129 research outputs found
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
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
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
Computer aided synthesis: a game theoretic approach
In this invited contribution, we propose a comprehensive introduction to game
theory applied in computer aided synthesis. In this context, we give some
classical results on two-player zero-sum games and then on multi-player non
zero-sum games. The simple case of one-player games is strongly related to
automata theory on infinite words. All along the article, we focus on general
approaches to solve the studied problems, and we provide several illustrative
examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language
Theory" (DLT 2017
Stochastic Games with Disjunctions of Multiple Objectives (Technical Report)
Stochastic games combine controllable and adversarial non-determinism with
stochastic behavior and are a common tool in control, verification and
synthesis of reactive systems facing uncertainty. Multi-objective stochastic
games are natural in situations where several - possibly conflicting -
performance criteria like time and energy consumption are relevant. Such
conjunctive combinations are the most studied multi-objective setting in the
literature. In this paper, we consider the dual disjunctive problem. More
concretely, we study turn-based stochastic two-player games on graphs where the
winning condition is to guarantee at least one reachability or safety objective
from a given set of alternatives. We present a fine-grained overview of
strategy and computational complexity of such \emph{disjunctive queries} (DQs)
and provide new lower and upper bounds for several variants of the problem,
significantly extending previous works. We also propose a novel value
iteration-style algorithm for approximating the set of Pareto optimal
thresholds for a given DQ.Comment: Technical report including appendix with detailed proofs, 29 page
Mungojerrie:Linear-Time Objectives in Model-Free Reinforcement Learning
Mungojerrie is an extensible tool that provides a framework to translate linear-time objectives into reward for reinforcement learning (RL). The tool provides convergent RL algorithms for stochastic games, reference implementations of existing reward translations for ω -regular objectives, and an internal probabilistic model checker for ω -regular objectives. This functionality is modular and operates on shared data structures, which enables fast development of new translation techniques. Mungojerrie supports finite models specified in PRISM and ω -automata specified in the HOA format, with an integrated command line interface to external linear temporal logic translators. Mungojerrie is distributed with a set of benchmarks for ω -regular objectives in RL.</p
Computer Aided Verification
The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic
- …