10,483 research outputs found
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
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53
Preface
Overview of the contents of "Foundations of Software Science and Computational Structures: Selected papers from FOSSACS 2005
Pure Nash Equilibria in Concurrent Deterministic Games
We study pure-strategy Nash equilibria in multi-player concurrent
deterministic games, for a variety of preference relations. We provide a novel
construction, called the suspect game, which transforms a multi-player
concurrent game into a two-player turn-based game which turns Nash equilibria
into winning strategies (for some objective that depends on the preference
relations of the players in the original game). We use that transformation to
design algorithms for computing Nash equilibria in finite games, which in most
cases have optimal worst-case complexity, for large classes of preference
relations. This includes the purely qualitative framework, where each player
has a single omega-regular objective that she wants to satisfy, but also the
larger class of semi-quantitative objectives, where each player has several
omega-regular objectives equipped with a preorder (for instance, a player may
want to satisfy all her objectives, or to maximise the number of objectives
that she achieves.)Comment: 72 page
Distances for Weighted Transition Systems: Games and Properties
We develop a general framework for reasoning about distances between
transition systems with quantitative information. Taking as starting point an
arbitrary distance on system traces, we show how this leads to natural
definitions of a linear and a branching distance on states of such a transition
system. We show that our framework generalizes and unifies a large variety of
previously considered system distances, and we develop some general properties
of our distances. We also show that if the trace distance admits a recursive
characterization, then the corresponding branching distance can be obtained as
a least fixed point to a similar recursive characterization. The central tool
in our work is a theory of infinite path-building games with quantitative
objectives.Comment: In Proceedings QAPL 2011, arXiv:1107.074
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