83 research outputs found
Multiple-Environment Markov Decision Processes
We introduce Multi-Environment Markov Decision Processes (MEMDPs) which are
MDPs with a set of probabilistic transition functions. The goal in a MEMDP is
to synthesize a single controller with guaranteed performances against all
environments even though the environment is unknown a priori. While MEMDPs can
be seen as a special class of partially observable MDPs, we show that several
verification problems that are undecidable for partially observable MDPs, are
decidable for MEMDPs and sometimes have even efficient solutions
Online Correlation Clustering
We study the online clustering problem where data items arrive in an online
fashion. The algorithm maintains a clustering of data items into similarity
classes. Upon arrival of v, the relation between v and previously arrived items
is revealed, so that for each u we are told whether v is similar to u. The
algorithm can create a new cluster for v and merge existing clusters.
When the objective is to minimize disagreements between the clustering and
the input, we prove that a natural greedy algorithm is O(n)-competitive, and
this is optimal.
When the objective is to maximize agreements between the clustering and the
input, we prove that the greedy algorithm is .5-competitive; that no online
algorithm can be better than .834-competitive; we prove that it is possible to
get better than 1/2, by exhibiting a randomized algorithm with competitive
ratio .5+c for a small positive fixed constant c.Comment: 12 pages, 1 figur
Assume-Admissible Synthesis
In this paper, we introduce a novel rule for synthesis of reactive systems,
applicable to systems made of n components which have each their own
objectives. It is based on the notion of admissible strategies. We compare our
novel rule with previous rules defined in the literature, and we show that
contrary to the previous proposals, our rule defines sets of solutions which
are rectangular. This property leads to solutions which are robust and
resilient. We provide algorithms with optimal complexity and also an
abstraction framework.Comment: 31 page
Compositional Algorithms for Succinct Safety Games
We study the synthesis of circuits for succinct safety specifications given
in the AIG format. We show how AIG safety specifications can be decomposed
automatically into sub specifications. Then we propose symbolic compositional
algorithms to solve the synthesis problem compositionally starting for the
sub-specifications. We have evaluated the compositional algorithms on a set of
benchmarks including those proposed for the first synthesis competition
organised in 2014 by the Synthesis Workshop affiliated to the CAV conference.
We show that a large number of benchmarks can be decomposed automatically and
solved more efficiently with the compositional algorithms that we propose in
this paper.Comment: In Proceedings SYNT 2015, arXiv:1602.0078
AbsSynthe: abstract synthesis from succinct safety specifications
In this paper, we describe a synthesis algorithm for safety specifications
described as circuits. Our algorithm is based on fixpoint computations,
abstraction and refinement, it uses binary decision diagrams as symbolic data
structure. We evaluate our tool on the benchmarks provided by the organizers of
the synthesis competition organized within the SYNT'14 workshop.Comment: In Proceedings SYNT 2014, arXiv:1407.493
Dynamic Network Congestion Games
Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games (NCGs), the resources correspond to simple paths in a graph, e.g. representing routing options from a source to a target. In this paper, we introduce a variant of NCGs, referred to as dynamic NCGs: in this setting, players take transitions synchronously, they select their next transitions dynamically, and they are charged a cost that depends on the number of players simultaneously using the same transition.
We study, from a complexity perspective, standard concepts of game theory in dynamic NCGs: social optima, Nash equilibria, and subgame perfect equilibria. Our contributions are the following: the existence of a strategy profile with social cost bounded by a constant is in PSPACE and NP-hard. (Pure) Nash equilibria always exist in dynamic NCGs; the existence of a Nash equilibrium with bounded cost can be decided in EXPSPACE, and computing a witnessing strategy profile can be done in doubly-exponential time. The existence of a subgame perfect equilibrium with bounded cost can be decided in 2EXPSPACE, and a witnessing strategy profile can be computed in triply-exponential time
Semilinear Representations for Series-Parallel Atomic Congestion Games
We consider atomic congestion games on series-parallel networks, and study the structure of the sets of Nash equilibria and social local optima on a given network when the number of players varies. We establish that these sets are definable in Presburger arithmetic and that they admit semilinear representations whose all period vectors have a common direction. As an application, we prove that the prices of anarchy and stability converge to 1 as the number of players goes to infinity, and show how to exploit these semilinear representations to compute these ratios precisely for a given network and number of players
Quantified Linear Temporal Logic over Probabilistic Systems with an Application to Vacuity Checking
Quantified linear temporal logic (QLTL) is an ?-regular extension of LTL allowing quantification over propositional variables. We study the model checking problem of QLTL-formulas over Markov chains and Markov decision processes (MDPs) with respect to the number of quantifier alternations of formulas in prenex normal form. For formulas with k{-}1 quantifier alternations, we prove that all qualitative and quantitative model checking problems are k-EXPSPACE-complete over Markov chains and k{+}1-EXPTIME-complete over MDPs.
As an application of these results, we generalize vacuity checking for LTL specifications from the non-probabilistic to the probabilistic setting. We show how to check whether an LTL-formula is affected by a subformula, and also study inherent vacuity for probabilistic systems
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