Improved bounds for testing Dyck languages

In this paper we consider the problem of deciding membership in Dyck languages, a fundamental family of context-free languages, comprised of well-balanced strings of parentheses. In this problem we are given a string of length $n$ in the alphabet of parentheses of $m$ types and must decide if it is well-balanced. We consider this problem in the property testing setting, where one would like to make the decision while querying as few characters of the input as possible. Property testing of strings for Dyck language membership for $m=1$, with a number of queries independent of the input size $n$, was provided in [Alon, Krivelevich, Newman and Szegedy, SICOMP 2001]. Property testing of strings for Dyck language membership for $m \ge 2$ was first investigated in [Parnas, Ron and Rubinfeld, RSA 2003]. They showed an upper bound and a lower bound for distinguishing strings belonging to the language from strings that are far (in terms of the Hamming distance) from the language, which are respectively (up to polylogarithmic factors) the $2/3$ power and the $1/11$ power of the input size $n$. Here we improve the power of $n$ in both bounds. For the upper bound, we introduce a recursion technique, that together with a refinement of the methods in the original work provides a test for any power of $n$ larger than $2/5$. For the lower bound, we introduce a new problem called Truestring Equivalence, which is easily reducible to the $2$-type Dyck language property testing problem. For this new problem, we show a lower bound of $n$ to the power of $1/5$

Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and \LL(k) (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $\epsilon < 1/2$ must use $\Omega(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems

Recognizing well-parenthesized expressions in the streaming model

Motivated by a concrete problem and with the goal of understanding the sense in which the complexity of streaming algorithms is related to the complexity of formal languages, we investigate the problem Dyck(s) of checking matching parentheses, with $s$ different types of parenthesis. We present a one-pass randomized streaming algorithm for Dyck(2) with space \Order(\sqrt{n}\log n), time per letter \polylog (n), and one-sided error. We prove that this one-pass algorithm is optimal, up to a \polylog n factor, even when two-sided error is allowed. For the lower bound, we prove a direct sum result on hard instances by following the "information cost" approach, but with a few twists. Indeed, we play a subtle game between public and private coins. This mixture between public and private coins results from a balancing act between the direct sum result and a combinatorial lower bound for the base case. Surprisingly, the space requirement shrinks drastically if we have access to the input stream in reverse. We present a two-pass randomized streaming algorithm for Dyck(2) with space \Order((\log n)^2), time \polylog (n) and one-sided error, where the second pass is in the reverse direction. Both algorithms can be extended to Dyck(s) since this problem is reducible to Dyck(2) for a suitable notion of reduction in the streaming model.Comment: 20 pages, 5 figure

Trade, diaspora and migration to New Zealand

NZIER has always had a strong interest in understanding the way in which the New Zealand economy interacts with the rest of the world. We have a long history of producing research into trade liberalisation and globalisation. As the global economy becomes ever more complex, we are now turning our attention to issues such as services, investment, technology transfer and the role of people movement in promoting economic growth and productivity. NZIER is delighted to continue this tradition by funding this important and innovative piece of research by David Law, Murat Gen and John Bryant into the links between trade flows and the movement of people across borders. This research was funded by NZIER in celebration of our 50th Anniversary in 2008. During this very challenging period for the global economy, there has been a tendency for policy makers to implement inwards-focused policies aimed to protecting domestic jobs and promoting domestic economic activity. Such policies are politically popular, but can be economically inefficient and often come at the expense of deeper economic integration between countries. One particularly topical area of policy discussion is the role of immigration in promoting economic growth. New Zealand has long been reliant on immigration to boost its population and to fill gaps in the labour market. And many Kiwis love to travel overseas to gain life and work experience. Given these continual inflows and outflows, it is interesting to consider how people movements might affect the New Zealands exports and imports of goods and services, and thus how immigration policy might be used as a policy lever to boost our international linkages. The paper uses empirical techniques to investigate the links between trade, migration and New Zealands diaspora. It clearly shows that inwards and outwards migration has a positive effect on goods and tourism trade. This suggests that policy makers could design immigration policy with these links in mind in order to maximise the economic potential of migrants. If trade follows migration flows, then an important avenue for boosting New Zealands integration with the global economy may be encouraging migrants from important trading partners.Diaspora, trade, Migration, New Zealand, economic growth

Streaming Property Testing of Visibly Pushdown Languages

In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are $\varepsilon$-far from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming $\varepsilon$-property tester for visibly pushdown languages (VPL) with one-sided error using memory space $\mathrm{poly}((\log n) / \varepsilon)$. This constructions relies on a (non-streaming) property tester for weighted regular languages based on a previous tester by Alon et al. We provide a simple application of this tester for streaming testing special cases of instances of VPL that are already hard for both streaming algorithms and property testers. Our main algorithm is a combination of an original simulation of visibly pushdown automata using a stack with small height but possible items of linear size. In a second step, those items are replaced by small sketches. Those sketches relies on a notion of suffix-sampling we introduce. This sampling is the key idea connecting our streaming tester algorithm to property testers.Comment: 23 pages. Major modifications in the presentatio

Orderly Spanning Trees with Applications

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an {\em orderly pair} for any connected planar graph $G$, consisting of a plane graph $H$ of $G$, and an orderly spanning tree of $H$. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem, (2) the first area-optimal 2-visibility drawing of $G$, and (3) the best known encodings of $G$ with O(1)-time query support. All algorithms in this paper run in linear time.Comment: 25 pages, 7 figures, A preliminary version appeared in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), Washington D.C., USA, January 7-9, 2001, pp. 506-51

Short-run and long-run relationships in the consumption of alcohol in the Scandinavian countries

Traditionally, the Scandinavian countries have been characterized as spirits and beer consuming countries and a century ago the historical background was decades of relatively heavy drinking behaviour with spirit as the preferred beverage. Therefore, it might be expected that alcohol consumption – especially in the last part of the 19th century and the beginning of the 20th century – would behave in a counter-cyclical manner, i.e. heavy drinking during severe recessions characterized by harsh economic conditions. Using long-run time series data for alcohol consumption levels in the Scandinavian countries the question of a counter-cyclical or pro-cyclical behaviour is addressed – with the business cycle measured as the GDP – and the empirical findings are that generally, alcohol consumption behaves in a pro-cyclical manner in the short run, and with no long-run relationship concerning real income.Alcohol consumption; Business cycles; Scandinavia

Language Modeling by Clustering with Word Embeddings for Text Readability Assessment

We present a clustering-based language model using word embeddings for text readability prediction. Presumably, an Euclidean semantic space hypothesis holds true for word embeddings whose training is done by observing word co-occurrences. We argue that clustering with word embeddings in the metric space should yield feature representations in a higher semantic space appropriate for text regression. Also, by representing features in terms of histograms, our approach can naturally address documents of varying lengths. An empirical evaluation using the Common Core Standards corpus reveals that the features formed on our clustering-based language model significantly improve the previously known results for the same corpus in readability prediction. We also evaluate the task of sentence matching based on semantic relatedness using the Wiki-SimpleWiki corpus and find that our features lead to superior matching performance