4,721 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
The Large- Limit of the Two-Hermitian-matrix model by the hidden BRST method
This paper discusses the large N limit of the two-Hermitian-matrix model in
zero dimensions, using the hidden BRST method. A system of integral equations
previously found is solved, showing that it contained the exact solution of the
model in leading order of large .Comment: 19 pages, Latex,CERN--TH-6531/9
Discounting in LTL
In recent years, there is growing need and interest in formalizing and
reasoning about the quality of software and hardware systems. As opposed to
traditional verification, where one handles the question of whether a system
satisfies, or not, a given specification, reasoning about quality addresses the
question of \emph{how well} the system satisfies the specification. One
direction in this effort is to refine the "eventually" operators of temporal
logic to {\em discounting operators}: the satisfaction value of a specification
is a value in , where the longer it takes to fulfill eventuality
requirements, the smaller the satisfaction value is.
In this paper we introduce an augmentation by discounting of Linear Temporal
Logic (LTL), and study it, as well as its combination with propositional
quality operators. We show that one can augment LTL with an arbitrary set of
discounting functions, while preserving the decidability of the model-checking
problem. Further augmenting the logic with unary propositional quality
operators preserves decidability, whereas adding an average-operator makes some
problems undecidable. We also discuss the complexity of the problem, as well as
various extensions
Symbolic Magnifying Lens Abstraction in Markov Decision Processes
In this paper, we combine abstraction-refinement and symbolic techniques to fight the state-space explosion problem when model checking Markov decision processes (MDPs). The abstract-refinement technique, called "magnifying-lens abstraction" (MLA), partitions the state-space into regions and computes upper and lower bounds for reachability and safety properties on the regions, rather than the states. To compute such bounds, MLA iterates over the regions, analyzing the concrete states of each region in turn - as if one was sliding a magnifying lens across the system to view the states. The algorithm adaptively refines the regions, using smaller regions where more detail is required, until the difference between the bounds is below a specified accuracy. The symbolic technique is based on multi-terminal binary decision diagrams (MTBDDs) which have been used extensively to provide compact encodings of probabilistic models. We introduce a symbolic version of the MLA algorithm, called "symbolic MLA", which combines the power of both practical techniques when verifying MDPs. An implementation of symbolic MLA in the probabilistic model checker PRISM and experimental results to illustrate the advantages of our approach are presented
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
Imitation in Large Games
In games with a large number of players where players may have overlapping
objectives, the analysis of stable outcomes typically depends on player types.
A special case is when a large part of the player population consists of
imitation types: that of players who imitate choice of other (optimizing)
types. Game theorists typically study the evolution of such games in dynamical
systems with imitation rules. In the setting of games of infinite duration on
finite graphs with preference orderings on outcomes for player types, we
explore the possibility of imitation as a viable strategy. In our setup, the
optimising players play bounded memory strategies and the imitators play
according to specifications given by automata. We present algorithmic results
on the eventual survival of types
Field-enlarging transformations and chiral theories
A field-enlarging transformation in the chiral electrodynamics is performed.
This introduces an additional gauge symmetry to the model that is unitary and
anomaly-free and allows for comparison of different models discussed in the
literature. The problem of superfluous degrees of freedom and their influence
on quantization is discussed. Several "mysteries" are explained from this point
of view.Comment: 14 pages, LaTeX-file, BI-TP 93/0
Fermion propagators in space-time
The one- and the two-particle propagators for an infinite non-interacting
Fermi system are studied as functions of space-time coordinates. Their
behaviour at the origin and in the asymptotic region is discussed, as is their
scaling in the Fermi momentum. Both propagators are shown to have a divergence
at equal times. The impact of the interaction among the fermions on their
momentum distribution, on their pair correlation function and, hence, on the
Coulomb sum rule is explored using a phenomenological model. Finally the
problem of how the confinement is reflected in the momentum distribution of the
system's constituents is briefly addressed.Comment: 26 pages, 9 figures, accepted for publication on Phys. Rev.
Compositionality for Quantitative Specifications
We provide a framework for compositional and iterative design and
verification of systems with quantitative information, such as rewards, time or
energy. It is based on disjunctive modal transition systems where we allow
actions to bear various types of quantitative information. Throughout the
design process the actions can be further refined and the information made more
precise. We show how to compute the results of standard operations on the
systems, including the quotient (residual), which has not been previously
considered for quantitative non-deterministic systems. Our quantitative
framework has close connections to the modal nu-calculus and is compositional
with respect to general notions of distances between systems and the standard
operations
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