1,473 research outputs found
Computing Weakest Strategies for Safety Games of Imperfect Information
CEDAR (Counter Example Driven Antichain Refinement) is a new symbolic algorithm for computing weakest strategies for safety games of imperfect information. The algorithm computes a fixed point over the lattice of contravariant antichains. Here contravariant antichains are antichains over pairs consisting of an information set and an allow set representing the associated move. We demonstrate how the richer structure of contravariant antichains for representing antitone functions, as opposed to standard antichains for representing sets of downward closed sets, allows CEDAR to apply a significantly less complex controllable predecessor step than previous algorithms
Looking at Mean-Payoff through Foggy Windows
Mean-payoff games (MPGs) are infinite duration two-player zero-sum games
played on weighted graphs. Under the hypothesis of perfect information, they
admit memoryless optimal strategies for both players and can be solved in
NP-intersect-coNP. MPGs are suitable quantitative models for open reactive
systems. However, in this context the assumption of perfect information is not
always realistic. For the partial-observation case, the problem that asks if
the first player has an observation-based winning strategy that enforces a
given threshold on the mean-payoff, is undecidable. In this paper, we study the
window mean-payoff objectives that were introduced recently as an alternative
to the classical mean-payoff objectives. We show that, in sharp contrast to the
classical mean-payoff objectives, some of the window mean-payoff objectives are
decidable in games with partial-observation
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
Probabilistic Opacity for Markov Decision Processes
Opacity is a generic security property, that has been defined on (non
probabilistic) transition systems and later on Markov chains with labels. For a
secret predicate, given as a subset of runs, and a function describing the view
of an external observer, the value of interest for opacity is a measure of the
set of runs disclosing the secret. We extend this definition to the richer
framework of Markov decision processes, where non deterministic choice is
combined with probabilistic transitions, and we study related decidability
problems with partial or complete observation hypotheses for the schedulers. We
prove that all questions are decidable with complete observation and
-regular secrets. With partial observation, we prove that all
quantitative questions are undecidable but the question whether a system is
almost surely non opaque becomes decidable for a restricted class of
-regular secrets, as well as for all -regular secrets under
finite-memory schedulers
Uniform Strategies
We consider turn-based game arenas for which we investigate uniformity
properties of strategies. These properties involve bundles of plays, that arise
from some semantical motive. Typically, we can represent constraints on allowed
strategies, such as being observation-based. We propose a formal language to
specify uniformity properties and demonstrate its relevance by rephrasing
various known problems from the literature. Note that the ability to correlate
different plays cannot be achieved by any branching-time logic if not equipped
with an additional modality, so-called R in this contribution. We also study an
automated procedure to synthesize strategies subject to a uniformity property,
which strictly extends existing results based on, say standard temporal logics.
We exhibit a generic solution for the synthesis problem provided the bundles of
plays rely on any binary relation definable by a finite state transducer. This
solution yields a non-elementary procedure.Comment: (2012
Lossy Channel Games under Incomplete Information
In this paper we investigate lossy channel games under incomplete
information, where two players operate on a finite set of unbounded FIFO
channels and one player, representing a system component under consideration
operates under incomplete information, while the other player, representing the
component's environment is allowed to lose messages from the channels. We argue
that these games are a suitable model for synthesis of communication protocols
where processes communicate over unreliable channels. We show that in the case
of finite message alphabets, games with safety and reachability winning
conditions are decidable and finite-state observation-based strategies for the
component can be effectively computed. Undecidability for (weak) parity
objectives follows from the undecidability of (weak) parity perfect information
games where only one player can lose messages.Comment: In Proceedings SR 2013, arXiv:1303.007
Qualitative Analysis of Partially-observable Markov Decision Processes
We study observation-based strategies for partially-observable Markov
decision processes (POMDPs) with omega-regular objectives. An observation-based
strategy relies on partial information about the history of a play, namely, on
the past sequence of observations. We consider the qualitative analysis
problem: given a POMDP with an omega-regular objective, whether there is an
observation-based strategy to achieve the objective with probability~1
(almost-sure winning), or with positive probability (positive winning). Our
main results are twofold. First, we present a complete picture of the
computational complexity of the qualitative analysis of POMDP s with parity
objectives (a canonical form to express omega-regular objectives) and its
subclasses. Our contribution consists in establishing several upper and lower
bounds that were not known in literature. Second, we present optimal bounds
(matching upper and lower bounds) on the memory required by pure and randomized
observation-based strategies for the qualitative analysis of POMDP s with
parity objectives and its subclasses
A Backward-traversal-based Approach for Symbolic Model Checking of Uniform Strategies for Constrained Reachability
Since the introduction of Alternating-time Temporal Logic (ATL), many logics
have been proposed to reason about different strategic capabilities of the
agents of a system. In particular, some logics have been designed to reason
about the uniform memoryless strategies of such agents. These strategies are
the ones the agents can effectively play by only looking at what they observe
from the current state. ATL_ir can be seen as the core logic to reason about
such uniform strategies. Nevertheless, its model-checking problem is difficult
(it requires a polynomial number of calls to an NP oracle), and practical
algorithms to solve it appeared only recently.
This paper proposes a technique for model checking uniform memoryless
strategies. Existing techniques build the strategies from the states of
interest, such as the initial states, through a forward traversal of the
system. On the other hand, the proposed approach builds the winning strategies
from the target states through a backward traversal, making sure that only
uniform strategies are explored. Nevertheless, building the strategies from the
ground up limits its applicability to constrained reachability objectives only.
This paper describes the approach in details and compares it experimentally
with existing approaches implemented into a BDD-based framework. These
experiments show that the technique is competitive on the cases it can handle.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
How to Handle Assumptions in Synthesis
The increased interest in reactive synthesis over the last decade has led to
many improved solutions but also to many new questions. In this paper, we
discuss the question of how to deal with assumptions on environment behavior.
We present four goals that we think should be met and review several different
possibilities that have been proposed. We argue that each of them falls short
in at least one aspect.Comment: In Proceedings SYNT 2014, arXiv:1407.493
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