
Undecidability of Inferring Linear Integer Invariants
We show that the problem of determining the existence of an inductive in...
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Termination of Triangular Integer Loops is Decidable
We consider the problem whether termination of affine integer loops is d...
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On Termination of Integer Linear Loops
We consider the problem of determining termination of singlepath loops ...
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Monitoring of Traffic Manoeuvres with Imprecise Information
In monitoring, we algorithmically check if a single behavior satisfies a...
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Termination of Linear Loops over the Integers
We consider the problem of deciding termination of singlepath while loo...
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Monadic Decomposition in Integer Linear Arithmetic (Technical Report)
Monadic decomposability is a notion of variable independence, which asks...
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Proving Nontermination by Program Reversal
We present a new approach to proving nontermination of nondeterministi...
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Reflections on Termination of Linear Loops
This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear integer arithmetic has a best model as a deterministic affine transition system. Second, we show that for any linear dynamical system f with integer eigenvalues and any integer arithmetic formula G, there is a linear integer arithmetic formula that holds exactly for the states of f for which G is eventually invariant. Combining the two, we develop a monotone conditional termination analysis for general loops.
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