849 research outputs found
Structure Theorem and Strict Alternation Hierarchy for FO^2 on Words
It is well-known that every first-order property on words is expressible
using at most three variables. The subclass of properties expressible with only
two variables is also quite interesting and well-studied. We prove precise
structure theorems that characterize the exact expressive power of first-order
logic with two variables on words. Our results apply to both the case with and
without a successor relation. For both languages, our structure theorems show
exactly what is expressible using a given quantifier depth, n, and using m
blocks of alternating quantifiers, for any m \leq n. Using these
characterizations, we prove, among other results, that there is a strict
hierarchy of alternating quantifiers for both languages. The question whether
there was such a hierarchy had been completely open. As another consequence of
our structural results, we show that satisfiability for first-order logic with
two variables without successor, which is NEXP-complete in general, becomes
NP-complete once we only consider alphabets of a bounded size
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
Analyzing Satisfiability and Refutability in Selected Constraint Systems
This dissertation is concerned with the satisfiability and refutability problems for several constraint systems. We examine both Boolean constraint systems, in which each variable is limited to the values true and false, and polyhedral constraint systems, in which each variable is limited to the set of real numbers R in the case of linear polyhedral systems or the set of integers Z in the case of integer polyhedral systems. An important aspect of our research is that we focus on providing certificates. That is, we provide satisfying assignments or easily checkable proofs of infeasibility depending on whether the instance is feasible or not. Providing easily checkable certificates has become a much sought after feature in algorithms, especially in light of spectacular failures in the implementations of some well-known algorithms. There exist a number of problems in the constraint-solving domain for which efficient algorithms have been proposed, but which lack a certifying counterpart. When examining Boolean constraint systems, we specifically look at systems of 2-CNF clauses and systems of Horn clauses. When examining polyhedral constraint systems, we specifically look at systems of difference constraints, systems of UTVPI constraints, and systems of Horn constraints.
For each examined system, we determine several properties of general refutations and determine the complexity of finding restricted refutations. These restricted forms of refutation include read-once refutations, in which each constraint can be used at most once; literal-once refutations, in which for each literal at most one constraint containing that literal can be used; and unit refutations, in which each step of the refutation must use a constraint containing exactly one literal. The advantage of read-once refutations is that they are guaranteed to be short. Thus, while not every constraint system has a read-once refutation, the small size of the refutation guarantees easy checkability
An Approximate Inner Bound to the QoS Aware Throughput Region of a Tree Network under IEEE 802.15.4 CSMA/CA and Application to Wireless Sensor Network Design
We consider a tree network spanning a set of source nodes that generate
measurement packets, a set of additional relay nodes that only forward packets
from the sources, and a data sink. We assume that the paths from the sources to
the sink have bounded hop count. We assume that the nodes use the IEEE 802.15.4
CSMA/CA for medium access control, and that there are no hidden terminals. In
this setting, starting with a set of simple fixed point equations, we derive
sufficient conditions for the tree network to approximately satisfy certain
given QoS targets such as end-to-end delivery probability and delay under a
given rate of generation of measurement packets at the sources (arrival rates
vector). The structures of our sufficient conditions provide insight on the
dependence of the network performance on the arrival rate vector, and the
topological properties of the network. Furthermore, for the special case of
equal arrival rates, default backoff parameters, and for a range of values of
target QoS, we show that among all path-length-bounded trees (spanning a given
set of sources and BS) that meet the sufficient conditions, a shortest path
tree achieves the maximum throughput
Performance Guarantees for Distributed Reachability Queries
In the real world a graph is often fragmented and distributed across
different sites. This highlights the need for evaluating queries on distributed
graphs. This paper proposes distributed evaluation algorithms for three classes
of queries: reachability for determining whether one node can reach another,
bounded reachability for deciding whether there exists a path of a bounded
length between a pair of nodes, and regular reachability for checking whether
there exists a path connecting two nodes such that the node labels on the path
form a string in a given regular expression. We develop these algorithms based
on partial evaluation, to explore parallel computation. When evaluating a query
Q on a distributed graph G, we show that these algorithms possess the following
performance guarantees, no matter how G is fragmented and distributed: (1) each
site is visited only once; (2) the total network traffic is determined by the
size of Q and the fragmentation of G, independent of the size of G; and (3) the
response time is decided by the largest fragment of G rather than the entire G.
In addition, we show that these algorithms can be readily implemented in the
MapReduce framework. Using synthetic and real-life data, we experimentally
verify that these algorithms are scalable on large graphs, regardless of how
the graphs are distributed.Comment: VLDB201
Model Checking Probabilistic Pushdown Automata
We consider the model checking problem for probabilistic pushdown automata
(pPDA) and properties expressible in various probabilistic logics. We start
with properties that can be formulated as instances of a generalized random
walk problem. We prove that both qualitative and quantitative model checking
for this class of properties and pPDA is decidable. Then we show that model
checking for the qualitative fragment of the logic PCTL and pPDA is also
decidable. Moreover, we develop an error-tolerant model checking algorithm for
PCTL and the subclass of stateless pPDA. Finally, we consider the class of
omega-regular properties and show that both qualitative and quantitative model
checking for pPDA is decidable
- ā¦