Hilbert's tenth problem
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Deciding stability and mortality of piecewise affine dynamical systems
Theoretical Computer Science
Termination analysis of integer linear loops
CONCUR 2005 - Concurrency Theory
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Linear ranking with reachability
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Discovering non-linear ranking functions by solving semi-algebraic systems
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Closed-Form Upper Bounds in Static Cost Analysis
Journal of Automated Reasoning
Termination of loop programs with polynomial guards
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
On the termination of integer loops
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Deciding conditional termination
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
On the Termination of Integer Loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic termination analysis of solvable loops
Journal of Symbolic Computation
Non-termination sets of simple linear loops
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
Termination proofs for linear simple loops
SAS'12 Proceedings of the 19th international conference on Static Analysis
On the linear ranking problem for integer linear-constraint loops
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The orbit problem in higher dimensions
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Eventual linear ranking functions
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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We show that termination of a simple class of linear loops over the integers is decidable. Namely we show that termination of deterministic linear loops is decidable over the integers in the homogeneous case, and over the rationals in the general case. This is done by analyzing the powers of a matrix symbolically using its eigenvalues. Our results generalize the work of Tiwari [Tiw04], where similar results were derived for termination over the reals. We also gain some insights into termination of non-homogeneous integer programs, that are very common in practice.