conference paper published yes Udi Boker author 31E297B6-F248-11E8-B48F-1D18A9856A87 Thomas A Henzinger author 40876CD8-F248-11E8-B48F-1D18A9856A870000−0002−2985−7724 ToHe department FSTTCS: Foundations of Software Technology and Theoretical Computer Science Rigorous Systems Engineering project Quantitative Reactive Modeling project Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential of approximate determinization. We define approximate determinization with respect to a distance function, and investigate this potential. We show that sum automata cannot be determinized approximately with respect to any distance function. However, restricting to nonnegative weights allows for approximate determinization with respect to some distance functions. Discounted-sum automata allow for approximate determinization, as the influence of a word’s suffix is decaying. However, the naive approach, of unfolding the automaton computations up to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states. We prove matching lower bounds, showing exponential dependency on each of these three parameters. Average and limit-average automata are shown to prohibit approximate determinization with respect to any distance function, and this is the case even for two weights, 0 and 1. https://research-explorer.ista.ac.at/download/2891/4826/IST-2017-805-v1+1_34.pdf application/pdfno https://creativecommons.org/licenses/by-nc-nd/4.0/ Schloss Dagstuhl - Leibniz-Zentrum für Informatik2012Hyderabad, India eng 10.4230/LIPIcs.FSTTCS.2012.362 18362 - 373 Boker, Udi, and Thomas A Henzinger. “Approximate Determinization of Quantitative Automata.” In <i>Leibniz International Proceedings in Informatics</i>, 18:362–73. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. <a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362">https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362</a>. U. Boker, T.A. Henzinger, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 362–373. Boker U, Henzinger TA. 2012. Approximate determinization of quantitative automata. Leibniz International Proceedings in Informatics. FSTTCS: Foundations of Software Technology and Theoretical Computer Science, LIPIcs, vol. 18, 362–373. U. Boker and T. A. Henzinger, “Approximate determinization of quantitative automata,” in <i>Leibniz International Proceedings in Informatics</i>, Hyderabad, India, 2012, vol. 18, pp. 362–373. Boker, U., &#38; Henzinger, T. A. (2012). Approximate determinization of quantitative automata. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 18, pp. 362–373). Hyderabad, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362">https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362</a> Boker, Udi, and Thomas A. Henzinger. “Approximate Determinization of Quantitative Automata.” <i>Leibniz International Proceedings in Informatics</i>, vol. 18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 362–73, doi:<a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362">10.4230/LIPIcs.FSTTCS.2012.362</a>. Boker U, Henzinger TA. Approximate determinization of quantitative automata. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2012:362-373. doi:<a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362">10.4230/LIPIcs.FSTTCS.2012.362</a> 28912018-12-11T12:00:10Z2024-10-09T20:54:57Z