MATRIX EQUATIONS AND HILBERT'S TENTH PROBLEM

DOI10.1142/S0218196708004925zbMath1173.03009MaRDI QIDQ3601323

Juhani Karhumäki, Igor Potapov, Paul C. Bell, Vesa Halava, Tero J.Harju

Publication date: 10 February 2009

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

zbMATH Keywords

undecidabilitymatrix equationsdiophantine equations

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25) Matrices, determinants in number theory (11C20)

Related Items (11)

On the decidability and complexity of problems for restricted hierarchical hybrid systems ⋮ Products of matrices and recursively enumerable sets ⋮ On the Identity Problem for the Special Linear Group and the Heisenberg Group. ⋮ Vector and scalar reachability problems in \(\operatorname{SL}(2, \mathbb{Z})\) ⋮ The freeness problem over matrix semigroups and bounded languages ⋮ On Post correspondence problem for letter monotonic languages ⋮ Freeness properties of weighted and probabilistic automata over bounded languages ⋮ On the mortality problem: from multiplicative matrix equations to linear recurrence sequences and beyond ⋮ Post Correspondence Problem and Small Dimensional Matrices ⋮ On the Mortality Problem: From Multiplicative Matrix Equations to Linear Recurrence Sequences and Beyond ⋮ Rational subsets of unitriangular groups

Cites Work

• On the membership of invertible diagonal and scalar matrices
• On the definition of a family of automata
• On a Theorem of R. Jungen
• Polynomial-time algorithm for the orbit problem
• ON THE UNDECIDABILITY OF FREENESS OF MATRIX SEMIGROUPS
• ON THE UNDECIDABILITY OF THE FREENESS OF INTEGER MATRIX SEMIGROUPS
• Unnamed Item

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