14 research outputs found
On the local invertibility of finite state information lossless automata
Рассматриваются вопросы восстановления фрагментов входных слов конечных автоматов без потери информации по известным выходным словам (локальное обращение). Показана связь локального обращения автомата из этого класса со свойством синхронизируемости ассоциированного с ним автомата без выхода. Найдены новые классы регистров сдвига с фильтрующими булевыми функциями, допускающих локальное обращение
Synchronizing heuristics for weakly connected automata with various topologies
Since the problem of finding a shortest synchronizing sequence for an automaton is known to be NP-hard, heuristics algorithms are used to find synchronizing sequences. There are several heuristic algorithms in the literature for this purpose. However, even the most efficient heuristic algorithm in the literature has a quadratic complexity in terms of the number of states of the automaton, and therefore can only scale up to a couple of thousands of states. It was also shown before that if an automaton is not strongly connected, then these heuristic algorithms can be used on each strongly connected component separately. This approach speeds up these heuristic algorithms and allows them to scale to much larger number of states easily. In this paper, we investigate the effect of the topology of the automaton on the performance increase obtained by these heuristic algorithms. To this end, we consider various topologies and provide an extensive experimental study on the performance increase obtained on the existing heuristic algorithms. Depending on the size and the number of components, we obtain speed-up values as high as 10000x and more
Exact synchronization in partial deterministic automata
An automaton is a synchronizing if it has an input word that transfers it from any state to a particular state. There are two versions of synchronization in partial deterministic automata: Careful synchronization and exact synchronization. In this paper we focus on the exact version; we survey the complexity of testing exact synchronization and describe a SAT solver based algorithm for calculating the length of the shortest exact synchronizing word. © Published under licence by IOP Publishing Ltd
Limit Synchronization in Markov Decision Processes
Markov decision processes (MDP) are finite-state systems with both strategic
and probabilistic choices. After fixing a strategy, an MDP produces a sequence
of probability distributions over states. The sequence is eventually
synchronizing if the probability mass accumulates in a single state, possibly
in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a
probability distribution in the sequence assigns probability at least p to some
state, and we distinguish three synchronization modes: (i) sure winning if
there exists a strategy that produces a 1-synchronizing sequence; (ii)
almost-sure winning if there exists a strategy that produces a sequence that
is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure
winning if for all epsilon > 0, there exists a strategy that produces a
(1-epsilon)-synchronizing sequence.
We consider the problem of deciding whether an MDP is sure, almost-sure,
limit-sure winning, and we establish the decidability and optimal complexity
for all modes, as well as the memory requirements for winning strategies. Our
main contributions are as follows: (a) for each winning modes we present
characterizations that give a PSPACE complexity for the decision problems, and
we establish matching PSPACE lower bounds; (b) we show that for sure winning
strategies, exponential memory is sufficient and may be necessary, and that in
general infinite memory is necessary for almost-sure winning, and unbounded
memory is necessary for limit-sure winning; (c) along with our results, we
establish new complexity results for alternating finite automata over a
one-letter alphabet
Synchronizing Objectives for Markov Decision Processes
We introduce synchronizing objectives for Markov decision processes (MDP).
Intuitively, a synchronizing objective requires that eventually, at every step
there is a state which concentrates almost all the probability mass. In
particular, it implies that the probabilistic system behaves in the long run
like a deterministic system: eventually, the current state of the MDP can be
identified with almost certainty.
We study the problem of deciding the existence of a strategy to enforce a
synchronizing objective in MDPs. We show that the problem is decidable for
general strategies, as well as for blind strategies where the player cannot
observe the current state of the MDP. We also show that pure strategies are
sufficient, but memory may be necessary.Comment: In Proceedings iWIGP 2011, arXiv:1102.374