Empty Word Research Articles

The word problem for inverse monoids presented by one idempotent relator

We study inverse monoids presented by a finite set of generators and one relation e = 1, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvable by a polynomial-time algorithm; (2) every congruence class (in the free monoid) with respect to such a presentation is a deterministic context-free language. Such congruence classes can be viewed as generalizations of parenthesis languages; and (3) the word problem is solvable by a linear-time algorithm in the more special case where e is a “positively labeled” idempotent.

Pattern languages with and without erasing

The paper deals with the problems related to finding a pattern common to all words in a given set. We restrict our attention to patterns expressible by the use of variables ranging over words. Two essentially different cases result, depending on whether or not the empty word belongs to the range. We investigate equivalence and inclusion problems, patterns descriptive for a set, as well as some complexity issues. The inclusion problem between two pattern languages turns out to be of fundamental theoretical importance because many problems in the classical combinatorics of words can be reduced to it.

The Möbius function of factor order

Intervals in the factor ordering of a free monoid are investigated. It was shown by Farmer (1982) that such intervals (β, α) are contractible or homotopy spheres in case β is the empty word. We observe here that the same is true in general. This implies that the Möbius function of factor order takes values in {0, + 1, −1}. A recursive rule for this Möbius function is given, which allows efficient computation via the Knuth—Morris—Pratt algorithm. The Möbius function of subword order was studied in Björner (1990). We give here a simpler proof (a parity-changing involution) for its combinatorial interpretation.

La notion de classe moyenne indépendante. Un bilan des travaux

The notion of an independent middle class. A survey of research, François Gresle. Unshakable and learned, the sociologists — followed by the historians ? — deny the middle classes their independent status. What if independence was not an empty word ? If it was necessary to look, far from the statistics, at internalized values and a certain appetite for the quality of life ? A monotonous bibliography reread.

Who's Talking/Who's Talking Back? The Subject of Personal NarrativeTelling Lies in Modern American Autobiography. Timothy Dow AdamsJessie Bernard: The Making of a Feminist. Robert C. BannisterRevealing Lives: Autobiography, Biography, and Gender. Susan Groag Bell , Marilyn YalomSadie Brower Neakok: An Inupiaq Woman. Margaret B. BlackmanBlack Women Writing Autobiography. Joanne M. BraxtonWinged Words: American Indian Writers Speak. Laura ColtelliCrested Kimono: Power

Moving from silence into speech is for the oppressed, the colonized, the exploited, and those who stand and struggle side by side a gesture of defiance that heals, that makes new life and new growth possible. It is that act of speech, of talking back, that is no mere gesture of empty words, that is the expression of our movement from object to subject-the liberated voice. [BELL HOOKS, Talking Back]

Applying rewriting methods to special monoids

A special monoid is a monoid presented by generators and defining relations of the form w = e, where w is a non-empty word on generators and e is the empty word. Groups are special monoids. But there exist special monoids that are not groups. Special monoids have been extensively studied by Adjan[1] and Makanin[7] (see also [2]).

Completing a finite special string-rewriting system on the congruence class of the empty word

Based on a polynomial-time test for determining whether a finite special string-rewriting systemR ise-confluent, a procedure for completing a finite special systemR on[e]R is derived. The correctness and completeness of this procedure are proved. In addition, the special case of finite special string-rewriting systems presenting groups is considered.

Analysis of Children’s Word-Finding Skills in Discourse

This investigation analyzed children's word-finding skills in discourse. The subjects, 16 children with word-finding problems and 16 normal children in Grades 1-6, were matched for sex, age, grade, ethnicity, socioeconomic status, geographic region, and receptive language. Subjects' narratives, produced in response to three pictures and five probes, were tape recorded, transcribed, and analyzed with respect to the following word-finding indices: language productivity and the incidence of word-finding characteristics (repetitions, reformulations, substitutions, delays, empty words, time fillers, and insertions). Group comparisons were made with respect to these indices. Children with word-finding disorders did not differ from normal children in language productivity but manifested significantly more word-finding characteristics in their narratives. These findings are discussed with respect to characteristics and assessment of and intervention for children with word-finding disorders in discourse.

Not Who Is Guilty, But What to Do?!

Education was gravely ill. The whole system—from kindergartens to graduate school. The diagnosis (in the ancient Greek): anachronism. Translated into everyday language: what had been built two thirds of a century ago under one set of conditions, to deal with one set of social tasks, had ceased to be suitable under different conditions, for dealing with completely new tasks. Almost one and a half decades ago people thought they could get by with therapy—"improvement of the system of public education." Ten years later it was discovered that empty words and good intentions do not count as medicine. Almost five years ago it was decided to resort to surgery—"reform." Hardly three years had passed, however, when it was found that the gurney carrying the sick school was spinning its wheels and would never make it to the operating room.

Thue-Morse sequence and p-adic topology for the free monoid

Given two words u and υ, the binomial coefficient ( u υ ) is the number of ways υ appears as a subword (or subsequence) of u. The Thue-Morse sequence is the infinite word t= abbabaab⋯obtained by iteration of the morphism ɽ(a)=ab and ɽ(b)=ba. We show that, for every prime p, and every positive integer n, there exists an integer m= f( p, n), such that, for every non-empty word v of length less than or equal to n, the binomial coefficient ( ɽ⌊ m ⌋ υ) is congruent to 0 mod p. In fact f( p, n)=2 n p 1+⌊ log p n⌋ for p≠2 and f(2, n)=2 k if F k −1 ⩽ n ⩽ F k , where F k denotes the kth Fibonacci number. It follows that, for each prime number p, there exists a sequence of left factors of t of increasing length, the limit of which is the empty word in the p-adic topology of the free monoid.

SOCIALISM WITHOUT LIBERATION: Land Reclamation Projects in Guinea‐Bissau

National liberation, the struggle against colonialism ... will be empty words without significance for the people, unless they are translated into real improvement of the conditions of life. (Amilcar Cabral 1956) Abstract: One of the outstanding aims of most liberation movements has been to increase the economic well-being of their people, Guinea-Bissau being no exception in this respect. How far has the new Nation State succeeded in fulfilling this aim? A comparative analysis of the implementation of land reclamation projects during colonial and post-colonial times reveals astonishing similarities: especially the centralization of development efforts in the hands of administrators disconnected from the grassroots, lack of target group analysis and misconceptions about the aims and needs, as well as the resources, of the population involved in the development efforts, on the part of the administration. The effects of this negative conditioning process of 'development' over many years on the chances of cooperation between peasants and the administration are still largely unknown. Any development planner who wants to encourage the local population to take their future into their own hands, would have to take account of this negative conditioning process.

Rhetorical Constructions: Dialogue and Commitment

In Pedagogy of the Oppressed Paulo Freire introduces the concept of praxis, by which he signifies the two dimensions of authentic discourse, that of reflection and that of action, the process of naming reality and the process of changing reality. Reflection alone, he argues, is insufficient because it is mere verbalism, empty word . . . which cannot denounce the Action alone is similarly inadequate, mere activism, where the energy for choosing exists apart from critical awareness and direction. In true naming always entails transformation because the process of naming renders the world problematic, an object within history, a choice from among possible choices and therefore a limitation to be challenged. At the same time, action, the process of transforming, always entails a new naming because the emergence of reality is only possible through a struggle to articulate. As expression is achieved, it permits the conscious scrutiny that induces occasions and conditions of further transforming. The ultimate motive for any transformation is, according to Freire, the need to be more fully human, the need to participate more completely and more freely in the world. The instrument of transforming is dialogue, where competing representations of reality dynamically challenge each other to compose alternative forms of action. In the absence of dialogue, with the erasure of anyone's word, with the prohibition of critical inquiry, with the maintenance of dominating conditions, however subtly validated as necessity, tradition, or evolution, the possibility of becoming more fully human is curtailed. Erosion of that possibility constitutes the inauthentic discourse-the stagnant reality-of oppression (60 ff.). Freire has applied his concept of praxis with dramatic results to the circumstances of teachers and students in classrooms concerned with literacy, helping the disenfranchised in particular to assert their power to name and transform the world. I want to apply the concept here as well, but as a kind of probe with which to examine some philosophical issues that teaching and thinking about teaching regularly bring to mind: first, the relationship between intellectual argument (reflection) and teaching practice (action); second, the conflict between dialogue (the free, collective examination of choices) and commitment (the decision to act); third, the ideological perversion that attends a privileging of

Increasing Food Production in Sub‐Saharan Africa: Comment

American Journal of Agricultural EconomicsVolume 68, Issue 4 p. 998-999 Comments and Replie Increasing Food Production in Sub-Saharan Africa: Comment Arthur J. Dommen, Arthur J. Dommen Research Section Leader Africa and Middle East Branch, International Economics Division, Economic Research Service, U.S. Department of AgricultureSearch for more papers by this author Arthur J. Dommen, Arthur J. Dommen Research Section Leader Africa and Middle East Branch, International Economics Division, Economic Research Service, U.S. Department of AgricultureSearch for more papers by this author First published: 01 November 1986 https://doi.org/10.2307/1242148Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume68, Issue4November 1986Pages 998-999 RelatedInformation

E-convex infix codes

Two partial orders that play an important role in the combinatorics of words, can be defined in a natural way on the free monoid X* generated by the finite alphabet X: the infix and the embedding orders. A set C of nonempty words is called an infix code (hypercode) over X if C is an antichain with respect to the infix (embedding) order. A set of words is said to be e-convex if it is convex with respect to the embedding order. Two characterizations of the e-convex infix codes are given as well as a sufficient condition for such codes to be finite. It is shown that the family EIC(X) of the e-convex infix codes with the empty word forms, under the operation of concatenation, a free submonoid of the free monoid B(X) of the biprefix codes and that the generating alphabet of EIC(X) is a sub-alphabet of the generating alphabet of B(X).

Density of grammar forms. part I

We give two characterizations for dense intervals consisting of grammatical families. These results are general enough to cover the eases of context-free grammar forms, general grammar forms and synchronized EOL forms. By means of the characterizations it is proved that denseness is undecidable for context-free forms. The characterization theorems also enable us to investigate the maximality of dense intervals. The paper is divided into two parts. The results mentioned above are presented in Part II. This first part contains definitions and preliminary results. Also in Part I, we investigate language families defined by subregular forms and clarify the role of the empty word in form theory.

Language disintegration in dementia: Effects of etiology and severity

The speech characteristics on a standardized picture description task of 26 subjects with presumed senile dementia of the Alzheimer type (SDAT) and 13 subjects with stroke-related dementia (SRD) were compared to 15 normal subjects over age 59 years. Compared to the normal subjects, the dementia subjects used fewer total words, fewer unique words, fewer prepositional phrases, fewer subordinate clauses, and more incomplete sentence fragments. Lexical deficits tended to be more severe than syntactic ones, confirming prior suggestions that lexicon is more vulnerable to disruption in dementia than syntax. Greater dementia severity among the SDAT subjects was associated with marked difficulties in accessing the mental lexicon (increased use of empty words, indefinite anaphora, and pronouns). Greater dementia severity in the SRD subjects was associated with laconic speech that was syntactially less complex. Diffuse brain injury (as typified by SDAT) appears to disproportionately affect lexicon whereas multifocal injury (as typified by SRD) has a disproportionate effect on syntax (assuming that focal lesions of the posterior language zone have been excluded). The speech characteristics of the mild SDAT subjects showed similarities to those of anomic or semantic aphasia whereas the speech of the more advanced SDAT subjects showed similarities to Wernicke aphasia or transcortical sensory aphasia. The speech of the subjects with more severe SRD showed some similarities to Broca aphasia. The most important nonlinguistic deficit in both the SRD and the SDAT groups was a failure to make relevant observations during the picture description task. Perseverations were present in the speech of both the SRD and SDAT subjects, whereas aposiopesis, logorrhea, and palilalia were more typical of the SDAT subjects. Laconic speech was more characteristic of the SRD subjects.

Documents Relating to the Sentimental Agents in the Volyen Empire

From Doris Lessing, winner of the Nobel Prize for Literature, the fifth and final instalment in the visionary novel cycle 'Canopus in Argos: Archives'. 'The Sentimental Agents ...' is set in the declining Volyen Empire as the empires of Sirius and Shammat compete to overwhelm it with rhetoric and false sentiment. The Canopean Empire deploys covert agents to help the Volyens resist. But one of these agents, Incent, succumbs to 'Undulant Rhetoric', and Agent Klorathy must go to Volyen to help him see through the empty words that have beguiled him. Once more employing alien races to identify human failings, Lessing uses social and political satire to show how we misuse speech (and speeches) and delude ourselves with self-aggrandizing notions about the primacy of emotion. Her renowned insight into human behaviour goes hand in hand here with a vein of humour that sees her writing in the tradition of Voltaire and Swift.

On binary equality sets and a solution to the test set conjecture in the binary case

K. Culik II and J. Karhumäki ( RAIRO Inform. Theor. 14 (1980), 349–369] conjectured that the equality set of two injective morphisms over a binary alphabet is of the form { u, v} ∗ for some (possibly empty) words u and v. Here we show that such an equality set is always either of the above form or of the form (uw ∗v) ∗ for some words u, w, and v. As an application we give a simple proof for the Test Set Conjecture in the binary case; cf. K. Culik II and A. Salomaa [ J. Comput. System Sci. 20 (1980), 379–396]. In fact, we show that a test set can always be chosen to contain no more than three words.

On regularity of context-free languages

This paper considers conditions under which a context-free language is regular and conditions which imposed on (productions of) a rewriting system generating a context-free language will guarantee that the generated language is regular. In particular: 1. (1) necessary and sufficient conditions on productions of a unitary grammar are given that guarantee the generated language to be regular (a unitary grammar is a semi-Thue system in which the left-hand of each production is the empty word), and 2. (2) it is proved that commutativity of a linear language implies its regularity. To obtain the former result, we give a generalization of the Myhill–Nerode characterization of the regular languages in terms of well-quasi orders, along with a generalization of Higman's well-quasi order result concerning the subsequence embedding relation on Σ *. In obtaining the latter results, we introduce the class of periodic languages, and demonstrate how they can be used to characterize the commutative regular languages. Here we also utilize the theory of well-quasi orders.

Maximal chains of subwords and up-down sequences of permutations

The free monoid generated by two letters is a poset for the relation “ u is a subword of v .” Two bijections between permutations and maximal chains starting from the empty word, involving the classical up-down sequence and the so-called odd-even height sequence, are given. For arbitrary alphabet, symmetric polynomials in s variables appear, generalizing the Eulerian polynomials and refining polynomials studied by Carlitz, Gessel, Riordan, and Stanley. The skewhook property of Foulkes is extended.