134 Works

Deductive Verification of Continuous Dynamical Systems

Ankur Taly & Ashish Tiwari
We define the notion of inductive invariants for continuous dynamical systems and use it to present inference rules for safety verification of polynomial continuous dynamical systems. We present two different sound and complete inference rules, but neither of these rules can be effectively applied. We then present several simpler and practical inference rules that are sound and relatively complete for different classes of inductive invariants. The simpler inference rules can be effectively checked when all...

A Fine-grained Analysis of a Simple Independent Set Algorithm

Joachim Kneis, Alexander Langer & Peter Rossmanith
We present a simple exact algorithm for the \is\ problem with a runtime bounded by $O(\rt^n \poly(n))$. This bound is obtained by, firstly, applying a new branching rule and, secondly, by a distinct, computer-aided case analysis. The new branching rule uses the concept of satellites and has previously only been used in an algorithm for sparse graphs. The computer-aided case analysis allows us to capture the behavior of our algorithm in more detail than in...

Using Elimination Theory to construct Rigid Matrices

Abhinav Kumar, Satyanarayana V. Lokam, Vijay M. Patankar & Jayalal Sarma M. N.
The rigidity of a matrix $A$ for target rank $r$ is the minimum number of entries of $A$ that must be changed to ensure that the rank of the altered matrix is at most $r$. Since its introduction by Valiant \cite{Val77}, rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all $\nbyn$ matrices over an infinite field have a rigidity of $(n-r)^2$. It is...

On Nondeterministic Unranked Tree Automata with Sibling Constraints

Christof Löding & Karianto Wong
We continue the study of bottom-up unranked tree automata with equality and disequality constraints between direct subtrees. In particular, we show that the emptiness problem for the nondeterministic automata is decidable. In addition, we show that the universality problem, in contrast, is undecidable.

Functionally Private Approximations of Negligibly-Biased Estimators

André Madeira & S. Muthukrishnan
We study functionally private approximations. An approximation function $g$ is {\em functionally private} with respect to $f$ if, for any input $x$, $g(x)$ reveals no more information about $x$ than $f(x)$. Our main result states that a function $f$ admits an efficiently-computable functionally private approximation $g$ if there exists an efficiently-computable and negligibly-biased estimator for $f$. Contrary to previous generic results, our theorem is more general and has a wider application reach.We provide two distinct...

Bounded Size Graph Clustering with Applications to Stream Processing

Rohit Khandekar, Kirsten Hildrum, Sujay Parekh, Deepak Rajan, Jay Sethuraman & Joel Wolf
We introduce a graph clustering problem motivated by a stream processing application. Input to our problem is an undirected graph with vertex and edge weights. A cluster is a subset of the vertices. The {\em size} of a cluster is defined as the total vertex weight in the subset plus the total edge weight at the boundary of the cluster. The bounded size graph clustering problem ($\GC$) is to partition the vertices into clusters of...

Kolmogorov Complexity in Randomness Extraction

John M. Hitchcock, Aduri Pavan & N. V. Vinodchandran
We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity extractor, thus establishing a fundamental equivalence between two forms of extraction studied in the literature: Kolmogorov extraction and randomness extraction. We present a distribution ${\cal M}_k$ based on Kolmogorov complexity that is complete for randomness extraction in the sense that a computable...

Non-Local Box Complexity and Secure Function Evaluation

Marc Kaplan, Iordanis Kerenidis, Sophie Laplante & Jérémie Roland
A non-local box is an abstract device into which Alice and Bob input bits $x$ and $y$ respectively and receive outputs $a$ and $b$ respectively, where $a,b$ are uniformly distributed and $a \oplus b = x \wedge y$. Such boxes have been central to the study of quantum or generalized non-locality as well as the simulation of non-signaling distributions. In this paper, we start by studying how many non-local boxes Alice and Bob need in...

Donation Center Location Problem

Chien-Chung Huang & Zoya Svitkina
We introduce and study the {\em donation center location} problem, which has an additional application in network testing and may also be of independent interest as a general graph-theoreticproblem.Given a set of agents and a set of centers, where agents have preferences over centers and centers have capacities, the goal is to open a subset of centers and to assign a maximum-sized subset of agents to their most-preferred open centers, while respecting the capacity constraints....

Verification and Refutation of Probabilistic Specifications via Games

Mark Kattenbelt & Michael Huth
We develop an abstraction-based framework to check probabilistic specifications of Markov Decision Processes (MDPs) using the stochastic two-player game abstractions (\ie ``games'') developed by Kwiatkowska et al.\ as a foundation. We define an abstraction preorder for these game abstractions which enables us to identify many new game abstractions for each MDP --- ranging from compact and imprecise to complex and precise. This added ability to trade precision for efficiency is crucial for scalable software model...

Approximating Fault-Tolerant Group-Steiner Problems

Rohit Khandekar, Guy Kortsarz & Zeev Nutov
In this paper, we initiate the study of designing approximation algorithms for {\sf Fault-Tolerant Group-Steiner} ({\sf FTGS}) problems. The motivation is to protect the well-studied group-Steiner networks from edge or vertex failures. In {\sf Fault-Tolerant Group-Steiner} problems, we are given a graph with edge- (or vertex-) costs, a root vertex, and a collection of subsets of vertices called groups. The objective is to find a minimum-cost subgraph that has two edge- (or vertex-) disjoint paths...

On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities

Konstantinos Georgiou, Avner Magen & Iannis Tourlakis
We show that the integrality gap of the standard SDP for \vc~on instances of $n$ vertices remains $2-o(1)$ even after the addition of \emph{all} hypermetric inequalities. Our lower bound requires new insights into the structure of SDP solutions behaving like $\ell_1$ metric spaces when one point is removed. We also show that the addition of all $\ell_1$ inequalities eliminates any solutions that are not convex combination of integral solutions. Consequently, we provide the strongest possible...

Simulation based security in the applied pi calculus

Stéphanie Delaune, Steve Kremer & Olivier Pereira
We present a symbolic framework for refinement and composition of security protocols. The framework uses the notion of ideal functionalities. These are abstract systems which are secure by construction and which can be combined into larger systems. They can be separately refined in order to obtain concrete protocols implementing them. Our work builds on ideas from the ``trusted party paradigm'' used in computational cryptography models. The underlying language we use is the applied pi calculus...

Subexponential Algorithms for Partial Cover Problems

Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman & Saket Saurabh
Partial Cover problems are optimization versions of fundamental and well studied problems like {\sc Vertex Cover} and {\sc Dominating Set}. Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number ($k$) of vertices, rather than covering all edges (or vertices). In general graphs, these problems are hard for parameterized complexity classes when parameterized by $k$. It was recently shown by Amini et. al. [{\em FSTTCS 08}\,]...

Graph Isomorphism for K_{3,3}-free and K_5-free graphs is in Log-space

Samir Datta, Prajakta Nimbhorkar, Thomas Thierauf & Fabian Wagner
Graph isomorphism is an important and widely studied computational problem with a yet unsettled complexity. However, the exact complexity is known for isomorphism of various classes of graphs. Recently, \cite{DLNTW09} proved that planar isomorphism is complete for log-space. We extend this result %of \cite{DLNTW09} further to the classes of graphs which exclude $K_{3,3}$ or $K_5$ as a minor, and give a log-space algorithm. Our algorithm decomposes $K_{3,3}$ minor-free graphs into biconnected and those further into...

The Wadge Hierarchy of Max-Regular Languages

Jérémie Cabessa, Jacques Duparc, Alessandro Facchini & Filip Murlak
Recently, Miko{\l}aj Boja{\'n}czyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving manyof its usual properties. This new class can be seen as a different way of generalising the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity.It is proved that up to Wadge equivalence the classes coincide. Moreover, when restricted to $\mathbf{\Delta}^0_2$-languages, the classes contain virtually the...

Automata and temporal logic over arbitrary linear time

Julien Cristau
Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time, using words indexed by arbitrary linear orderings. We investigate the connections between temporal logic and automata on linear orderings, as introduced by Bruyere and Carton. We provide a doubly exponential procedure to compute from any LTL formula with...

Domination Problems in Nowhere-Dense Classes

Anuj Dawar & Stephan Kreutzer
We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distance-$d$ dominating-set problem, also known as the $(k,d)$-centres problem, is fixed-parameter tractable on any class that is nowhere dense and closed under induced subgraphs. This generalises known results about the dominating set problem on $H$-minor free classes, classes with locally excluded minors and classes of graphs of...

Covering of ordinals

Laurent Braud
The paper focuses on the structure of fundamental sequences of ordinals smaller than $\e$. A first result is the construction of a monadic second-order formula identifying a given structure, whereas such a formula cannot exist for ordinals themselves. The structures are precisely classified in the pushdown hierarchy. Ordinals are also located in the hierarchy, and a direct presentation is given.

Fractional Pebbling and Thrifty Branching Programs

Mark Braverman, Stephen Cook, Pierre McKenzie, Rahul Santhanam & Dustin Wehr
We study the branching program complexity of the {\em tree evaluation problem}, introduced in \cite{BrCoMcSaWe09} as a candidate for separating \nl\ from\logcfl. The input to the problem is a rooted, balanced $d$-ary tree of height$h$, whose internal nodes are labelled with $d$-ary functions on$[k]=\{1,\ldots,k\}$, and whose leaves are labelled with elements of $[k]$.Each node obtains a value in $[k]$ equal to its $d$-ary function applied to the values of its $d$ children. The output is...

Deterministic Automata and Extensions of Weak MSO

Mikolaj Bojanczyk & Szymon Torunczyk
We introduce a new class of automata on infinite words, called min-automata. We prove that min-automata have the same expressive power as weak monadic second-order logic (weak MSO) extended with a new quantifier, the recurrence quantifier. These results are dual to a framework presented in \cite{max-automata}, where max-automata were proved equivalent to weak MSO extended with an unbounding quantifier. We also present a general framework, which tries to explain which types of automata on infinite...

Arithmetic Circuits and the Hadamard Product of Polynomials

Vikraman Arvind, Pushkar S. Joglekar & Srikanth Srinivasan
Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. \begin{itemize} \item[$\bullet$] We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class $\ceql$, and over fields of characteristic $p$ the problem is in $\ModpL/\Poly$. \item[$\bullet$]...

Continuous-Time Stochastic Games with Time-Bounded Reachability

Tomas Brazdil, Vojtech Forejt, Jan Krcal, Jan Kretinsky & Antonin Kucera
We study continuous-time stochastic games with time-bounded reachability objectives. We show that each vertex in such a game has a \emph{value} (i.e., an equilibrium probability), and we classify the conditions under which optimal strategies exist. Finally, we show how to compute optimal strategies in finite uniform games, and how to compute $\varepsilon$-optimal strategies in finitely-branching games with bounded rates (for finite games, we provide detailed complexity estimations).

Kernels for Feedback Arc Set In Tournaments

Stéphane Bessy, Fedor V. Fomin, Serge Gaspers, Christophe Paul, Anthony Perez, Saket Saurabh & Stéphan Thomassé
A tournament $T = (V,A)$ is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on $n$ vertices and an integer parameter $k$, the {\sc Feedback Arc Set} problem asks whether thegiven digraph has a set of $k$ arcs whose removal results in an acyclicdigraph. The {\sc Feedback Arc Set} problem restricted to tournaments is knownas the {\sc $k$-Feedback Arc Set in Tournaments ($k$-FAST)} problem....

On the Memory Consumption of Probabilistic Pushdown Automata

Tomas Brazdil, Javier Esparza & Stefan Kiefer
We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a runof a pPDA is the maximal height reached by the stack during the run. Theproblem is motivated by the investigation of depth-first computations that playan important role for space-efficient schedulings of multithreaded programs. We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that...

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