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We present an autonomous robot designed to optimize and to make secure the process of putting vineyard post during trellising. The principle is as follows: The robot goes at the location of the post in an autonomous way with a centimetric accuracy, the user provides the post, and then the robot drives the post into earth without additional user intervention. The robot is designed from a small backhoe loader. The tool of the backhoe loader has been replaced by a hydraulic hammer. All the hydraulic functions of the machine are controlled, including the hammer and the tracks. The robot is geolocalized with a differential global navigation satellite systems (GNSS for short) mono-frequency low-cost system relying on a mix of triple and double differences.

The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability result holds even if the probabilistic automata have only one probabilistic transition. Our main contribution is to introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is shown decidable (and PSPACE-complete). We construct an algorithm based on the computation of a monoid abstracting the behaviours of the automaton, and rely on algebraic techniques developed by Simon for the correctness proof. The class of leaktight automata is decidable in PSPACE, subsumes all subclasses of probabilistic automata whose value 1 problem is known to be decidable (in particular deterministic automata), and is closed under two natural composition operators., Comment: arXiv admin note: significant text overlap with arXiv:1104.3054