Clause Density Research Articles

Linguistic diagnostics of written texts in two school-age populations

The paper considers the writing abilities of Hebrew-speaking grade school and middle school students from mid-high compared with low SES backgrounds, as reflected in stories and compositions they wrote on the topic of friendship. A range of linguistic means of expression were employed as diagnostic of school-age written text construction, focusing on the lexicon and including both devices applicable in different languages (overall text length in words and clauses, syntactic clause density, and lexical diversity and density as reflected in proportions of content words) as well as Hebrew-specific features (verb-pattern morphology and construct-state noun compounds). Analyses showed these features to differentiate across the independent variables of the study-age-schooling level, and SES background, and text genre (narrative vs. expository). In terms of genre, expository-type essays usually had denser and more lexically diverse texture than stories. In developmental perspective, lexical diagnostics improved in the texts produced by 13–14 year-olds in comparison with those of 9–10 year-olds. Finally, texts produced by middle-class children attending well-established schools were in general of better lexical quality than those produced by children from disadvantaged backgrounds attending low-achieving schools. Keywords:linguistic usage; school-age language development; SES background; discourse genre; clause length; text length, lexical quality; Hebrew

Finite-size scaling in randomK-satisfiability problems

We provide a comprehensive view of various phase transitions in random K-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically important and practically useful in analyzing finite systems. Using the FSS theory of nonequilibrium absorbing phase transitions, we show that the density of unsatisfied clauses clearly indicates the transition from the solvable (absorbing) phase to the unsolvable (active) phase as varying the noise parameter and the density of constraints. Based on the solution clustering (percolation-type) argument, we conjecture two possible values of the FSS exponent, which are confirmed reasonably well in numerical simulations for 2 ≤ K ≤ 3.

'과학동아' 지구과학 기사의 언어적 특성으로 본 과학 잡지의 과학 대중화 기제

과학 잡지가 과학자와 일반인 사이의 접점 역할을 수행하며 과학의 대중화에 기여할 수 있게 해 주는 기제를 과학 잡지 텍스트의 언어적 특성에서 찾기 위하여 과학 동아에 수록된 지구과학 관련 기사 12편을 선정하였다. 선정된 과학 잡지 텍스트의 언어적 특성을 규명하기 위하여 레지스터 분석을 실시하였다. 연구 결과, 1) 기자가 쓴 글은 과학자의 사유와 대화를 표현하는 인식적 술어와 발화적 술어의 비율이 높았다. 2) 기자의 글에는 문장의 주체가 사람으로 드러나는 비율이 높지만 과학자의 글에는 사람은 거의 드러나지 않으며 주체가 생략된 경우도 많았다. 3) 과학자의 글은 대부분 평서형 서법을 사용하지만, 기자가 쓴 글에서는 의문형과 청유형 서법, 생략 등의 비평서형 문장이 많았다. 4) 문장 속에 포함된 절의 밀도는 기자의 글이나 과학자의 글 모두 비슷하였다. 5) 정보의 구조 또한, 기자의 글은 단순한 정보의 발전 형태를 띠었고, 과학자의 글은 그에 비해 다소 복잡한 정보 구조를 나타내었다. 과학 잡지 텍스트의 언어적 특징을 통해 과학 잡지는 기자의 글을 통해 어려운 과학 내용을 쉽고 친숙한 텍스트로 제시함으로써 과학의 대중화에 기여할 뿐 아니라, 과학자가 쓴 순화된 과학 텍스트를 통해 일반인들을 과학의 언어라는 과학의 문화에 친숙하게 함으로써 과학의 대중화에 기여하게 됨을 밝혀 내었다. The purpose of this study was to investigate how a science magazine played a role in filling the gap between scientists and the general public, and how it contributed to science popularization. We analyzed the linguistic features of the texts used in a science magazine. We used 12 articles (six written by journalists, and six written by scientists) from the Science Donga. Register analysis was conducted in order to define the linguistic features of the texts in terms of ideational meaning, interpersonal meaning and, textual meaning. Results of this study are as follows: (1) the articles written by journalists used a higher mental and verbal processes in which the conversations and thoughts of scientists were expressed. (2) Human agents were relatively explicit in the journalists' articles. However, they were implicit or omitted in the articles of scientists. (3) Interrogative sentences and inclusive imperative sentences, and even omissions were frequently found in the journalists' articles whereas scientists' articles mainly used declarative statements. (4) The clause density of journalist' articles and scientists' were similarly lower than that of science textbooks. (5) The information structure revealed by the patterns of Theme and Rheme that the journalists' articles used in science magazines was simpler than that of science textbooks, while the structure of scientists' articles was more complex than that of journalists'. Based on the linguistic features of the texts used in science magazines, we found that a science magazine contributes to science popularization in two faces: One is in that the articles of journalists present science contents in a way that the readers can follow with ease and feel well-acquainted. The other is that the modified articles of scientists help the general public get familiar with the culuture of science in terms of use of science language.

Random quantum satisfiability

Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA$_1$-complete quantum satisfiability (QSAT) problem introduced by Bravyi \cite{Bravyi:2006p4315}. QSAT appropriately generalizes the NP-complete classical satisfiability (SAT) problem. We show that, as the density of clauses/projectors is varied, the ensembles exhibit quantum phase transitions between phases that are satisfiable and unsatisfiable. Remarkably, almost all instances of QSAT for \emph{any} hypergraph exhibit the same dimension of the satisfying manifold. This establishes the QSAT decision problem as equivalent to a, potentially new, graph theoretic problem and that the hardest typical instances are likely to be localized in a bounded range of clause density.

A comparison of the linguistic and interactional features of language learning websites and textbooks1

Self-study is playing an increasingly important role in the learning and instruction of many subjects, including second and foreign languages. With the rapid development of the internet, language websites for self-study are flourishing. While the language of print-based teaching materials has received some attention, the linguistic and interactional features of websites are largely ignored by educationists, and online learning materials are regarded as simply duplicates of their print-based counterparts. This is far from satisfactory because web-based and print-based materials are very different tools with which participants negotiate their learning activities. This paper examines the linguistic and interactional features of English learning websites in terms of (1) their lexical density/clause length; (2) referential cohesion, particularly the use of personal pronouns; and (3) the presence of involvement strategies and other interactional features. These features are compared with those in textbooks to examine how websites deviate from traditional instructional texts. It is found that both clause and lexical density are greater on websites than in traditional textbooks. Websites make more use of the personal pronouns ‘I’ and ‘you’, whereas textbooks make more use of the authoritative ‘we’. Websites are also more interactional in terms of their use of involvement strategies, imperative structures and modals. These findings highlight the different contexts of textbooks and websites, particularly the different nature of the two channels and their credibility as information sources. This has practical implications for the design of appropriate online instructional resources.

Pairs of SAT-assignments in random Boolean formulæ

We investigate geometrical properties of the random K -satisfiability problem using the notion of x -satisfiability: a formula is x -satisfiable is there exist two SAT-assignments differing in N x variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K , we prove that there exists a region of clause density, below the satisfiability threshold, where the landscape of Hamming distances between SAT-assignments experiences a gap: pairs of SAT-assignments exist at small x , and around x = 1 2 , but they do not exist at intermediate values of x . This result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis (the cavity method), and its algorithmic counterpart (the survey propagation algorithm). Our method uses elementary probabilistic arguments (first and second moment methods), and might be useful in other problems of computational and physical interest where similar phenomena appear.

Random 2-SAT with Prescribed Literal Degrees

Two classic "phase transitions" in discrete mathematics are the emergence of a giant component in a random graph as the density of edges increases, and the transition of a random 2-SAT formula from satisfiable to unsatisfiable as the density of clauses increases. The random-graph result has been extended to the case of prescribed degree sequences, where the almost-sure nonexistence or existence of a giant component is related to a simple property of the degree sequence. We similarly extend the satisfiability result, by relating the almost-sure satisfiability or unsatisfiability of a random 2-SAT formula to an analogous property of its prescribed literal-degree sequence. The extension has proved useful in analyzing literal-degree-based algorithms for (uniform) random 3-SAT.

Linear Upper Bounds for Random Walk on Small Density Random 3‐CNFs

We analyze the efficiency of the random walk algorithm on random $3$-CNF instances and prove linear upper bounds on the running time of this algorithm for small clause density, less than $1.63$. This is the first subexponential upper bound on the running time of a local improvement algorithm on random instances. Our proof introduces a simple, yet powerful tool for analyzing such algorithms, which may be of further use. This object, called a terminator, is a weighted satisfying assignment. We show that any CNF having a good (small weight) terminator is assured to be solved quickly by the random walk algorithm. This raises the natural question of the terminator threshold which is the maximal clause density for which such assignments exist (with high probability). We use the analysis of the pure literal heuristic presented by Broder, Frieze, and Upfal [Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, 1993, pp. 322-330] and Luby, Mitzenmacher, and Shokrollahi [Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, pp. 364-373] and show that for small clause densities good terminators exist. Thus we show that the pure literal threshold ($\approx$1.63) is a lower bound on the terminator threshold. (We conjecture the terminator threshold to be in fact higher.) One nice property of terminators is that they can be found efficiently via linear programming. This makes tractable the future investigation of the terminator threshold and also provides an efficiently computable certificate for short running time of the simple random walk heuristic.

Why almost all satisfiable $k$-CNF formulas are easy

Finding a satisfying assignment for a $k$-CNF formula $(k \geq 3)$, assuming such exists, is a notoriously hard problem. In this work we consider the uniform distribution over satisfiable $k$-CNF formulas with a linear number of clauses (clause-variable ratio greater than some constant). We rigorously analyze the structure of the space of satisfying assignments of a random formula in that distribution, showing that basically all satisfying assignments are clustered in one cluster, and agree on all but a small, though linear, number of variables. This observation enables us to describe a polynomial time algorithm that finds $\textit{whp}$ a satisfying assignment for such formulas, thus asserting that most satisfiable $k$-CNF formulas are easy (whenever the clause-variable ratio is greater than some constant). This should be contrasted with the setting of very sparse $k$-CNF formulas (which are satisfiable $\textit{whp}$), where experimental results show some regime of clause density to be difficult for many SAT heuristics. One explanation for this phenomena, backed up by partially non-rigorous analytical tools from statistical physics, is the complicated clustering of the solution space at that regime, unlike the more "regular" structure that denser formulas possess. Thus in some sense, our result rigorously supports this explanation.

The Resolution Complexity of Random Constraint Satisfaction Problems

We consider random instances of constraint satisfaction problems where each variable has domain size d and each constraint contains t restrictions on k variables. For each $(d,k,t)$ we determine whether the resolution complexity is a.s. constant, polynomial, or exponential in the number of variables. For a particular range of $(d,k,t)$, we determine a sharp threshold for resolution complexity where the resolution complexity drops from a.s. exponential to a.s. polynomial when the clause density passes a specific value.

Space complexity of random formulae in resolution

AbstractWe study the space complexity of refuting unsatisfiable random k‐CNFs in the Resolution proof system. We prove that for Δ ≥ 1 and any ϵ > 0, with high probability a random k‐CNF over n variables and Δn clauses requires resolution clause space of Ω(n/Δ1+ϵ). For constant Δ, this gives us linear, optimal, lower bounds on the clause space. One consequence of this lower bound is the first lower bound for size of treelike resolution refutations of random 3‐CNFs with clause density Δ ≫ n. This bound is nearly tight. Specifically, we show that with high probability, a random 3‐CNF with Δn clauses requires treelike refutation size of exp(Ω(n/Δ1+ϵ)), for any ϵ > 0. Our space lower bound is the consequence of three main contributions: (1) We introduce a 2‐player Matching Game on bipartite graphs G to prove that there are no perfect matchings in G. (2) We reduce lower bounds for the clause space of a formula F in Resolution to lower bounds for the complexity of the game played on the bipartite graph G(F) associated with F. (3) We prove that the complexity of the game is large whenever G is an expander graph. Finally, a simple probabilistic analysis shows that for a random formula F, with high probability G(F) is an expander. We also extend our result to the case of G‐PHP, a generalization of the Pigeonhole principle based on bipartite graphs G. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 92–109, 2003

Measures of Syntax in School-Age Children and Adolescents

Syntactic measures developed for preschool children are insensitive to later-developing forms produced by older children. Information concerning syntax in school-age children and adolescents is available but has not yet emerged as a set of measures widely used by speech-language pathologists. This article identifies several sources of information about syntax from language samples (spoken and written) and from standardized language tests. Language samples yield information on sentence length, clause density, and use of higher level, discourse-motivated structures. Syntactic subtests from three standardized language tests for school-age children and adolescents are analyzed in order to determine structural content and processing format.