3,609 research outputs found
Dynamic Traitor Tracing for Arbitrary Alphabets: Divide and Conquer
We give a generic divide-and-conquer approach for constructing
collusion-resistant probabilistic dynamic traitor tracing schemes with larger
alphabets from schemes with smaller alphabets. This construction offers a
linear tradeoff between the alphabet size and the codelength. In particular, we
show that applying our results to the binary dynamic Tardos scheme of Laarhoven
et al. leads to schemes that are shorter by a factor equal to half the alphabet
size. Asymptotically, these codelengths correspond, up to a constant factor, to
the fingerprinting capacity for static probabilistic schemes. This gives a
hierarchy of probabilistic dynamic traitor tracing schemes, and bridges the gap
between the low bandwidth, high codelength scheme of Laarhoven et al. and the
high bandwidth, low codelength scheme of Fiat and Tassa.Comment: 6 pages, 1 figur
Improved Approximation Algorithms for Projection Games
The projection games (aka Label-Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label-Cover. In this paper we design several approximation algorithms for projection games:
1. A polynomial-time approximation algorithm that improves on the previous best approximation by Charikar, Hajiaghayi and Karloff [7].
2. A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games.
3. A PTAS for planar graphs.National Science Foundation (U.S.) (Grant 1218547
Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives
Given a model and a specification, the fundamental model-checking problem
asks for algorithmic verification of whether the model satisfies the
specification. We consider graphs and Markov decision processes (MDPs), which
are fundamental models for reactive systems. One of the very basic
specifications that arise in verification of reactive systems is the strong
fairness (aka Streett) objective. Given different types of requests and
corresponding grants, the objective requires that for each type, if the request
event happens infinitely often, then the corresponding grant event must also
happen infinitely often. All -regular objectives can be expressed as
Streett objectives and hence they are canonical in verification. To handle the
state-space explosion, symbolic algorithms are required that operate on a
succinct implicit representation of the system rather than explicitly accessing
the system. While explicit algorithms for graphs and MDPs with Streett
objectives have been widely studied, there has been no improvement of the basic
symbolic algorithms. The worst-case numbers of symbolic steps required for the
basic symbolic algorithms are as follows: quadratic for graphs and cubic for
MDPs. In this work we present the first sub-quadratic symbolic algorithm for
graphs with Streett objectives, and our algorithm is sub-quadratic even for
MDPs. Based on our algorithmic insights we present an implementation of the new
symbolic approach and show that it improves the existing approach on several
academic benchmark examples.Comment: Full version of the paper. To appear in CAV 201
- …