Pure Grammar Research Articles

Decidability Questions for Insertion Systems and Related Models

Insertion systems or insertion grammars are a generative formalism in which words can only be generated by starting with some axioms and by iteratively inserting strings subject to certain contexts of a fixed maximal length. It is known that languages generated by such systems are always context sensitive and that the corresponding language classes are incomparable with the regular languages. On the other hand, it is possible to generate non-semilinear languages with systems having contexts of length two. Here, we study decidability questions for insertion systems. On the one hand, it can be seen that emptiness and universality are decidable. Moreover, the fixed membership problem is solvable in deterministic polynomial time. On the other hand, the usually studied decidability questions such as, for example, finiteness, inclusion, equivalence, regularity, inclusion in a regular language, and inclusion of a regular language turn out to be undecidable. Interestingly, the latter undecidability results can be carried over to other models which are basically able to handle the mechanism of inserting strings depending on contexts. In particular, new undecidability results are obtained for pure grammars, restarting automata, clearing restarting automata, and forgetting automata.

Learning metamorphic malware signatures from samples

Metamorphic malware are self-modifying programs which apply semantic preserving transformations to their own code in order to foil detection systems based on signature matching. Metamorphism impacts both software security and code protection technologies: it is used by malware writers to evade detection systems based on pattern matching and by software developers for preventing malicious host attacks through software diversification. In this paper, we consider the problem of automatically extracting metamorphic signatures from the analysis of metamorphic malware variants. We define a metamorphic signature as an abstract program representation that ideally captures all the possible code variants that might be generated during the execution of a metamorphic program. For this purpose, we developed MetaSign: a tool that takes as input a collection of metamorphic code variants and produces, as output, a set of transformation rules that could have been used to generate the considered metamorphic variants. MetaSign starts from a control flow graph representation of the input variants and agglomerates them into an automaton which approximates the considered code variants. The upper approximation process is based on the concept of widening automata, while the semantic preserving transformation rules, used by the metamorphic program, can be viewed as rewriting rules and modeled as grammar productions. In this setting, the grammar recognizes the language of code variants, while the production rules model the metamorphic transformations. In particular, we formalize the language of code variants in terms of pure context-free grammars, which are similar to context-free grammars with no terminal symbols. After the widening process, we create a positive set of samples from which we extract the productions of the grammar by applying a learning grammar technique. This allows us to learn the transformation rules used by the metamorphic engine to generate the considered code variants. We validate the results of MetaSign on some case studies.

What Is the Sense in Logic and Philosophy of Language

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions.

Expressiveness and complexity of regular pure two-dimensional context-free languages

Picture languages generalize classical string languages to two-dimensional arrays. Several approaches have been proposed during the years; consequently, a general classification and a detailed comparison of the proposed classes turn to be necessary. In this paper, we study some closure properties of (regularly controlled) pure two-dimensional context-free grammars, for which we also prove that the parsing is NP-hard. Moreover, we draw some comparisons with other interesting picture grammars like (regional) tile grammars, Pruša grammars and local languages, clarifying, in some cases, their mutual relationship with respect to expressiveness.

Controlled Pure Grammar Systems

This paper discusses grammar systems that have only terminals, work in the leftmost way, and generate their languages under the regulation by control lan- guages over rule labels. It establishes three results concerning their generative power. First, without any control languages, these systems are not even able to generate all context-free languages. Second, with regular control languages, these systems, hav- ing no more than two components, characterize the family of recursively enumerable languages. Finally, with control languages that are themselves generated by regular- controlled context-free grammars, these systems over unary alphabets generate nothing but regular languages. In its introductory section, the paper gives a motivation for in- troducing these systems, and in the concluding section, it formulates several open problems.

POSITIONED AGENTS IN ECO-GRAMMAR SYSTEMS

Positioned eco-grammar systems (PEG systems, for short) were introduced in [9]. Motivation of introducing positioned eco-grammar systems is an attempt to describe interplay between evolving environment and community of agents living in this environment whereas we focus on the positions of agents in the environment. PEG systems bring a new view to investigating interplay between community of agents and environment. Our approach allows to study local changes in evolving environment caused by agents moreover the position of the agent is strictly given by special symbol and we are able to predict its behavior and control the evolution of environment as well. In this paper we compare generative power of the PEG systems with three types of pure (regulated) grammars.

Romanticism & The Rise of English by Andrew Elfenbein, and: Language and Revolution in Burke, Wollstonecraft, Paine, and Godwin by Jane Hodson

Andrew Elfenbein. Romanticism & The Rise of English. Stanford: Stanford University Press, 2009. Pp. 278. $55.00 cloth/$21.95 paper. Jane Hodson. Language and Revolution in Burke, Wollstonecraft, Paine, and Godwin. Aldershot, UK and Burlington, VT: Ashgate Press, 2007. Pp. 226. $99.95. Both Elfenbein's and Hodson's books invite at least four questions on the views of grammarians during the decades of Romanticism and on practices of contemporary dramatists, essayists, novelists, and poets. (1) What evidence supports an argument that the grammarians' views enjoyed some influence among them? (2) As for readers of literature and periodicals in decades, how fully did they accept the teachings on pure advanced by grammarians such as Hugh Blair and James Beattie? (3) How influential was pure English on critical reviews, both in contemporary literature and discursive texts? (4) Lastly, quite apart from clear responses to rules recommended by grammarians, do the works that Elfenbein and Hodson examine give credence in themselves to influences attributable to pure English? Taken together, these questions on uses of pure grammar in the Romantic period also prompt an engagement with the structures and methods of Elfenbein's and Hodson's works in historical criticism. To begin with the structure of each book, Hodson proposes to consider as one pervasive theme the functions of grammar in political discourse, mainly in the 1790s. Her initial chapter--The Language of Politics and the Politics of Language'--resourcefully introduces discursive responses to the French Revolution as texts enough for sufficient analysis. The analysis proposed offers to explore diverse attitudes representatively manifest in Romantic responses to Burke, Wollstonecraft, Paine, and Godwin's discourses but also to contemporary grammarians and their works. Her second chapter, as groundwork for the study of discourses on the French Revolution, surveys fifty grammars, their analyses not all alike, published in the late eighteenth century. This survey reveals that despite a desire for an inherently correct English, the grammarians' arguments on such topics as syntax, diction, and public speaking brought the Romantic decades no unanimity. Chapters Three through Six examine in order Hodson's four chosen discourses on the revolution in France. Her method in each chapter is consistent. Chapter Three has several subtopics under which to appreciate Burke's Reflections on the Revolution in France: (1) modern criticism, (2) contemporary reviews, (3) his other writings, (4) his linguistic practices, (5) his concepts of language. Chapters Four through Six contain these subtopics, each also including, respectively, some comparison of Wollstonecraft, Paine, and Godwin's linguistic practices to Burke's as well as their commentaries on his Reflections. For the political writing of Wollstonecraft, Hodson chooses A Vindication of the Rights of Men; for Paine, Rights of Man; for Godwin, Enquiry Concerning Political Justice. This consistent structure in the chapters offering exposition on discourse presents a methodological possibility for recovering patterns of grammar and politics in the historical context of the Romantic period. The structure of Elfenbein's book supports an argument that philological procedures, valuable for analyses of Romantic literature, ought to spur new thinking in graduate studies on literary English. The book's introduction recounts the lapse of philological methods from graduate study, outlines their value in appreciating Romantic literature, and provides a conspectus of the chapters to follow. Chapter 1, Purifying English, explores the Romantic project for establishing prescriptive rules in order to enhance the opportunity for common ground between authors and readers. This project set barriers, however, between those who did and did not use the prestige language and willy-nilly diminished in English an earthiness associated with primitive speech (14). …

Can the APT be a theory of Multiple Grammars and a minimal theory of parsing?

This essay by Truscott and Sharwood-Smith is a valiant attempt with a laudable goal. It seeks to show how different perspectives and disciplines can capture what is happening in acquisition and notably in L2 acquisition. Nonetheless, I think that the results are much closer to an elaborated grammatical theory than an elaborated processing theory (thus it seems less important to me than to the authors to choose one label over the other). Their essential, sensible idea is that where different grammars provide independent analyses of constructions, both are computed (even where the lexical items belong to only one grammar). Therefore conflict is experienced which produces computational demands. However this is pure grammar – just a more sophisticated situation where, as I like to argue, the L2 person has Multiple Grammars (Roeper, 1999), creating more computational work as well. In this respect, the situation is no different from L1 acquisition, where the course of acquisition involves generation and maintenance of multiple grammars, some of which are shed and some retained in the Final State.

Pure Logical Grammar: Anticipatory Categoriality and Articulated Categoriality

In reworking his Logical Investigations Husserl adopts two positions that were not actually incorporated into later editions of the Investigations but do appear in other writings: (1) a new distinction between signitive and significative intentions, and (2) the claim that even naming and perceiving acts are categorially formed. This paper investigates Husserl's notion of noematic sense and the pure grammatical 'categories' intimated therein in order to shed light on these new positions. The paper argues that the development of the theories of the noema and of pure grammar allows us to recognize how even merely perceived or named things have a certain categoriality belonging to them, but that this development also requires us to distinguish between an anticipatory categoriality and an articulated categoriality.

Limits of Pure Grammars with Monotone Productions

The grammatical inference problem is solved for a class of languages which can be generated by pure grammars with non-shortening productions. Necessary and sufficient condition for determination whether a language belongs to this class is formulated and proved. Finally, an algorithm for assigning a pure grammar to any language from the class is described.

Pregrammars Versus Submonoids

Prelanguages and pregrammars introduced in [8] present a generalization of languages and pure grammars. Relation of domination and double domination may be easily transferred from languages to prelanguages. In the present paper submonoids of a commutative monoid are characterized by means of their relations of domination; subgroups of a commutative group are characterized by means of their relations of double domination. The submonoid generated by a subset of a commutative monoid is constructed using a suitable pregrammar.

Reduction of Pregrammars

In [13] pure generalized grammars were studied, in particular, the problem of reducing a pure generalized grammar to a pure grammar. These results are transferred to the so called pregrammars in the present paper. The obtained results may be applied not only to pure generalized grammars but also to other structures.

Pattern Ambiguities for Pure Context—Free Grammars

We consider here some special forms of ambiguity for pure context-free grammars, namely pattern avoiding ambiguity, pattern preserving ambiguity, pattern ambiguity, and grammar avoiding ambiguity. The first two properties are undecidable for arbitrary pure context-free grammars, and in a particular but general enough case we can effectively decide whether or not a pure context-free grammar is pattern preserving ambiguous.

On Peirce’s Pure Grammar as a general theory of cognition: From the thought-sign of 1868 to the semeiotic theory of assertion

L'A. montre que l'articulation de la theorie de la pensee-signe avec le pragmatisme et la semeiotique permet de developper une idee de Peirce du debut des annees 1900. Cette idee est que la theorie de l'assertion dans la Grammaire Pure peut etre consideree comme une theorie non psychologique de la cognition. En outre, il montre que le parallele fait entre la theorie du signe et la theorie de la cognition dans la Grammaire Pure doit etre aussi interprete au-dela du contexte philosophique et psychologique. Il considere ainsi que la semeiotique decrit la vraie structure d'une theorie generale des processus cognitifs et des processus d'acquisition des connaissances, en ce qui concerne les intelligences scientifiques

On Pure Context-Free Languages and Left Szilard Languages

It is shown that left Szilard languages of context-free grammars are pure context-free languages. This is one of the few exceptions among the numerous negative results concerning the generative capacity of pure languages. Moreover, we characterize pure context-free languages and left Szilard languages of pure context-free grammars as certain homomorphic images.

On form-equivalence of deterministic pure grammar forms

Pure grammars are grammars without non-terminals. In this paper we show as one main result that any two acyclic deterministic pure (dP) grammars that generate the same finite language are isomorphic. Furthermore, the notion of a pure grammar form is investigated. As the second main result we show that the form-equivalence problem for dP grammar forms is decidable.

Pure grammars and pure languages†

The notion of “pure grammar” is introduced as a semi-Thue system with no non-terminals. The basic properties of pure grammars and the “pure languages” that they generate are investigated. Other topics introduced are “definite Turing machines” that accept pure languages, pure parallel languages, pure relations and pure Post canonical systems.

Pure grammars

This paper investigates generative grammars with only one type of symbol: no distinction is made between terminals and nonterminals. This means that all intermediate words in a derivation are necessarily in the language generated and, consequently, such languages differ considerably from languages generated by grammars, where nonterminals can be used to exclude words from the language. We investigate in this paper basic question concerning language hierarchies, ambiguity and decidability. Also some more general models of pure grammars will be considered.