Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
Factoring sparse multivariate polynomials
Journal of Computer and System Sciences
Fast parallel absolute irreducibility testing
Journal of Symbolic Computation
Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
Computational complexities of diophantine equations with parameters
Journal of Algorithms
Factoring multivariate polynomials over algebraic number fields
SIAM Journal on Computing
Generalized Riemann hypothesis and factoring polynomials over finite fields
Journal of Algorithms
Polynomial time algorithms for sentences over number fields
Information and Computation
Computational complexity of arithmetical sentences
Information and Computation
Sentences over integral domains and their computational complexities
Information and Computation
Computational arithmetic geometry: Sentences nearly in the polynomials hierarchy
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Elements of the Theory of Computation
Elements of the Theory of Computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Absolute Primality of Polynomials is Decidable in Random Polynomial Time in the Number of Variables
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Modern Computer Algebra
Factoring Polynomials over Algebraic Number Fields
SIAM Journal on Computing
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Hilbert's Irreducibility Theorem is applied to find the upper bounds of the time complexities of various decision problems in arithmetical sentences and the following results are proved:1.The decision problem of @?@? sentences over an algebraic number field is in P. 2.The decision problem of @?@? sentences over the collection of all fields with characteristic 0 is in P. 3.The decision problem of @?@? sentences over a function field with characteristic p is polynomial time reducible to the factorization of polynomials over Z"p. 4.The decision problem of @?@? sentences over the collection of all fields with characteristic p is polynomial time reducible to the factorization of polynomials over Z"p. 5.The decision problem of @?@? sentences over the collection of all fields is polynomial time reducible to the factorization of integers over Z and the factorization of polynomials over finite fields.