46 research outputs found
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
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
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
Sensor Synthesis for POMDPs with Reachability Objectives
Partially observable Markov decision processes (POMDPs) are widely used in
probabilistic planning problems in which an agent interacts with an environment
using noisy and imprecise sensors. We study a setting in which the sensors are
only partially defined and the goal is to synthesize "weakest" additional
sensors, such that in the resulting POMDP, there is a small-memory policy for
the agent that almost-surely (with probability~1) satisfies a reachability
objective. We show that the problem is NP-complete, and present a symbolic
algorithm by encoding the problem into SAT instances. We illustrate trade-offs
between the amount of memory of the policy and the number of additional sensors
on a simple example. We have implemented our approach and consider three
classical POMDP examples from the literature, and show that in all the examples
the number of sensors can be significantly decreased (as compared to the
existing solutions in the literature) without increasing the complexity of the
policies.Comment: arXiv admin note: text overlap with arXiv:1511.0845
Model-Checking an Alternating-time Temporal Logic with Knowledge, Imperfect Information, Perfect Recall and Communicating Coalitions
We present a variant of ATL with distributed knowledge operators based on a
synchronous and perfect recall semantics. The coalition modalities in this
logic are based on partial observation of the full history, and incorporate a
form of cooperation between members of the coalition in which agents issue
their actions based on the distributed knowledge, for that coalition, of the
system history. We show that model-checking is decidable for this logic. The
technique utilizes two variants of games with imperfect information and
partially observable objectives, as well as a subset construction for
identifying states whose histories are indistinguishable to the considered
coalition