63 research outputs found
On the Control of Asynchronous Automata
The decidability of the distributed version of the Ramadge and Wonham
controller synthesis problem,where both the plant and the controllers are
modeled as asynchronous automataand the controllers have causal memoryis a
challenging open problem.There exist three classes of plants for which the
existence of a correct controller with causal memory has been shown decidable:
when the dependency graph of actions is series-parallel, when the processes are
connectedly communicating and when the dependency graph of processes is a tree.
We design a class of plants, called decomposable games, with a decidable
controller synthesis problem.This provides a unified proof of the three
existing decidability results as well as new examples of decidable plants
Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-Positional
We consider zero-sum stochastic games with perfect information and finitely
many states and actions. The payoff is computed by a payoff function which
associates to each infinite sequence of states and actions a real number. We
prove that if the the payoff function is both shift-invariant and submixing,
then the game is half-positional, i.e. the first player has an optimal strategy
which is both deterministic and stationary. This result relies on the existence
of -subgame-perfect equilibria in shift-invariant games, a second
contribution of the paper
Pushing undecidability of the isolation problem for probabilistic automata
This short note aims at proving that the isolation problem is undecidable for
probabilistic automata with only one probabilistic transition. This problem is
known to be undecidable for general probabilistic automata, without restriction
on the number of probabilistic transitions. In this note, we develop a
simulation technique that allows to simulate any probabilistic automaton with
one having only one probabilistic transition
Determinacy and Decidability of Reachability Games with Partial Observation on Both Sides
We prove two determinacy and decidability results about two-players
stochastic reachability games with partial observation on both sides and
finitely many states, signals and actions
Blackwell-Optimal Strategies in Priority Mean-Payoff Games
We examine perfect information stochastic mean-payoff games - a class of
games containing as special sub-classes the usual mean-payoff games and parity
games. We show that deterministic memoryless strategies that are optimal for
discounted games with state-dependent discount factors close to 1 are optimal
for priority mean-payoff games establishing a strong link between these two
classes
Deciding the value 1 problem for probabilistic leaktight automata
The value 1 problem is a decision problem for probabilistic automata over
finite words: given a probabilistic automaton, are there words accepted with
probability arbitrarily close to 1? This problem was proved undecidable
recently; to overcome this, several classes of probabilistic automata of
different nature were proposed, for which the value 1 problem has been shown
decidable. In this paper, we introduce yet another class of probabilistic
automata, called leaktight automata, which strictly subsumes all classes of
probabilistic automata whose value 1 problem is known to be decidable. We prove
that for leaktight automata, the value 1 problem is decidable (in fact,
PSPACE-complete) by constructing a saturation algorithm based on the
computation of a monoid abstracting the behaviours of the automaton. We rely on
algebraic techniques developed by Simon to prove that this abstraction is
complete. Furthermore, we adapt this saturation algorithm to decide whether an
automaton is leaktight. Finally, we show a reduction allowing to extend our
decidability results from finite words to infinite ones, implying that the
value 1 problem for probabilistic leaktight parity automata is decidable
Applying Blackwell optimality: priority mean-payoff games as limits of multi-discounted game
International audienceWe define and examine priority mean-payoff games - a natural extension of parity games. By adapting the notion of Blackwell optimality borrowed from the theory of Markov decision processes we show that priority mean-payoff games can be seen as a limit of special multi-discounted games
Deciding the Value 1 Problem for #-acyclic Partially Observable Markov Decision Processes
The value 1 problem is a natural decision problem in algorithmic game theory. For partially observable Markov decision processes with reachability objective, this problem is defined as follows: are there strategies that achieve the reachability objective with probability arbitrarily close to 1? This problem was shown undecidable recently. Our contribution is to introduce a class of partially observable Markov decision processes, namely #-acyclic partially observable Markov decision processes, for which the value 1 problem is decidable. Our algorithm is based on the construction of a two-player perfect information game, called the knowledge game, abstracting the behaviour of a #-acyclic partially observable Markov decision process M such that the first player has a winning strategy in the knowledge game if and only if the value of M is 1
Solving Simple Stochastic Games with Few Random Vertices
Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The "permutation-enumeration" algorithm performs an exhaustive search among these strategies, while the "permutation-improvement'' algorithm is based on successive improvements, Ă la Hoffman-Karp. Our algorithms improve previously known algorithms in several aspects. First they run in polynomial time when the number of random vertices is fixed, so the problem of solving simple stochastic games is fixed-parameter tractable when the parameter is the number of random vertices. Furthermore, our algorithms do not require the input game to be transformed into a stopping game. Finally, the permutation-enumeration algorithm does not use linear programming, while the permutation-improvement algorithm may run in polynomial time
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