30,758 research outputs found
Optimal Strategy Synthesis for Request-Response Games
We show the existence and effective computability of optimal winning
strategies for request-response games in case the quality of a play is measured
by the limit superior of the mean accumulated waiting times between requests
and their responses.Comment: The present paper is a revised version with simplified proofs of
results announced in the conference paper of the same name presented at ATVA
2008, which in turn extended results of the third author's dissertatio
Parity and Streett Games with Costs
We consider two-player games played on finite graphs equipped with costs on
edges and introduce two winning conditions, cost-parity and cost-Streett, which
require bounds on the cost between requests and their responses. Both
conditions generalize the corresponding classical omega-regular conditions and
the corresponding finitary conditions. For parity games with costs we show that
the first player has positional winning strategies and that determining the
winner lies in NP and coNP. For Streett games with costs we show that the first
player has finite-state winning strategies and that determining the winner is
EXPTIME-complete. The second player might need infinite memory in both games.
Both types of games with costs can be solved by solving linearly many instances
of their classical variants.Comment: A preliminary version of this work appeared in FSTTCS 2012 under the
name "Cost-parity and Cost-Streett Games". The research leading to these
results has received funding from the European Union's Seventh Framework
Programme (FP7/2007-2013) under grant agreements 259454 (GALE) and 239850
(SOSNA
Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL
We continue the investigation of parameterized extensions of Linear Temporal
Logic (LTL) that retain the attractive algorithmic properties of LTL: a
polynomial space model checking algorithm and a doubly-exponential time
algorithm for solving games. Alur et al. and Kupferman et al. showed that this
is the case for Parametric LTL (PLTL) and PROMPT-LTL respectively, which have
temporal operators equipped with variables that bound their scope in time.
Later, this was also shown to be true for Parametric LDL (PLDL), which extends
PLTL to be able to express all omega-regular properties.
Here, we generalize PLTL to systems with costs, i.e., we do not bound the
scope of operators in time, but bound the scope in terms of the cost
accumulated during time. Again, we show that model checking and solving games
for specifications in PLTL with costs is not harder than the corresponding
problems for LTL. Finally, we discuss PLDL with costs and extensions to
multiple cost functions.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Prompt Delay
Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. Recently, such
games with quantitative winning conditions in weak MSO with the unbounding
quantifier were studied, but their properties turned out to be unsatisfactory.
In particular, unbounded lookahead is in general necessary. Here, we study
delay games with winning conditions given by Prompt-LTL, Linear Temporal Logic
equipped with a parameterized eventually operator whose scope is bounded. Our
main result shows that solving Prompt-LTL delay games is complete for
triply-exponential time. Furthermore, we give tight triply-exponential bounds
on the necessary lookahead and on the scope of the parameterized eventually
operator. Thus, we identify Prompt-LTL as the first known class of well-behaved
quantitative winning conditions for delay games. Finally, we show that applying
our techniques to delay games with \omega-regular winning conditions answers
open questions in the cases where the winning conditions are given by
non-deterministic, universal, or alternating automata
Approximating Optimal Bounds in Prompt-LTL Realizability in Doubly-exponential Time
We consider the optimization variant of the realizability problem for Prompt
Linear Temporal Logic, an extension of Linear Temporal Logic (LTL) by the
prompt eventually operator whose scope is bounded by some parameter. In the
realizability optimization problem, one is interested in computing the minimal
such bound that allows to realize a given specification. It is known that this
problem is solvable in triply-exponential time, but not whether it can be done
in doubly-exponential time, i.e., whether it is just as hard as solving LTL
realizability.
We take a step towards resolving this problem by showing that the optimum can
be approximated within a factor of two in doubly-exponential time. Also, we
report on a proof-of-concept implementation of the algorithm based on bounded
LTL synthesis, which computes the smallest implementation of a given
specification. In our experiments, we observe a tradeoff between the size of
the implementation and the bound it realizes. We investigate this tradeoff in
the general case and prove upper bounds, which reduce the search space for the
algorithm, and matching lower bounds.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
Multiplayer Cost Games with Simple Nash Equilibria
Multiplayer games with selfish agents naturally occur in the design of
distributed and embedded systems. As the goals of selfish agents are usually
neither equivalent nor antagonistic to each other, such games are non zero-sum
games. We study such games and show that a large class of these games,
including games where the individual objectives are mean- or discounted-payoff,
or quantitative reachability, and show that they do not only have a solution,
but a simple solution. We establish the existence of Nash equilibria that are
composed of k memoryless strategies for each agent in a setting with k agents,
one main and k-1 minor strategies. The main strategy describes what happens
when all agents comply, whereas the minor strategies ensure that all other
agents immediately start to co-operate against the agent who first deviates
from the plan. This simplicity is important, as rational agents are an
idealisation. Realistically, agents have to decide on their moves with very
limited resources, and complicated strategies that require exponential--or even
non-elementary--implementations cannot realistically be implemented. The
existence of simple strategies that we prove in this paper therefore holds a
promise of implementability.Comment: 23 page
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