161 research outputs found
Succinct progress measures for solving parity games
The recent breakthrough paper by Calude et al. has given the first algorithm
for solving parity games in quasi-polynomial time, where previously the best
algorithms were mildly subexponential. We devise an alternative
quasi-polynomial time algorithm based on progress measures, which allows us to
reduce the space required from quasi-polynomial to nearly linear. Our key
technical tools are a novel concept of ordered tree coding, and a succinct tree
coding result that we prove using bounded adaptive multi-counters, both of
which are interesting in their own right
LNCS
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as angelic and demonic non-determinism. Lexicographic order allows to consider multiple objectives with a strict preference order over the satisfaction of the objectives. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. We establish determinacy of such games and present strategy and computational complexity results. For strategy complexity, we show that lexicographically optimal strategies exist that are deterministic and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP , matching the current known bound for single objectives; and in general the decision problem is PSPACE -hard and can be solved in NEXPTIME∩coNEXPTIME . We present an algorithm that computes the lexicographically optimal strategies via a reduction to computation of optimal strategies in a sequence of single-objectives games. We have implemented our algorithm and report experimental results on various case studies
Most General Winning Secure Equilibria Synthesis in Graph Games
This paper considers the problem of co-synthesis in -player games over a
finite graph where each player has an individual -regular specification
. In this context, a secure equilibrium (SE) is a Nash equilibrium
w.r.t. the lexicographically ordered objectives of each player to first satisfy
their own specification, and second, to falsify other players' specifications.
A winning secure equilibrium (WSE) is an SE strategy profile
that ensures the specification
if no player deviates from their strategy
. Distributed implementations generated from a WSE make components act
rationally by ensuring that a deviation from the WSE strategy profile is
immediately punished by a retaliating strategy that makes the involved players
lose.
In this paper, we move from deviation punishment in WSE-based implementations
to a distributed, assume-guarantee based realization of WSE. This shift is
obtained by generalizing WSE from strategy profiles to specification profiles
with , which
we call most general winning secure equilibria (GWSE). Such GWSE have the
property that each player can individually pick a strategy winning for
(against all other players) and all resulting strategy profiles
are guaranteed to be a WSE. The obtained flexibility in
players' strategy choices can be utilized for robustness and adaptability of
local implementations.
Concretely, our contribution is three-fold: (1) we formalize GWSE for
-player games over finite graphs, where each player has an -regular
specification ; (2) we devise an iterative semi-algorithm for GWSE
synthesis in such games, and (3) obtain an exponential-time algorithm for GWSE
synthesis with parity specifications .Comment: TACAS 202
Stochastic Games with Lexicographic Reachability-Safety Objectives
We study turn-based stochastic zero-sum games with lexicographic preferences
over reachability and safety objectives. Stochastic games are standard models
in control, verification, and synthesis of stochastic reactive systems that
exhibit both randomness as well as angelic and demonic non-determinism.
Lexicographic order allows to consider multiple objectives with a strict
preference order over the satisfaction of the objectives. To the best of our
knowledge, stochastic games with lexicographic objectives have not been studied
before. We establish determinacy of such games and present strategy and
computational complexity results. For strategy complexity, we show that
lexicographically optimal strategies exist that are deterministic and memory is
only required to remember the already satisfied and violated objectives. For a
constant number of objectives, we show that the relevant decision problem is in
NP coNP, matching the current known bound for single objectives; and in
general the decision problem is PSPACE-hard and can be solved in NEXPTIME
coNEXPTIME. We present an algorithm that computes the lexicographically
optimal strategies via a reduction to computation of optimal strategies in a
sequence of single-objectives games. We have implemented our algorithm and
report experimental results on various case studies.Comment: Full version (33 pages) of CAV20 conference paper; including an
appendix with technical proof
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
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