Deciding Fast Termination for Probabilistic VASS with Nondeterminism
| Autor: | Petr Novotný, Krishnendu Chatterjee, Tomáš Brázdil, Antonín Kučera, Dominik Velan |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
050101 languages & linguistics Computer science 05 social sciences Probabilistic logic Markov process 02 engineering and technology State (functional analysis) Expected value Blocking (computing) Decidability symbols.namesake Integer 0202 electrical engineering electronic engineering information engineering symbols 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences Time complexity |
| Zdroj: | Automated Technology for Verification and Analysis ISBN: 9783030317836 ATVA |
| DOI: | 10.1007/978-3-030-31784-3_27 |
| Popis: | 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 \(\varOmega (n^2)\). |
| Databáze: | OpenAIRE |
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