Recently,Greenfeld and Tao(2024)disproved the conjecture that translational tilings of a single tile can always be periodic.In another paper(Greenfeld and Tao(2025)),they also showed that if the dimension n is part of...Recently,Greenfeld and Tao(2024)disproved the conjecture that translational tilings of a single tile can always be periodic.In another paper(Greenfeld and Tao(2025)),they also showed that if the dimension n is part of the input,the translational tiling for subsets of Z^(n) with one tile is undecidable.These two results are very strong pieces of evidence for the conjecture that translational tiling of Z^(n) with a monotile is undecidable for some fixed n.In this paper,we show that translational tiling of the 3-dimensional space with a set of 5 polycubes is undecidable.By introducing a technique that lifts a set of polycubes and its tiling from the 3-dimensional space to the 4-dimensional space,we manage to show that translational tiling of the 4-dimensional space with a set of 4 tiles is undecidable.This is a step towards the attempt to settle the conjecture of the undecidability of translational tiling of the n-dimensional space with a monotile for some fixed n.展开更多
By analyzing An Enemy of the People in a deconstructive approach,this thesis endeavors to dismantle the binary oppositions long established in the text:minority privileging over majority,morality over authority and ve...By analyzing An Enemy of the People in a deconstructive approach,this thesis endeavors to dismantle the binary oppositions long established in the text:minority privileging over majority,morality over authority and verity over falsity.It comes to the conclusion that the meaning of the drama is undecidable,which helps to arrive at new findings in literary studies.展开更多
In this paper,the author first reviews the history of Hilbert’s Tenth Problem,and then study mixed quantifier prefixes over Diophantine equations with integer variables.For example,the author proves that■^(2)■^(4) ...In this paper,the author first reviews the history of Hilbert’s Tenth Problem,and then study mixed quantifier prefixes over Diophantine equations with integer variables.For example,the author proves that■^(2)■^(4) over Z is undecidable,that is,there is no algorithm to determine for any P(x_(1),···,x_(6))∈Z[x_(1),···,x_(6)]whether■x_(1)■x_(2)■x_(3)■x_(4)■x_(5)■x_(6)(P(x_(1),···,x_(6))=0),where x_(1),···,x_(6) are integer variables.The author also has some similar undecidable results with universal quantifies bounded,for example,■^(2)■^(2)■^(2) over Z with ■ bounded is undecidable.The author conjectures that■^(2)■^(2) over Z is undecidable.展开更多
Hilbert’s Tenth Problem(HTP)asks for an algorithm to test whether an arbitrary polynomial Diophantine equation with integer coefficients has solutions over the ring Z of integers.This was finally solved negatively by...Hilbert’s Tenth Problem(HTP)asks for an algorithm to test whether an arbitrary polynomial Diophantine equation with integer coefficients has solutions over the ring Z of integers.This was finally solved negatively by Matiyasevich in 1970.In this paper we obtain some further results on HTP over Z.We prove that there is no algorithm to determine for any P(z1,...,z9)∈Z[z1,...,z9]whether the equation P(z1,...,z9)=0 has integral solutions with z9≥0.Consequently,there is no algorithm to test whether an arbitrary polynomial Diophantine equation P(z1,...,z11)=0(with integer coefficients)in 11 unknowns has integral solutions,which provides the best record on the original HTP over Z.We also prove that there is no algorithm to test for any P(z1,...,z17)∈Z[z1,...,z17]whether P(z12,...,z172)=0 has integral solutions,and that there is a polynomial Q(z1,...,z20)∈Z[z1,...,z20]such that{Q(z12,...,z202):z1,...,z20∈Z}∩{0,1,2,...}coincides with the set of all primes.展开更多
In this paper some undecidable problems on approximability of NP op-timization problems are investigated. In particular, the following problems are all undecidable: (1) Given an NP optimization problem, is it approal-...In this paper some undecidable problems on approximability of NP op-timization problems are investigated. In particular, the following problems are all undecidable: (1) Given an NP optimization problem, is it approal-mable in polynomial time? (2) For any polynomialtime computable function r(n), given a polynomial time approkimable NP optimization problem, has it a polynomialtime approximation algorithm with approkimation performance ratio r(n) (r(n)-approkimable)? (3) For any polynomial-time computable func-tions r(n), r'(n), where r'(n) < r(n) a.e., given an r(n)-approkimable NP opti-mization problem, is it r'(n)-approalmable?展开更多
The article indicates the essential tasks of a semiotics of artificial intelligence:studying the way it simulates the expression of intelligence;the way it produces content that is creatively endowed;the ideological a...The article indicates the essential tasks of a semiotics of artificial intelligence:studying the way it simulates the expression of intelligence;the way it produces content that is creatively endowed;the ideological assumptions of artificial intelligence within the culture that produces it.Artificial intelligence is,from a semiotic point of view,the predominant technology of fakery in the current era.On the strength of its studies on the false,semiotics can therefore also be applied to the analysis of the fake that,in increasingly sophisticated forms,is produced through artificial intelligence and through the deep learning of neural networks.The article focuses on the adversarial ones,trying to highlight their ideological assumptions and cultural developments,which seem to indicate the entry of human societies and cultures into the‘realm of the absolute fake'.展开更多
<正> To process the data with strong historical features, such as data in earthquake research,weather forecast, medical records and census, a new mathematical model of historical datasystem is proposed. This mod...<正> To process the data with strong historical features, such as data in earthquake research,weather forecast, medical records and census, a new mathematical model of historical datasystem is proposed. This model can be characterized as ' relational database with timemark + histotical rule base = historical database', and it is easy to implement. The formaldescription of historical database and a special class of historical rules-premonitory de-pendency (abbreviated as PD)-are discussed, the poperties and inference axioms of PDare investigated. The soundness and completeness of the axioms are proved. The problemsabout the true-set of historical rules, such as the problems of emptyness, infiniteness,equivalence and containment are proved to be undecidable.展开更多
基金supported by the Research Fund of Guangdong University of Foreign Studies(Grant Nos.297-ZW200011 and 297-ZW230018)National Natural Science Foundation of China(Grant No.61976104).
文摘Recently,Greenfeld and Tao(2024)disproved the conjecture that translational tilings of a single tile can always be periodic.In another paper(Greenfeld and Tao(2025)),they also showed that if the dimension n is part of the input,the translational tiling for subsets of Z^(n) with one tile is undecidable.These two results are very strong pieces of evidence for the conjecture that translational tiling of Z^(n) with a monotile is undecidable for some fixed n.In this paper,we show that translational tiling of the 3-dimensional space with a set of 5 polycubes is undecidable.By introducing a technique that lifts a set of polycubes and its tiling from the 3-dimensional space to the 4-dimensional space,we manage to show that translational tiling of the 4-dimensional space with a set of 4 tiles is undecidable.This is a step towards the attempt to settle the conjecture of the undecidability of translational tiling of the n-dimensional space with a monotile for some fixed n.
文摘By analyzing An Enemy of the People in a deconstructive approach,this thesis endeavors to dismantle the binary oppositions long established in the text:minority privileging over majority,morality over authority and verity over falsity.It comes to the conclusion that the meaning of the drama is undecidable,which helps to arrive at new findings in literary studies.
基金supported by the National Natural Science Foundation of China under Grant No.12371004。
文摘In this paper,the author first reviews the history of Hilbert’s Tenth Problem,and then study mixed quantifier prefixes over Diophantine equations with integer variables.For example,the author proves that■^(2)■^(4) over Z is undecidable,that is,there is no algorithm to determine for any P(x_(1),···,x_(6))∈Z[x_(1),···,x_(6)]whether■x_(1)■x_(2)■x_(3)■x_(4)■x_(5)■x_(6)(P(x_(1),···,x_(6))=0),where x_(1),···,x_(6) are integer variables.The author also has some similar undecidable results with universal quantifies bounded,for example,■^(2)■^(2)■^(2) over Z with ■ bounded is undecidable.The author conjectures that■^(2)■^(2) over Z is undecidable.
基金supported by National Natural Science Foundation of China(Grant No.11971222)。
文摘Hilbert’s Tenth Problem(HTP)asks for an algorithm to test whether an arbitrary polynomial Diophantine equation with integer coefficients has solutions over the ring Z of integers.This was finally solved negatively by Matiyasevich in 1970.In this paper we obtain some further results on HTP over Z.We prove that there is no algorithm to determine for any P(z1,...,z9)∈Z[z1,...,z9]whether the equation P(z1,...,z9)=0 has integral solutions with z9≥0.Consequently,there is no algorithm to test whether an arbitrary polynomial Diophantine equation P(z1,...,z11)=0(with integer coefficients)in 11 unknowns has integral solutions,which provides the best record on the original HTP over Z.We also prove that there is no algorithm to test for any P(z1,...,z17)∈Z[z1,...,z17]whether P(z12,...,z172)=0 has integral solutions,and that there is a polynomial Q(z1,...,z20)∈Z[z1,...,z20]such that{Q(z12,...,z202):z1,...,z20∈Z}∩{0,1,2,...}coincides with the set of all primes.
文摘In this paper some undecidable problems on approximability of NP op-timization problems are investigated. In particular, the following problems are all undecidable: (1) Given an NP optimization problem, is it approal-mable in polynomial time? (2) For any polynomialtime computable function r(n), given a polynomial time approkimable NP optimization problem, has it a polynomialtime approximation algorithm with approkimation performance ratio r(n) (r(n)-approkimable)? (3) For any polynomial-time computable func-tions r(n), r'(n), where r'(n) < r(n) a.e., given an r(n)-approkimable NP opti-mization problem, is it r'(n)-approalmable?
基金funding from the European Research Council(ERC)under the European Union's Horizon 2020 research and innovation program(Grant Agreement No 819649-FACETS,http://dx.doi.0rg/10.13039/501100000781).
文摘The article indicates the essential tasks of a semiotics of artificial intelligence:studying the way it simulates the expression of intelligence;the way it produces content that is creatively endowed;the ideological assumptions of artificial intelligence within the culture that produces it.Artificial intelligence is,from a semiotic point of view,the predominant technology of fakery in the current era.On the strength of its studies on the false,semiotics can therefore also be applied to the analysis of the fake that,in increasingly sophisticated forms,is produced through artificial intelligence and through the deep learning of neural networks.The article focuses on the adversarial ones,trying to highlight their ideological assumptions and cultural developments,which seem to indicate the entry of human societies and cultures into the‘realm of the absolute fake'.
基金Project supported by the National Natural Science Foundation of China.
文摘<正> To process the data with strong historical features, such as data in earthquake research,weather forecast, medical records and census, a new mathematical model of historical datasystem is proposed. This model can be characterized as ' relational database with timemark + histotical rule base = historical database', and it is easy to implement. The formaldescription of historical database and a special class of historical rules-premonitory de-pendency (abbreviated as PD)-are discussed, the poperties and inference axioms of PDare investigated. The soundness and completeness of the axioms are proved. The problemsabout the true-set of historical rules, such as the problems of emptyness, infiniteness,equivalence and containment are proved to be undecidable.
