3,989 research outputs found
Parity and Streett Games with Costs
We consider two-player games played on finite graphs equipped with costs on
edges and introduce two winning conditions, cost-parity and cost-Streett, which
require bounds on the cost between requests and their responses. Both
conditions generalize the corresponding classical omega-regular conditions and
the corresponding finitary conditions. For parity games with costs we show that
the first player has positional winning strategies and that determining the
winner lies in NP and coNP. For Streett games with costs we show that the first
player has finite-state winning strategies and that determining the winner is
EXPTIME-complete. The second player might need infinite memory in both games.
Both types of games with costs can be solved by solving linearly many instances
of their classical variants.Comment: A preliminary version of this work appeared in FSTTCS 2012 under the
name "Cost-parity and Cost-Streett Games". The research leading to these
results has received funding from the European Union's Seventh Framework
Programme (FP7/2007-2013) under grant agreements 259454 (GALE) and 239850
(SOSNA
On the Complexity of the Equivalence Problem for Probabilistic Automata
Checking two probabilistic automata for equivalence has been shown to be a
key problem for efficiently establishing various behavioural and anonymity
properties of probabilistic systems. In recent experiments a randomised
equivalence test based on polynomial identity testing outperformed
deterministic algorithms. In this paper we show that polynomial identity
testing yields efficient algorithms for various generalisations of the
equivalence problem. First, we provide a randomized NC procedure that also
outputs a counterexample trace in case of inequivalence. Second, we show how to
check for equivalence two probabilistic automata with (cumulative) rewards. Our
algorithm runs in deterministic polynomial time, if the number of reward
counters is fixed. Finally we show that the equivalence problem for
probabilistic visibly pushdown automata is logspace equivalent to the
Arithmetic Circuit Identity Testing problem, which is to decide whether a
polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape
Model Checking One-clock Priced Timed Automata
We consider the model of priced (a.k.a. weighted) timed automata, an
extension of timed automata with cost information on both locations and
transitions, and we study various model-checking problems for that model based
on extensions of classical temporal logics with cost constraints on modalities.
We prove that, under the assumption that the model has only one clock,
model-checking this class of models against the logic WCTL, CTL with
cost-constrained modalities, is PSPACE-complete (while it has been shown
undecidable as soon as the model has three clocks). We also prove that
model-checking WMTL, LTL with cost-constrained modalities, is decidable only if
there is a single clock in the model and a single stopwatch cost variable
(i.e., whose slopes lie in {0,1}).Comment: 28 page
Streaming Verification of Graph Properties
Streaming interactive proofs (SIPs) are a framework for outsourced
computation. A computationally limited streaming client (the verifier) hands
over a large data set to an untrusted server (the prover) in the cloud and the
two parties run a protocol to confirm the correctness of result with high
probability. SIPs are particularly interesting for problems that are hard to
solve (or even approximate) well in a streaming setting. The most notable of
these problems is finding maximum matchings, which has received intense
interest in recent years but has strong lower bounds even for constant factor
approximations.
In this paper, we present efficient streaming interactive proofs that can
verify maximum matchings exactly. Our results cover all flavors of matchings
(bipartite/non-bipartite and weighted). In addition, we also present streaming
verifiers for approximate metric TSP. In particular, these are the first
efficient results for weighted matchings and for metric TSP in any streaming
verification model.Comment: 26 pages, 2 figure, 1 tabl
PAC Classification based on PAC Estimates of Label Class Distributions
A standard approach in pattern classification is to estimate the
distributions of the label classes, and then to apply the Bayes classifier to
the estimates of the distributions in order to classify unlabeled examples. As
one might expect, the better our estimates of the label class distributions,
the better the resulting classifier will be. In this paper we make this
observation precise by identifying risk bounds of a classifier in terms of the
quality of the estimates of the label class distributions. We show how PAC
learnability relates to estimates of the distributions that have a PAC
guarantee on their distance from the true distribution, and we bound the
increase in negative log likelihood risk in terms of PAC bounds on the
KL-divergence. We give an inefficient but general-purpose smoothing method for
converting an estimated distribution that is good under the metric into a
distribution that is good under the KL-divergence.Comment: 14 page
Prompt Delay
Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. Recently, such
games with quantitative winning conditions in weak MSO with the unbounding
quantifier were studied, but their properties turned out to be unsatisfactory.
In particular, unbounded lookahead is in general necessary. Here, we study
delay games with winning conditions given by Prompt-LTL, Linear Temporal Logic
equipped with a parameterized eventually operator whose scope is bounded. Our
main result shows that solving Prompt-LTL delay games is complete for
triply-exponential time. Furthermore, we give tight triply-exponential bounds
on the necessary lookahead and on the scope of the parameterized eventually
operator. Thus, we identify Prompt-LTL as the first known class of well-behaved
quantitative winning conditions for delay games. Finally, we show that applying
our techniques to delay games with \omega-regular winning conditions answers
open questions in the cases where the winning conditions are given by
non-deterministic, universal, or alternating automata
Limit Your Consumption! Finding Bounds in Average-energy Games
Energy games are infinite two-player games played in weighted arenas with
quantitative objectives that restrict the consumption of a resource modeled by
the weights, e.g., a battery that is charged and drained. Typically, upper
and/or lower bounds on the battery capacity are part of the problem
description. Here, we consider the problem of determining upper bounds on the
average accumulated energy or on the capacity while satisfying a given lower
bound, i.e., we do not determine whether a given bound is sufficient to meet
the specification, but if there exists a sufficient bound to meet it.
In the classical setting with positive and negative weights, we show that the
problem of determining the existence of a sufficient bound on the long-run
average accumulated energy can be solved in doubly-exponential time. Then, we
consider recharge games: here, all weights are negative, but there are recharge
edges that recharge the energy to some fixed capacity. We show that bounding
the long-run average energy in such games is complete for exponential time.
Then, we consider the existential version of the problem, which turns out to be
solvable in polynomial time: here, we ask whether there is a recharge capacity
that allows the system player to win the game.
We conclude by studying tradeoffs between the memory needed to implement
strategies and the bounds they realize. We give an example showing that memory
can be traded for bounds and vice versa. Also, we show that increasing the
capacity allows to lower the average accumulated energy.Comment: In Proceedings QAPL'16, arXiv:1610.0769
A Fast Algorithm Finding the Shortest Reset Words
In this paper we present a new fast algorithm finding minimal reset words for
finite synchronizing automata. The problem is know to be computationally hard,
and our algorithm is exponential. Yet, it is faster than the algorithms used so
far and it works well in practice. The main idea is to use a bidirectional BFS
and radix (Patricia) tries to store and compare resulted subsets. We give both
theoretical and practical arguments showing that the branching factor is
reduced efficiently. As a practical test we perform an experimental study of
the length of the shortest reset word for random automata with states and 2
input letters. We follow Skvorsov and Tipikin, who have performed such a study
using a SAT solver and considering automata up to states. With our
algorithm we are able to consider much larger sample of automata with up to
states. In particular, we obtain a new more precise estimation of the
expected length of the shortest reset word .Comment: COCOON 2013. The final publication is available at
http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1
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