
Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs
Probabilistic programs extend classical imperative programs with realva...
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Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a wellknown and fund...
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Efficient Algorithms for Checking Fast Termination in VASS
Vector Addition Systems with States (VASS) consists of a finite state sp...
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The Probabilistic Termination Tool Amber
We describe the Amber tool for proving and refuting the termination of a...
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Automated Termination Analysis of Polynomial Probabilistic Programs
The termination behavior of probabilistic programs depends on the outcom...
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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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The Polynomial Complexity of Vector Addition Systems with States
Vector addition systems are an important model in theoretical computer s...
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Deciding Fast Termination for Probabilistic VASS with Nondeterminism
A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with nonnegative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter to decrease below zero. The pVASS can be used as abstractions of probabilistic programs with many decidable properties. The use of pVASS as abstractions requires the presence of nondeterminism in the model. In this paper, we develop techniques for checking fast termination of pVASS with nondeterminism. That is, for every initial configuration of size n, we consider the worst expected number of transitions needed to reach a configuration with some counter negative (the expected termination time). We show that the problem whether the asymptotic expected termination time is linear is decidable in polynomial time for a certain natural class of pVASS with nondeterminism. Furthermore, we show the following dichotomy: if the asymptotic expected termination time is not linear, then it is at least quadratic, i.e., in Ω(n^2).
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