Polynomial-time algorithm for the orbit problem
Journal of the ACM (JACM)
A simple proof of the Skolem-Mahler-Lech Theorem
Theoretical Computer Science
A course in computational algebraic number theory
A course in computational algebraic number theory
The Complexity of the A B C Problem
SIAM Journal on Computing
Lectures on Linear Sequential Machines
Lectures on Linear Sequential Machines
On the Power of Random Access Machines
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
The orbit problem is decidable
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Reachability in Linear Dynamical Systems
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
On the Complexity of Numerical Analysis
SIAM Journal on Computing
The orbit problem is in the GapL hierarchy
Journal of Combinatorial Optimization
Orbits of linear maps and regular languages
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Termination of integer linear programs
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
On the Termination of Integer Loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Decision problems for linear recurrence sequences
RP'12 Proceedings of the 6th international conference on Reachability Problems
The orbit problem in higher dimensions
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The orbit problem in higher dimensions
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We consider higher-dimensional versions of Kannan and Lipton's Orbit Problem---determining whether a target vector space V may be reached from a starting point x under repeated applications of a linear transformation A. Answering two questions posed by Kannan and Lipton in the 1980s, we show that when V has dimension one, this problem is solvable in polynomial time, and when V has dimension two or three, the problem is in NPRP.