Abstract
This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transitions.
We show that the two following properties of numberless probabilistic automata are recursively inseparable:
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all instances of the numberless automaton have value 1,
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no instance of the numberless automaton has value 1.
The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 259454 (GALE) and from the French Agence Nationale de la Recherche projects EQINOCS (ANR-11-BS02-004) and STOCH-MC (ANR-13-BS02-0011-01).
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Fijalkow, N., Gimbert, H., Horn, F., Oualhadj, Y. (2014). Two Recursively Inseparable Problems for Probabilistic Automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_23
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DOI: https://doi.org/10.1007/978-3-662-44522-8_23
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