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Cited by 49
Observability of Turing Machines: A Refinement of the Theory of Computation

A New Computational Approach to Infinity for Modelling Physical Phenomena
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-00297-2_35
Book  Springer Proceedings in Physics (Frontiers of Fundamental Physics and Physics Education Research) Volume 145 (2014), p. 353
A New Computational Methodology Using Infinite and Infinitesimal Numbers
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-642-15979-4_72
Book  Lecture Notes in Computer Science (Cellular Automata) Volume 6350 (2010), p. 646
A New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-030-93642-6_1
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 3
A Simulink-Based Infinity Computer Simulator and Some Applications
Alberto Falcone, Alfredo Garro, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-030-40616-5_31
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11974 (2020), p. 362
A classification of one-dimensional cellular automata using infinite computations
Louis D’Alotto
https://doi.org/10.1016/j.amc.2014.06.087
Journal  Applied Mathematics and Computation Volume 255 (2015), p. 15
A constructive sequence algebra for the calculus of indications
Rocco Gangle, Gianluca Caterina, Fernando Tohmé
https://doi.org/10.1007/s00500-020-05121-1
Journal  Soft Computing Volume 24, Issue 23 (2020), p. 17621
A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic
P. Amodio, F. Iavernaro, F. Mazzia, M.S. Mukhametzhanov, Ya.D. Sergeyev
https://doi.org/10.1016/j.matcom.2016.03.007
Journal  Mathematics and Computers in Simulation Volume 141 (2017), p. 24
A new approach to the Z-transform through infinite computation
Fabio Caldarola, Mario Maiolo, Viviana Solferino
https://doi.org/10.1016/j.cnsns.2019.105019
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 82 (2020), p. 105019
AIP Conference Proceedings
Davide Rizza
https://doi.org/10.1063/1.4965369
Conference  Volume 1776 (2016), p. 090005
AIP Conference Proceedings
Yaroslav D. Sergeyev
https://doi.org/10.1063/1.5043649
Conference  Volume 1978 (2018), p. 020004
AIP Conference Proceedings
Yaroslav D. Sergeyev
https://doi.org/10.1063/1.4951756
Conference  Volume 1738 (2016), p. 020012
AIP Conference Proceedings
Louis D’Alotto
https://doi.org/10.1063/1.4965309
Conference  Volume 1776 (2016), p. 020003
Addressing Ill-Conditioning in Global Optimization Using a Software Implementation of the Infinity Computer
Marat S. Mukhametzhanov, Dmitri E. Kvasov
https://doi.org/10.1007/978-3-030-93642-6_14
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 347
An application of Grossone to the study of a family of tilings of the hyperbolic plane
Maurice Margenstern
https://doi.org/10.1016/j.amc.2011.04.014
Journal  Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8005
Combinators as Observable Presheaves: A Characterization in the Grossone Framework
Rocco Gangle, Fernando Tohmé, Gianluca Caterina
https://doi.org/10.1007/978-3-031-81247-7_7
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 84
Computations with Grossone-Based Infinities
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-21819-9_6
Book  Lecture Notes in Computer Science (Unconventional Computation and Natural Computation) Volume 9252 (2015), p. 89
Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs
Fernando Tohmé, Gianluca Caterina, Rocco Gangle
https://doi.org/10.1016/j.amc.2020.125343
Journal  Applied Mathematics and Computation Volume 385 (2020), p. 125343
Conjugate-symplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer
F. Iavernaro, F. Mazzia, M.S. Mukhametzhanov, Ya.D. Sergeyev
https://doi.org/10.1016/j.apnum.2019.06.011
Journal  Applied Numerical Mathematics Volume 155 (2020), p. 58
East-West paths to unconventional computing
Andrew Adamatzky, Selim Akl, Mark Burgin, Cristian S. Calude, José Félix Costa, Mohammad Mahdi Dehshibi, Yukio-Pegio Gunji, Zoran Konkoli, Bruce MacLennan, Bruno Marchal, Maurice Margenstern, Genaro J. Martínez, Richard Mayne, Kenichi Morita, Andrew Schumann, Yaroslav D. Sergeyev, Georgios Ch. Sirakoulis, Susan Stepney, Karl Svozil, Hector Zenil
https://doi.org/10.1016/j.pbiomolbio.2017.08.004
Journal  Progress in Biophysics and Molecular Biology Volume 131 (2017), p. 469
Exact Numerical Differentiation on the Infinity Computer and Applications in Global Optimization
Maria Chiara Nasso, Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-030-93642-6_9
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 221
Examples of the Usage of Infinities and Infinitesimals in Numerical Computations
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-12745-3_15
Book  Communications in Computer and Information Science (Advances in Artificial Life and Evolutionary Computation) Volume 445 (2014), p. 190
Finite and Infinite Computations and a Classification of Two-Dimensional Cellular Automata Using Infinite Computations
Louis D’Alotto
https://doi.org/10.1007/978-3-319-62932-2_17
Book  Lecture Notes in Computer Science (Parallel Computing Technologies) Volume 10421 (2017), p. 183
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019
Marat S. Mukhametzhanov, Yaroslav D. Sergeyev
https://doi.org/10.1063/5.0026820
Conference  Volume 2293 (2020), p. 420045
Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite
Yaroslav D. Sergeyev
https://doi.org/10.1007/s10699-018-9566-y
Journal  Foundations of Science Volume 24, Issue 1 (2019), p. 153
Infinite Games on Finite Graphs Using Grossone
Louis D’Alotto
https://doi.org/10.1007/978-3-030-40616-5_29
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11974 (2020), p. 346
Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves
Luigi Antoniotti, Fabio Caldarola, Mario Maiolo
https://doi.org/10.1007/s00009-020-01531-5
Journal  Mediterranean Journal of Mathematics Volume 17, Issue 3 (2020)
Infinite computations and the generic finite
Louis H. Kauffman
https://doi.org/10.1016/j.amc.2014.06.054
Journal  Applied Mathematics and Computation Volume 255 (2015), p. 25
Infinite games on finite graphs using grossone
Louis D’Alotto
https://doi.org/10.1007/s00500-020-05167-1
Journal  Soft Computing Volume 24, Issue 23 (2020), p. 17509
Infinity computations in cellular automaton forest-fire model
D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa
https://doi.org/10.1016/j.cnsns.2014.06.031
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 20, Issue 3 (2015), p. 861
Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm
Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev
https://doi.org/10.1016/j.amc.2017.05.058
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 298
Modeling Infinite Games on Finite Graphs Using Numerical Infinities
Louis D’Alotto
https://doi.org/10.1007/978-3-030-93642-6_12
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 297
Non-Archimedean game theory: A numerical approach
Lorenzo Fiaschi, Marco Cococcioni
https://doi.org/10.1016/j.amc.2020.125356
Journal  Applied Mathematics and Computation Volume 409 (2021), p. 125356
Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications
Renato De Leone
https://doi.org/10.1016/j.amc.2017.03.029
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 290
Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-1-4614-7582-8_1
Book  Springer Proceedings in Mathematics & Statistics (Dynamics of Information Systems: Algorithmic Approaches) Volume 51 (2013), p. 1
Observability in the Univalent Universe
Fernando Tohmé, Gianluca Caterina, Rocco Gangle
https://doi.org/10.1007/s00009-022-02121-3
Journal  Mediterranean Journal of Mathematics Volume 19, Issue 5 (2022)
On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function
Yaroslav D. Sergeyev
https://doi.org/10.1134/S2070046611020051
Journal  P-Adic Numbers, Ultrametric Analysis, and Applications Volume 3, Issue 2 (2011), p. 129
On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales
Yaroslav D. Sergeyev, Dmitri E. Kvasov, Marat S. Mukhametzhanov
https://doi.org/10.1016/j.cnsns.2017.11.013
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 59 (2018), p. 319
On the topological convergence of multi-rule sequences of sets and fractal patterns
Fabio Caldarola, Mario Maiolo
https://doi.org/10.1007/s00500-020-05358-w
Journal  Soft Computing Volume 24, Issue 23 (2020), p. 17737
Percolation Transition and Related Phenomena in Terms of Grossone Infinity Computations
Dmitry I. Iudin, Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-33924-5_11
Book  Emergence, Complexity and Computation (Advances in Unconventional Computing) Volume 22 (2017), p. 239
Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming
Renato De Leone, Giovanni Fasano, Yaroslav D. Sergeyev
https://doi.org/10.1007/s10589-017-9957-y
Journal  Computational Optimization and Applications Volume 71, Issue 1 (2018), p. 73
Reprint of Infinity computations in cellular automaton forest-fire model
D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa
https://doi.org/10.1016/j.cnsns.2014.10.019
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 190
Single-tape and multi-tape Turing machines through the lens of the Grossone methodology
Yaroslav D. Sergeyev, Alfredo Garro
https://doi.org/10.1007/s11227-013-0894-y
Journal  The Journal of Supercomputing Volume 65, Issue 2 (2013), p. 645
Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically
Yaroslav D. Sergeyev
https://doi.org/10.1016/j.amc.2013.04.019
Journal  Applied Mathematics and Computation Volume 219, Issue 22 (2013), p. 10668
Some Paradoxes of Infinity Revisited
Yaroslav D. Sergeyev
https://doi.org/10.1007/s00009-022-02063-w
Journal  Mediterranean Journal of Mathematics Volume 19, Issue 3 (2022)
The Grossone Methodology Perspective on Turing Machines
Yaroslav D. Sergeyev, Alfredo Garro
https://doi.org/10.1007/978-3-319-09039-9_7
Book  Emergence, Complexity and Computation (Automata, Universality, Computation) Volume 12 (2015), p. 139
The Olympic Medals Ranks, Lexicographic Ordering, and Numerical Infinities
Yaroslav D. Sergeyev
https://doi.org/10.1007/s00283-014-9511-z
Journal  The Mathematical Intelligencer Volume 37, Issue 2 (2015), p. 4
The Sierpinski curve viewed by numerical computations with infinities and infinitesimals
Fabio Caldarola
https://doi.org/10.1016/j.amc.2017.06.024
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 321
The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area
Yaroslav D. Sergeyev
https://doi.org/10.1016/j.cnsns.2015.07.004
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 31, Issue 1-3 (2016), p. 21
The exact measures of the Sierpiński d-dimensional tetrahedron in connection with a Diophantine nonlinear system
Fabio Caldarola
https://doi.org/10.1016/j.cnsns.2018.02.026
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 63 (2018), p. 228


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