53,803 research outputs found
2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties
The solution to a Nash or a nonsymmetric bargaining game is obtained by
maximizing a concave function over a convex set, i.e., it is the solution to a
convex program. We show that each 2-player game whose convex program has linear
constraints, admits a rational solution and such a solution can be found in
polynomial time using only an LP solver. If in addition, the game is succinct,
i.e., the coefficients in its convex program are ``small'', then its solution
can be found in strongly polynomial time. We also give a non-succinct linear
game whose solution can be found in strongly polynomial time
Characterizing mixing and measurement in quantum mechanics
What fundamental constraints characterize the relationship between a mixture
of quantum states, the states being mixed,
and the probabilities ? What fundamental constraints characterize the
relationship between prior and posterior states in a quantum measurement? In
this paper we show that there are many surprisingly strong constraints on these
mixing and measurement processes that can be expressed simply in terms of the
eigenvalues of the quantum states involved. These constraints capture in a
succinct fashion what it means to say that a quantum measurement acquires
information about the system being measured, and considerably simplify the
proofs of many results about entanglement transformation.Comment: 12 page
Discrete-time rewards model-checked
This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and succinct way. Algorithms to efficiently analyze such formulae are introduced. The approach is illustrated by model-checking a probabilistic cost model of the IPv4 zeroconf protocol for distributed address assignment in ad-hoc networks
Stochastic Shortest Path with Energy Constraints in POMDPs
We consider partially observable Markov decision processes (POMDPs) with a
set of target states and positive integer costs associated with every
transition. The traditional optimization objective (stochastic shortest path)
asks to minimize the expected total cost until the target set is reached. We
extend the traditional framework of POMDPs to model energy consumption, which
represents a hard constraint. The energy levels may increase and decrease with
transitions, and the hard constraint requires that the energy level must remain
positive in all steps till the target is reached. First, we present a novel
algorithm for solving POMDPs with energy levels, developing on existing POMDP
solvers and using RTDP as its main method. Our second contribution is related
to policy representation. For larger POMDP instances the policies computed by
existing solvers are too large to be understandable. We present an automated
procedure based on machine learning techniques that automatically extracts
important decisions of the policy allowing us to compute succinct human
readable policies. Finally, we show experimentally that our algorithm performs
well and computes succinct policies on a number of POMDP instances from the
literature that were naturally enhanced with energy levels.Comment: Technical report accompanying a paper published in proceedings of
AAMAS 201
Constraints in Non-Boolean Contexts
In high-level constraint modelling languages, constraints can occur in non-Boolean contexts: implicitly, in the form of partial functions, or more explicitly, in the form of constraints on local variables in non-Boolean expressions. Specifications using these facilities are often more succinct. However, these specifications are typically executed on solvers that only support questions of the form of existentially quantified conjunctions of constraints.
We show how we can translate expressions with constraints appearing in non-Boolean contexts into conjunctions of ordinary constraints. The translation is clearly structured into constrained type elimination, local variable lifting and partial function elimination. We explain our approach in the context of the modelling language Zinc. An implementation of it is an integral part of our Zinc compiler
Schulze and Ranked-Pairs Voting are Fixed-Parameter Tractable to Bribe, Manipulate, and Control
Schulze and ranked-pairs elections have received much attention recently, and
the former has quickly become a quite widely used election system. For many
cases these systems have been proven resistant to bribery, control, or
manipulation, with ranked pairs being particularly praised for being NP-hard
for all three of those. Nonetheless, the present paper shows that with respect
to the number of candidates, Schulze and ranked-pairs elections are
fixed-parameter tractable to bribe, control, and manipulate: we obtain uniform,
polynomial-time algorithms whose degree does not depend on the number of
candidates. We also provide such algorithms for some weighted variants of these
problems
Reachability in Parametric Interval Markov Chains using Constraints
Parametric Interval Markov Chains (pIMCs) are a specification formalism that
extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into
account imprecision in the transition probability values: transitions in pIMCs
are labeled with parametric intervals of probabilities. In this work, we study
the difference between pIMCs and other Markov Chain abstractions models and
investigate the two usual semantics for IMCs: once-and-for-all and
at-every-step. In particular, we prove that both semantics agree on the
maximal/minimal reachability probabilities of a given IMC. We then investigate
solutions to several parameter synthesis problems in the context of pIMCs --
consistency, qualitative reachability and quantitative reachability -- that
rely on constraint encodings. Finally, we propose a prototype implementation of
our constraint encodings with promising results
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