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The Membership Problem for hypergeometric sequences with quadratic parameters
Published 2023Subjects:Conference item -
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Invariants for continuous linear dynamical systems
Published 2020“…In particular, assuming Schanuel’s conjecture in transcendental number theory, we establish effective synthesis of o-minimal invariants in the case of semi-algebraic error sets. …”
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Coverings of Curves of Genus 2.
Published 2000“…This classical technique has recently been given a new lease of life by being combined with descent techniques on Jacobians of curves, Chabauty techniques, and the increased power of software to perform algebraic number theory. We shall survey recent applications during the last 5 years which have used Chabauty techniques and covering collections of curves of genus 2 obtained from pullbacks along isogenies on their Jacobians.…”
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What's decidable about linear loops?
Published 2022“…We also note that lifting either of these restrictions and retaining decidability would necessarily require major breakthroughs in number theory.…”
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Termination of linear loops over the integers
Published 2019“…For the class of loops considered in this paper, the question of deciding termination on a specific initial value is a longstanding open problem in number theory. The key to our decision procedure is in showing how to circumvent the difficulties inherent in deciding termination on a fixed initial value.…”
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Solvability of matrix-exponential equations
Published 2016“…Our decidability proof relies on a number of theorems from algebraic and transcendental number theory, most notably those of Baker, Kronecker, Lindemann, and Masser, as well as some useful geometric and linear-algebraic results, including the Minkowski-Weyl theorem and a new (to the best of our knowledge) result about the uniqueness of strictly upper triangular matrix logarithms of upper unitriangular matrices. …”
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On the Skolem Problem for continuous linear dynamical systems
Published 2016“…In this paper we show decidability of the bounded problem subject to Schanuel’s Conjecture, a unifying conjecture in transcendental number theory. We furthermore analyse the unbounded problem in terms of the frequencies of the differential equation, that is, the imaginary parts of the characteristic roots. …”
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On the skolem problem for continuous linear dynamical systems
Published 2016“…In this paper we show decidability of the bounded problem subject to Schanuel's Conjecture, a unifying conjecture in transcendental number theory. We furthermore analyse the unbounded problem in terms of the frequencies of the differential equation, that is, the imaginary parts of the characteristic roots. …”
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Identity testing for radical expressions
Published 2022“…Our proof relies on theorems from algebraic and analytic number theory, such as the Chebotarev density theorem and quadratic reciprocity.…”
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Solvability of matrix-exponential equations
Published 2016“…Our decidability proof relies on a number of theorems from algebraic and transcendental number theory, most notably those of Baker, Kronecker, Lindemann, and Masser, as well as some useful geometric and linear-algebraic results, including the MinkowskiWeyl theorem and a new (to the best of our knowledge) result about the uniqueness of strictly upper triangular matrix logarithms of upper unitriangular matrices. …”
Conference item -
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Solvability of matrix-exponential equations
Published 2016“…Our decidability proof relies on a number of theorems from algebraic and transcendental number theory, most notably those of Baker, Kronecker, Lindemann, and Masser, as well as some useful geometric and linear-algebraic results, including the MinkowskiWeyl theorem and a new (to the best of our knowledge) result about the uniqueness of strictly upper triangular matrix logarithms of upper unitriangular matrices. …”
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The Semialgebraic Orbit Problem
Published 2019“…Our decision procedure relies on separation bounds for algebraic numbers as well as a classical result of transcendental number theory - Baker's theorem on linear forms in logarithms of algebraic numbers. …”
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On the decidability of monadic second-order logic with arithmetic predicates
Published 2024“…</li></ul> These results are obtained by exploiting and combining techniques from dynamical systems, number theory, and automata theory.…”
Conference item