662 research outputs found
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
Real-Time Synthesis is Hard!
We study the reactive synthesis problem (RS) for specifications given in
Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very
general setting, but on infinite words only; and only the very restrictive BRRS
subcase is known to be decidable (see D'Souza et al. and Bouyer et al.). In
this paper, we precise the decidability border of MITL synthesis. We show RS is
undecidable on finite words too, and present a landscape of restrictions (both
on the logic and on the possible controllers) that are still undecidable. On
the positive side, we revisit BRRS and introduce an efficient on-the-fly
algorithm to solve it
Language Emptiness of Continuous-Time Parametric Timed Automata
Parametric timed automata extend the standard timed automata with the
possibility to use parameters in the clock guards. In general, if the
parameters are real-valued, the problem of language emptiness of such automata
is undecidable even for various restricted subclasses. We thus focus on the
case where parameters are assumed to be integer-valued, while the time still
remains continuous. On the one hand, we show that the problem remains
undecidable for parametric timed automata with three clocks and one parameter.
On the other hand, for the case with arbitrary many clocks where only one of
these clocks is compared with (an arbitrary number of) parameters, we show that
the parametric language emptiness is decidable. The undecidability result
tightens the bounds of a previous result which assumed six parameters, while
the decidability result extends the existing approaches that deal with
discrete-time semantics only. To the best of our knowledge, this is the first
positive result in the case of continuous-time and unbounded integer
parameters, except for the rather simple case of single-clock automata
Timed Parity Games: Complexity and Robustness
We consider two-player games played in real time on game structures with
clocks where the objectives of players are described using parity conditions.
The games are \emph{concurrent} in that at each turn, both players
independently propose a time delay and an action, and the action with the
shorter delay is chosen. To prevent a player from winning by blocking time, we
restrict each player to play strategies that ensure that the player cannot be
responsible for causing a zeno run. First, we present an efficient reduction of
these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state}
(i.e., untimed) parity games. Our reduction improves the best known complexity
for solving timed parity games. Moreover, the rich class of algorithms for
classical parity games can now be applied to timed parity games. The states of
the resulting game are based on clock regions of the original game, and the
state space of the finite game is linear in the size of the region graph.
Second, we consider two restricted classes of strategies for the player that
represents the controller in a real-time synthesis problem, namely,
\emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a
limit-robust winning strategy, the controller cannot choose an exact
real-valued time delay but must allow for some nonzero jitter in each of its
actions. If there is a given lower bound on the jitter, then the strategy is
bounded-robust winning. We show that exact strategies are more powerful than
limit-robust strategies, which are more powerful than bounded-robust winning
strategies for any bound. For both kinds of robust strategies, we present
efficient reductions to standard timed automaton games. These reductions
provide algorithms for the synthesis of robust real-time controllers
Using Strategy Improvement to Stay Alive
We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides
solving an MPG in the usual sense, our algorithm computes more information
about the game, information that is important with respect to applications. The
weights of the edges of an MPG can be thought of as a gained/consumed energy --
depending on the sign. For each vertex, our algorithm computes the minimum
amount of initial energy that is sufficient for player Max to ensure that in a
play starting from the vertex, the energy level never goes below zero. Our
algorithm is not the first algorithm that computes the minimum sufficient
initial energies, but according to our experimental study it is the fastest
algorithm that computes them. The reason is that it utilizes the strategy
improvement technique which is very efficient in practice
Operationalizing Sustainability as a Safe Policy Space
It is possible to frame sustainability as occurring when the global or local system is within a set of limits and boundaries, such as the concept of safe operating spaces within planetary boundaries. However, such framings, whilst highly useful conceptually, have been difficult to translate into operation, especially in the development of policies. Here we show how it is possible to define a safe operating space, bounded by sets of constraints. These constraints can be of a variety of forms (e.g., income, or biodiversity), and, importantly, they need not all be converted to a single common metric such as money. The challenge is to identify a set of policy options that define the “safe policy space” which maintains the system within the safe operating space defined by boundaries. A formal methodology, Co-Viability Analysis (CVA), can be used to do this. This provides a coherent framework to operationalize sustainability and has a number of extra advantages. First, defining a safe policy space allows for a political choice of which policies and so is not prescriptive—such as would be the case if a single policy option were defined. Secondly, by allowing each boundary to be defined with its own scale of measurement, it avoids the necessity of having to value natural capital or ecosystem services in financial terms. This framework, therefore, has the potential to allow decision-makers to genuinely meet the needs of their people, now and in the future
Divergence in Dialogue
Copyright: 2014 Healey et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This work was supported by the Economic and Social Research Council (ESRC; http://www.esrc.ac.uk/) through the DynDial project (Dynamics of Conversational Dialogue, RES-062-23-0962) and the Engineering and Physical Sciences Research Council (EPSRC; http://www.epsrc.ac.uk/) through the RISER
project (Robust Incremental Semantic Resources for Dialogue, EP/J010383/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
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