5,462 research outputs found
Well structured program equivalence is highly undecidable
We show that strict deterministic propositional dynamic logic with
intersection is highly undecidable, solving a problem in the Stanford
Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We
introduce the construction of program equivalence, which returns the value
precisely when two given programs are equivalent on halting
computations. We show that virtually any variant of propositional dynamic logic
has -hard validity problem if it can express even just the equivalence
of well-structured programs with the empty program \texttt{skip}. We also show,
in these cases, that the set of propositional statements valid over finite
models is not recursively enumerable, so there is not even an axiomatisation
for finitely valid propositions.Comment: 8 page
Matching Subsequences in Trees
Given two rooted, labeled trees and the tree path subsequence problem
is to determine which paths in are subsequences of which paths in . Here
a path begins at the root and ends at a leaf. In this paper we propose this
problem as a useful query primitive for XML data, and provide new algorithms
improving the previously best known time and space bounds.Comment: Minor correction of typos, et
Fast Arc-Annotated Subsequence Matching in Linear Space
An arc-annotated string is a string of characters, called bases, augmented
with a set of pairs, called arcs, each connecting two bases. Given
arc-annotated strings and the arc-preserving subsequence problem is to
determine if can be obtained from by deleting bases from . Whenever
a base is deleted any arc with an endpoint in that base is also deleted.
Arc-annotated strings where the arcs are ``nested'' are a natural model of RNA
molecules that captures both the primary and secondary structure of these. The
arc-preserving subsequence problem for nested arc-annotated strings is basic
primitive for investigating the function of RNA molecules. Gramm et al. [ACM
Trans. Algorithms 2006] gave an algorithm for this problem using time
and space, where and are the lengths of and , respectively. In
this paper we present a new algorithm using time and space,
thereby matching the previous time bound while significantly reducing the space
from a quadratic term to linear. This is essential to process large RNA
molecules where the space is likely to be a bottleneck. To obtain our result we
introduce several novel ideas which may be of independent interest for related
problems on arc-annotated strings.Comment: To appear in Algoritmic
Synthesizing Finite-state Protocols from Scenarios and Requirements
Scenarios, or Message Sequence Charts, offer an intuitive way of describing
the desired behaviors of a distributed protocol. In this paper we propose a new
way of specifying finite-state protocols using scenarios: we show that it is
possible to automatically derive a distributed implementation from a set of
scenarios augmented with a set of safety and liveness requirements, provided
the given scenarios adequately \emph{cover} all the states of the desired
implementation. We first derive incomplete state machines from the given
scenarios, and then synthesis corresponds to completing the transition relation
of individual processes so that the global product meets the specified
requirements. This completion problem, in general, has the same complexity,
PSPACE, as the verification problem, but unlike the verification problem, is
NP-complete for a constant number of processes. We present two algorithms for
solving the completion problem, one based on a heuristic search in the space of
possible completions and one based on OBDD-based symbolic fixpoint computation.
We evaluate the proposed methodology for protocol specification and the
effectiveness of the synthesis algorithms using the classical alternating-bit
protocol.Comment: This is the working draft of a paper currently in submission.
(February 10, 2014
Non-Holonomic Control IV : Coherence Protection in a Rubidium isotope
In this paper, we present a realistic application of the coherence protection
method proposed in the previous article. A qubit of information encoded on the
two spin states of a Rubidium isotope is protected from the action of electric
and magnetic fields
Non-Holonomic Control I
In this paper, we present a universal control technique, the non-holonomic
control, which allows us to impose any arbitrarily prescribed unitary evolution
to any quantum system through the alternate application of two well-chosen
perturbations
Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis
The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of studentsâ thinking â concept images as well as ability in symbolic manipulation â about the tangent line of a curve as it has developed through studentsâ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the studentsâ responses, we describe studentsâ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis
String Indexing for Patterns with Wildcards
We consider the problem of indexing a string of length to report the
occurrences of a query pattern containing characters and wildcards.
Let be the number of occurrences of in , and the size of
the alphabet. We obtain the following results.
- A linear space index with query time .
This significantly improves the previously best known linear space index by Lam
et al. [ISAAC 2007], which requires query time in the worst case.
- An index with query time using space , where is the maximum number of wildcards allowed in the pattern.
This is the first non-trivial bound with this query time.
- A time-space trade-off, generalizing the index by Cole et al. [STOC 2004].
We also show that these indexes can be generalized to allow variable length
gaps in the pattern. Our results are obtained using a novel combination of
well-known and new techniques, which could be of independent interest
- âŠ