908 research outputs found
Reachability games with relaxed energy constraints
We study games with reachability objectives under energy constraints. We first prove that under strict energy constraints (either only lower-bound constraint or interval constraint), those games are LOGSPACE-equivalent to energy games with the same energy constraints but without reachability objective (i.e., for infinite runs). We then consider two relaxations of the upper-bound constraints (while keeping the lower-bound constraint strict): in the first one, called weak upper bound, the upper bound is absorbing, i.e., when the upper bound is reached, the extra energy is not stored; in the second one, we allow for temporary violations of the upper bound, imposing limits on the number or on the amount of violations. We prove that when considering weak upper bound, reachability objectives require memory, but can still be solved in polynomial-time for one-player arenas ; we prove that they are in coNP in the two-player setting. Allowing for bounded violations makes the problem PSPACE-complete for one-player arenas and EXPTIME-complete for two players. We then address the problem of existence of bounds for a given arena. We show that with reachability objectives, existence can be a simpler problem than the game itself, and conversely that with infinite games, existence can be harder
Computing Nash Equilibrium in Wireless Ad Hoc Networks: A Simulation-Based Approach
This paper studies the problem of computing Nash equilibrium in wireless
networks modeled by Weighted Timed Automata. Such formalism comes together with
a logic that can be used to describe complex features such as timed energy
constraints. Our contribution is a method for solving this problem using
Statistical Model Checking. The method has been implemented in UPPAAL model
checker and has been applied to the analysis of Aloha CSMA/CD and IEEE 802.15.4
CSMA/CA protocols.Comment: In Proceedings IWIGP 2012, arXiv:1202.422
Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a well-known and
fundamental model for the analysis of concurrent processes, parameterized
systems, and are also used as abstract models of programs in resource bound
analysis. In this paper we study the problem of obtaining asymptotic bounds on
the termination time of a given VASS. In particular, we focus on the
practically important case of obtaining polynomial bounds on termination time.
Our main contributions are as follows: First, we present a polynomial-time
algorithm for deciding whether a given VASS has a linear asymptotic complexity.
We also show that if the complexity of a VASS is not linear, it is at least
quadratic. Second, we classify VASS according to quantitative properties of
their cycles. We show that certain singularities in these properties are the
key reason for non-polynomial asymptotic complexity of VASS. In absence of
singularities, we show that the asymptotic complexity is always polynomial and
of the form , for some integer , where is the
dimension of the VASS. We present a polynomial-time algorithm computing the
optimal . For general VASS, the same algorithm, which is based on a complete
technique for the construction of ranking functions in VASS, produces a valid
lower bound, i.e., a such that the termination complexity is .
Our results are based on new insights into the geometry of VASS dynamics, which
hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925
Percentile Queries in Multi-Dimensional Markov Decision Processes
Markov decision processes (MDPs) with multi-dimensional weights are useful to
analyze systems with multiple objectives that may be conflicting and require
the analysis of trade-offs. We study the complexity of percentile queries in
such MDPs and give algorithms to synthesize strategies that enforce such
constraints. Given a multi-dimensional weighted MDP and a quantitative payoff
function , thresholds (one per dimension), and probability thresholds
, we show how to compute a single strategy to enforce that for all
dimensions , the probability of outcomes satisfying is at least . We consider classical quantitative payoffs from
the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum,
discounted sum). Our work extends to the quantitative case the multi-objective
model checking problem studied by Etessami et al. in unweighted MDPs.Comment: Extended version of CAV 2015 pape
Efficient Symbolic Approaches for Quantitative Reactive Synthesis with Finite Tasks
This work introduces efficient symbolic algorithms for quantitative reactive
synthesis. We consider resource-constrained robotic manipulators that need to
interact with a human to achieve a complex task expressed in linear temporal
logic. Our framework generates reactive strategies that not only guarantee task
completion but also seek cooperation with the human when possible. We model the
interaction as a two-player game and consider regret-minimizing strategies to
encourage cooperation. We use symbolic representation of the game to enable
scalability. For synthesis, we first introduce value iteration algorithms for
such games with min-max objectives. Then, we extend our method to the
regret-minimizing objectives. Our benchmarks reveal that our symbolic framework
not only significantly improves computation time (up to an order of magnitude)
but also can scale up to much larger instances of manipulation problems with up
to 2x number of objects and locations than the state of the art.Comment: Submitted to IROS 202
- âŠ