460 research outputs found
An Algorithm for Probabilistic Alternating Simulation
In probabilistic game structures, probabilistic alternating simulation
(PA-simulation) relations preserve formulas defined in probabilistic
alternating-time temporal logic with respect to the behaviour of a subset of
players. We propose a partition based algorithm for computing the largest
PA-simulation, which is to our knowledge the first such algorithm that works in
polynomial time, by extending the generalised coarsest partition problem (GCPP)
in a game-based setting with mixed strategies. The algorithm has higher
complexities than those in the literature for non-probabilistic simulation and
probabilistic simulation without mixed actions, but slightly improves the
existing result for computing probabilistic simulation with respect to mixed
actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio
Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions
Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] and Hermanns et al. [2011] define a probabilistic Hennessy-Milner logic interpreted over probability distributions, whose corresponding logical equivalence/preorder when restricted to Dirac distributions coincide with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between (possibly non-Dirac) distributions in terms of a notion of bisimulation/simulation defined on a LTS whose states are distributions (dLTS). We show that the well-known spectrum of behavioral relations on nonprobabilistic LTSs as well as their corresponding logical characterizations in terms of Hennessy-Milner logic scales to the probabilistic setting when considering dLTSs
Automated Temporal Equilibrium Analysis: Verification and Synthesis of Multi-Player Games
In the context of multi-agent systems, the rational verification problem is
concerned with checking which temporal logic properties will hold in a system
when its constituent agents are assumed to behave rationally and strategically
in pursuit of individual objectives. Typically, those objectives are expressed
as temporal logic formulae which the relevant agent desires to see satisfied.
Unfortunately, rational verification is computationally complex, and requires
specialised techniques in order to obtain practically useable implementations.
In this paper, we present such a technique. This technique relies on a
reduction of the rational verification problem to the solution of a collection
of parity games. Our approach has been implemented in the Equilibrium
Verification Environment (EVE) system. The EVE system takes as input a model of
a concurrent/multi-agent system represented using the Simple Reactive Modules
Language (SRML), where agent goals are represented as Linear Temporal Logic
(LTL) formulae, together with a claim about the equilibrium behaviour of the
system, also expressed as an LTL formula. EVE can then check whether the LTL
claim holds on some (or every) computation of the system that could arise
through agents choosing Nash equilibrium strategies; it can also check whether
a system has a Nash equilibrium, and synthesise individual strategies for
players in the multi-player game. After presenting our basic framework, we
describe our new technique and prove its correctness. We then describe our
implementation in the EVE system, and present experimental results which show
that EVE performs favourably in comparison to other existing tools that support
rational verification
Bisimulations Meet PCTL Equivalences for Probabilistic Automata
Probabilistic automata (PAs) have been successfully applied in formal
verification of concurrent and stochastic systems. Efficient model checking
algorithms have been studied, where the most often used logics for expressing
properties are based on probabilistic computation tree logic (PCTL) and its
extension PCTL^*. Various behavioral equivalences are proposed, as a powerful
tool for abstraction and compositional minimization for PAs. Unfortunately, the
equivalences are well-known to be sound, but not complete with respect to the
logical equivalences induced by PCTL or PCTL*. The desire of a both sound and
complete behavioral equivalence has been pointed out by Segala in 1995, but
remains open throughout the years. In this paper we introduce novel notions of
strong bisimulation relations, which characterize PCTL and PCTL* exactly. We
extend weak bisimulations that characterize PCTL and PCTL* without next
operator, respectively. Further, we also extend the framework to simulation
preorders. Thus, our paper bridges the gap between logical and behavioral
equivalences and preorders in this setting.Comment: Long version of CONCUR'11 with the same title: added extension to
simulations, countable state
Playing with Trees and Logic
This document proposes an overview of my research sinc
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