1,195 research outputs found
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
Correct-by-synthesis reinforcement learning with temporal logic constraints
We consider a problem on the synthesis of reactive controllers that optimize
some a priori unknown performance criterion while interacting with an
uncontrolled environment such that the system satisfies a given temporal logic
specification. We decouple the problem into two subproblems. First, we extract
a (maximally) permissive strategy for the system, which encodes multiple
(possibly all) ways in which the system can react to the adversarial
environment and satisfy the specifications. Then, we quantify the a priori
unknown performance criterion as a (still unknown) reward function and compute
an optimal strategy for the system within the operating envelope allowed by the
permissive strategy by using the so-called maximin-Q learning algorithm. We
establish both correctness (with respect to the temporal logic specifications)
and optimality (with respect to the a priori unknown performance criterion) of
this two-step technique for a fragment of temporal logic specifications. For
specifications beyond this fragment, correctness can still be preserved, but
the learned strategy may be sub-optimal. We present an algorithm to the overall
problem, and demonstrate its use and computational requirements on a set of
robot motion planning examples.Comment: 8 pages, 3 figures, 2 tables, submitted to IROS 201
Minimizing Expected Cost Under Hard Boolean Constraints, with Applications to Quantitative Synthesis
In Boolean synthesis, we are given an LTL specification, and the goal is to
construct a transducer that realizes it against an adversarial environment.
Often, a specification contains both Boolean requirements that should be
satisfied against an adversarial environment, and multi-valued components that
refer to the quality of the satisfaction and whose expected cost we would like
to minimize with respect to a probabilistic environment.
In this work we study, for the first time, mean-payoff games in which the
system aims at minimizing the expected cost against a probabilistic
environment, while surely satisfying an -regular condition against an
adversarial environment. We consider the case the -regular condition is
given as a parity objective or by an LTL formula. We show that in general,
optimal strategies need not exist, and moreover, the limit value cannot be
approximated by finite-memory strategies. We thus focus on computing the
limit-value, and give tight complexity bounds for synthesizing
-optimal strategies for both finite-memory and infinite-memory
strategies.
We show that our game naturally arises in various contexts of synthesis with
Boolean and multi-valued objectives. Beyond direct applications, in synthesis
with costs and rewards to certain behaviors, it allows us to compute the
minimal sensing cost of -regular specifications -- a measure of quality
in which we look for a transducer that minimizes the expected number of signals
that are read from the input
Fault Tolerance in Cellular Automata at High Fault Rates
A commonly used model for fault-tolerant computation is that of cellular
automata. The essential difficulty of fault-tolerant computation is present in
the special case of simply remembering a bit in the presence of faults, and
that is the case we treat in this paper. We are concerned with the degree (the
number of neighboring cells on which the state transition function depends)
needed to achieve fault tolerance when the fault rate is high (nearly 1/2). We
consider both the traditional transient fault model (where faults occur
independently in time and space) and a recently introduced combined fault model
which also includes manufacturing faults (which occur independently in space,
but which affect cells for all time). We also consider both a purely
probabilistic fault model (in which the states of cells are perturbed at
exactly the fault rate) and an adversarial model (in which the occurrence of a
fault gives control of the state to an omniscient adversary). We show that
there are cellular automata that can tolerate a fault rate (with
) with degree , even with adversarial combined
faults. The simplest such automata are based on infinite regular trees, but our
results also apply to other structures (such as hyperbolic tessellations) that
contain infinite regular trees. We also obtain a lower bound of
, even with purely probabilistic transient faults only
Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs
Verification of PCTL properties of MDPs with convex uncertainties has been
investigated recently by Puggelli et al. However, model checking algorithms
typically suffer from state space explosion. In this paper, we address
probabilistic bisimulation to reduce the size of such an MDPs while preserving
PCTL properties it satisfies. We discuss different interpretations of
uncertainty in the models which are studied in the literature and that result
in two different definitions of bisimulations. We give algorithms to compute
the quotients of these bisimulations in time polynomial in the size of the
model and exponential in the uncertain branching. Finally, we show by a case
study that large models in practice can have small branching and that a
substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
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