science, Physical Sciences, Cryptography, Optical Encryption, FOS: Mathematics, algorithm, combinatorics, factorial, computation, Computer Vision and Pattern Recognition, Computational Depth, Mathematics, Cryptography and Error-Correcting Codes

Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels

Authors: Boche, Holger Grigorescu, Andrea Schaefer, Rafael F. et al.

Index Terms: Computer Science - Information Theory, text

URL: http://arxiv.org/abs/2501.11636

Pseudo-Normalization via Integer Fast Inverse Square Root and Its Application to Fast Computation without Division.

Authors: Kusaka, Takashi Tanaka, Takayuki

Source: Electronics (2079-9292); Aug2024, Vol. 13 Issue 15, p2955, 15p

Subject Terms: REAL numbers, RENDERING (Computer graphics), SQUARE root, FLOATING-point arithmetic, ARITHMETIC

Turing’s unpublished algorithm for normal numbers

Authors: Verónica Becher Santiago Figueira Rafael Eduardo Picchi

Source: Theor Comput Sci 2007;377(1-3):126-138
Biblioteca Digital (UBA-FCEN)
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN

Subject Terms: Computable absolutely normal numbers, Lebesgue measure, FOS: Political science, Mathematical proof, 01 natural sciences, Turing, Computable construction, Error correction, Floating-Point Arithmetic in Scientific Computation, Theorem proving, Political science, Universal Turing machine, Ecology, Text Compression and Indexing Algorithms, Super-recursive algorithm, Discrete mathematics, Minor (academic), Algorithm for normal numbers, Programming language, Algorithm, Normal numbers, Lemma (botany), Computational Theory and Mathematics, Physical Sciences, Set theory, Manuscripts, Algorithms, Computer Science(all), Geometry, Set (abstract data type), FOS: Law, Turing machines, 0102 computer and information sciences, Poaceae, Theoretical Computer Science, Turing machine, Turing's unpublished manuscript, Computational Complexity and Algorithmic Information Theory, Number theory, Artificial Intelligence, FOS: Mathematics, 0101 mathematics, Biology, Computability, Computer science, FOS: Biological sciences, Computer Science, Computation, Law, Mathematics

File Description: application/pdf

Access URL: http://hdl.handle.net/20.500.12110/paper_03043975_v377_n1-3_p126_Becher

Randomness extraction in computability theory.

Authors: Cenzer, Douglas Porter, Christopher P.

Source: Computability; 2023, Vol. 12 Issue 1, p1-21, 21p

Subject Terms: ALGORITHMIC randomness, DATA compression, PROBABILITY measures, COMPUTABLE functions, ARITHMETIC, FUNCTIONALS, RANDOM variables

People: VON Neumann, John, 1903-1957

Computability in infinite Galois theory and algorithmically random algebraic fields.

Authors: Calvert, Wesley Harizanov, Valentina Shlapentokh, Alexandra

Source: Journal of the London Mathematical Society; Nov2024, Vol. 110 Issue 5, p1-26, 26p

Subject Terms: ALGEBRAIC fields, ALGORITHMIC randomness, HAAR integral, RANDOM fields, RANDOM sets

Computability of the Zero-Error Capacity of Noisy Channels †.

Authors: Boche, Holger Deppe, Christian

Source: Information; Jul2025, Vol. 16 Issue 7, p571, 23p

Subject Terms: INFORMATION theory, ALGORITHMS

Towards applied theories based on computability logic

Authors: Japaridze, Giorgi

Source: J. Symbolic Logic 75, iss. 2 (2010), 565-601

Subject Terms: FOS: Computer and information sciences, Computer Science - Logic in Computer Science, constructive logics, 68Q10, Computer Science - Artificial Intelligence, secondary: 03F30, 68T30, 0102 computer and information sciences, 01 natural sciences, Peano arithmetic, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Mathematics - Number Theory, F.1.1, F.1.2, Mathematics - Logic, 16. Peace & justice, game semantics, 68T27, Logic in Computer Science (cs.LO), Computability logic, Artificial Intelligence (cs.AI), 03D75, Logic (math.LO), 03F50

File Description: application/pdf

Access URL: http://arxiv.org/pdf/0805.3521
http://arxiv.org/abs/0805.3521
http://projecteuclid.org/download/pdf_1/euclid.jsl/1268917495
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.312.4138&rep=rep1&type=pdf
https://projecteuclid.org/euclid.jsl/1268917495
https://dblp.uni-trier.de/db/journals/corr/corr0805.html#abs-0805-3521
https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/div-classtitletowards-applied-theories-based-on-computability-logicdiv/D1B4F8E794BA2178A47E20BA927C09F4
https://www.jstor.org/stable/info/25676797
http://export.arxiv.org/pdf/0805.3521
https://arxiv.org/pdf/0805.3521.pdf
https://ui.adsabs.harvard.edu/abs/2008arXiv0805.3521J/abstract
https://arxiv.org/abs/0805.3521
http://projecteuclid.org/euclid.jsl/1268917495

Program Correctness through Self-Certification.

Authors: Namjoshi, Kedar S. Zuck, Lenore D.

Source: Communications of the ACM; Feb2025, Vol. 68 Issue 2, p74-84, 11p

Subject Terms: COMPUTER programming, COMPUTER software testing, SOFTWARE verification, COMPUTERS, COMPUTER systems, SCALABILITY, SYSTEMS design, COMPUTER software

An arithmetic analysis of closed surfaces.

Authors: Harrison-Trainor, Matthew Melnikov, Alexander

Source: Transactions of the American Mathematical Society; Mar2024, Vol. 377 Issue 3, p1543-1596, 54p

Subject Terms: TOPOLOGICAL spaces, UNIT ball (Mathematics), HOMEOMORPHISMS, SURFACE structure, ARITHMETIC

Arithmetic terms for sums of multinomial coefficients.

Authors: Shunia, Joseph M. Sauras Altuzarra, Lorenzo

Source: Ramanujan Journal; Nov2025, Vol. 68 Issue 3, p1-12, 12p

Measure Student Aptitude in Learning Programming in Higher Education—A Data Analysis.

Authors: Pires, João Borges, Ana Rosa Bernardino, Jorge et al.

Source: Computers (2073-431X); Oct2025, Vol. 14 Issue 10, p428, 21p

Subject Terms: COMPUTER programming education, COGNITIVE testing, HIGHER education, PREDICTION models, EDUCATIONAL evaluation, ANALYTICAL skills, ACADEMIC achievement, DATA analysis

Separable Algorithmic Representations of Classical Systems and their Applications.

Authors: Kasymov, N. Kh. Dadazhanov, R. N. Ibragimov, F. N.

Source: Journal of Mathematical Sciences; Jan2024, Vol. 278 Issue 3, p476-519, 44p

Subject Terms: TOPOLOGICAL property, ARITHMETIC

On Non-Detectability of Non-Computability and the Degree of Non-Computability of Solutions of Circuit and Wave Equations on Digital Computers.

Authors: Boche, Holger Pohl, Volker

Source: IEEE Transactions on Information Theory; Aug2022, Vol. 68 Issue 8, p5561-5578, 18p

Subject Terms: TURING machines, DIFFERENTIABLE functions, QUANTUM computing, DIFFERENTIABLE dynamical systems, WAVE equation, COMPUTERS

Algorithmic procedures

Authors: Friedman, Harvey Mansfield, Richard

Source: Transactions of the American Mathematical Society. 332:297-312

Subject Terms: computability, definability, pairing functions, computations on rings and fields, program language, 0102 computer and information sciences, 0101 mathematics, Abstract and axiomatic computability and recursion theory, 01 natural sciences, abstract recursion theory, computable functions

File Description: application/xml

Access URL: https://www.ams.org/tran/1992-332-01/S0002-9947-1992-1055807-7/S0002-9947-1992-1055807-7.pdf
https://zbmath.org/90216
https://doi.org/10.2307/2154033

The language of the law vs. the language of the computer: a bilingual model of legal education in the age of technology and artificial intelligence.

Authors: Cinar, Ali Ekber

Source: Law, Innovation & Technology; Dec2024, Vol. 16 Issue 2, p558-598, 41p

Subject Terms: PROGRAMMING languages, LEGAL education, ARTIFICIAL intelligence, TECHNOLOGICAL innovations, LEGAL language

Prediction and MDL for infinite sequences.

Authors: Milovanov, Alexey

Source: Theory of Computing Systems; Oct2024, Vol. 68 Issue 5, p1124-1137, 14p

Subject Terms: SUM of squares, COMPUTER science, SOCIAL responsibility of business, FORECASTING, STATISTICS

Are two H-spaces homotopy equivalent? An algorithmic view point.

Authors: Šimková, Mária

Source: Journal of Topology & Analysis; Aug2025, Vol. 17 Issue 4, p1103-1136, 34p

Subject Terms: ALGORITHMS, DECISION making