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O-minimal invariants for discrete-time dynamical systems
Published 2022“…We establish two main decidability results, one of them conditional on Schanuel’s conjecture is transcendental number theory.…”
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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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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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6
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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9
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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10
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.…”
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First-order orbit queries
Published 2020“…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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The polytope-collision problem
Published 2017“…Using techniques from transcendental number theory, and separation bounds on algebraic numbers, we are able to solve such instances in PSPACE.…”
Journal article