5,462 research outputs found

    Well structured program equivalence is highly undecidable

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    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 T\mathsf{T} precisely when two given programs are equivalent on halting computations. We show that virtually any variant of propositional dynamic logic has Π11\Pi_1^1-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

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    Given two rooted, labeled trees PP and TT the tree path subsequence problem is to determine which paths in PP are subsequences of which paths in TT. 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

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    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 PP and QQ the arc-preserving subsequence problem is to determine if PP can be obtained from QQ by deleting bases from QQ. 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 O(nm)O(nm) time and space, where mm and nn are the lengths of PP and QQ, respectively. In this paper we present a new algorithm using O(nm)O(nm) time and O(n+m)O(n + m) 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

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    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

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    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

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    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

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    The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ 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 students’ responses, we describe students’ 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

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    We consider the problem of indexing a string tt of length nn to report the occurrences of a query pattern pp containing mm characters and jj wildcards. Let occocc be the number of occurrences of pp in tt, and σ\sigma the size of the alphabet. We obtain the following results. - A linear space index with query time O(m+σjlog⁥log⁥n+occ)O(m+\sigma^j \log \log n + occ). This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time Θ(jn)\Theta(jn) in the worst case. - An index with query time O(m+j+occ)O(m+j+occ) using space O(σk2nlog⁥klog⁥n)O(\sigma^{k^2} n \log^k \log n), where kk 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
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