conference paper published yes Tomás Brázdil author Krishnendu Chatterjee author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X Antonín Kucera author Petr Novotný author 3CC3B868-F248-11E8-B48F-1D18A9856A87 Dominik Velan author KrCh department ATVA: Automated TEchnology for Verification and Analysis Rigorous Systems Engineering project A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative 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(n2). Springer Nature2019Taipei, Taiwan eng 0302-9743 1611-3349 9783030317836 1907.11010 00072351570002710.1007/978-3-030-31784-3_27 11781462-478 Brázdil, Tomás, Krishnendu Chatterjee, Antonín Kucera, Petr Novotný, and Dominik Velan. “Deciding Fast Termination for Probabilistic VASS with Nondeterminism.” In <i>International Symposium on Automated Technology for Verification and Analysis</i>, 11781:462–78. Springer Nature, 2019. <a href="https://doi.org/10.1007/978-3-030-31784-3_27">https://doi.org/10.1007/978-3-030-31784-3_27</a>. T. Brázdil, K. Chatterjee, A. Kucera, P. Novotný, D. Velan, in:, International Symposium on Automated Technology for Verification and Analysis, Springer Nature, 2019, pp. 462–478. Brázdil T, Chatterjee K, Kucera A, Novotný P, Velan D. 2019. Deciding fast termination for probabilistic VASS with nondeterminism. International Symposium on Automated Technology for Verification and Analysis. ATVA: Automated TEchnology for Verification and Analysis, LNCS, vol. 11781, 462–478. Brázdil T, Chatterjee K, Kucera A, Novotný P, Velan D. Deciding fast termination for probabilistic VASS with nondeterminism. In: <i>International Symposium on Automated Technology for Verification and Analysis</i>. Vol 11781. Springer Nature; 2019:462-478. doi:<a href="https://doi.org/10.1007/978-3-030-31784-3_27">10.1007/978-3-030-31784-3_27</a> Brázdil, T., Chatterjee, K., Kucera, A., Novotný, P., &#38; Velan, D. (2019). Deciding fast termination for probabilistic VASS with nondeterminism. In <i>International Symposium on Automated Technology for Verification and Analysis</i> (Vol. 11781, pp. 462–478). Taipei, Taiwan: Springer Nature. <a href="https://doi.org/10.1007/978-3-030-31784-3_27">https://doi.org/10.1007/978-3-030-31784-3_27</a> T. Brázdil, K. Chatterjee, A. Kucera, P. Novotný, and D. Velan, “Deciding fast termination for probabilistic VASS with nondeterminism,” in <i>International Symposium on Automated Technology for Verification and Analysis</i>, Taipei, Taiwan, 2019, vol. 11781, pp. 462–478. Brázdil, Tomás, et al. “Deciding Fast Termination for Probabilistic VASS with Nondeterminism.” <i>International Symposium on Automated Technology for Verification and Analysis</i>, vol. 11781, Springer Nature, 2019, pp. 462–78, doi:<a href="https://doi.org/10.1007/978-3-030-31784-3_27">10.1007/978-3-030-31784-3_27</a>. 71832019-12-15T23:00:44Z2026-04-16T09:51:24Z