One-sided random context grammars

The notion of a one-sided random context grammar is defined as a context-free-based regulated grammar, in which a set of permitting symbols and a set of forbidding symbols are attached to every rule, and its set of rules is divided into the set of left random context rules and the set of right random context rules. A left random context rule can rewrite a nonterminal if each of its permitting symbols occurs to the left of the rewritten symbol in the current sentential form while each of its forbidding symbols does not occur there. A right random context rule is applied analogically except that the symbols are examined to the right of the rewritten symbol. The paper demonstrates that without erasing rules, one-sided random context grammars characterize the family of context-sensitive languages, and with erasing rules, these grammars characterize the family of recursively enumerable languages. In fact, these characterization results hold even if the set of left random context rules coincides with the set of right random context rules. Several special cases of these grammars are considered, and their generative power is established. In its conclusion, some important open problems are suggested to study in the future.     

Rewriting systems with limited distance permitting context

By restricting the permitting context symbols in a rewriting system to be within a specified distance from the symbol to be replaced, we strictly increase the generative power above that of rewriting systems where the context symbols can appear within arbitrary distances from the symbol to be replaced.     

One-sided forbidding grammars and selective substitution grammars

In one-sided forbidding grammars, the set of rules is divided into the set of left forbidding rules and the set of right forbidding rules. A left forbidding rule can rewrite a non-terminal if each of its forbidding symbols is absent to the left of the rewritten symbol in the current sentential form, while a right forbidding rule is applied analogically except that this absence is verified to the right. Apart from this, they work like ordinary forbidding grammars. As its main result, this paper proves that one-sided forbidding grammars are equivalent to selective substitution grammars. This equivalence is established in terms of grammars with and without erasing rules. Furthermore, this paper proves that one-sided forbidding grammars in which the set of left forbidding rules coincides with the set of right forbidding rules characterize the family of context-free languages. In the conclusion, the significance of the achieved results is discussed.     

A pumping lemma for random permitting context languages

Random context grammars belong to the class of context-free grammars with regulated rewriting. Their productions depend on context that may be randomly distributed in a sentential form. Context is classified as either permitting or forbidding, where permitting context enables the application of a production and forbidding context inhibits it. For random context languages of finite index a generalization of the well-known pumping lemma for context-free languages has been proven. We drop the finite index restriction and concentrate on non-erasing grammars that use permitting context only. We prove a pumping lemma for their languages that generalizes and refines the existing one, and show that these grammars are strictly weaker than the non-erasing random context grammars.     

Rewriting systems with a clocking mechanism

A new type of rewriting system is introduced in which every string in a derivation is preceded by one (clocking) symbol which must be rewritten at every moment of time, (hence in a parallel mode). The rest of the string is rewritten in a sequential mode, (i.e., one symbol at every moment of time). The communication from the clocking symbol to the rest of the string, and vice versa, is achieved by incorporating various types of context conditions in every production.     

On restricted context-free grammars

Context-free grammars are widely used for the simple form of their rules. A derivation step consists of the choice of a nonterminal of the sentential form and of an application of a rule rewriting it. Several regulations of the derivation process have been studied to increase the power of context-free grammars. In the resulting grammars, however, not only the symbols to be rewritten are restricted, but also the rules to be applied. In this paper, we study context-free grammars with a simpler restriction where only symbols to be rewritten are restricted, not the rules, in the sense that any rule rewriting the chosen nonterminal can be applied. We prove that these grammars have the same power as random context, matrix, or programmed grammars. We also present two improved normal forms and discuss the characterization of context-sensitive languages by a variant using strings of length at most two instead of symbols.     

Generalized one-sided forbidding grammars

In generalized one-sided forbidding grammars (GOFGs), each context-free rule has associated a finite set of forbidding strings, and the set of rules is divided into the sets of left and right forbidding rules. A left forbidding rule can rewrite a nonterminal if each of its forbidding strings is absent to the left of the rewritten symbol. A right forbidding rule is applied analogically. Apart from this, they work like any generalized forbidding grammar. This paper proves the following three results. (1) GOFGs where each forbidding string consists of at most two symbols characterize the family of recursively enumerable languages. (2) GOFGs where the rules in one of the two sets of rules contain only ordinary context-free rules without any forbidding strings characterize the family of context-free languages. (3) GOFGs with the set of left forbidding rules coinciding with the set of right forbidding rules characterize the family of context-free languages.     

Some notes on ETOL-languages

In this paper we investigate the effect of adding some regulated rewriting properties to ETOL-systems.

It follows that if we specify the order in which the tables of an ETOL-system must be applied, or if we add a forbidding context to the tables of the system, the generating power of the system is not increased. If a permitting context is added to the tables, then the resulting class of languages generated, coincides with a subclass of the class of context-free programmed languages.     

Reducibility of operation symbols in term rewriting systems and its application to behavioral specifications

In this paper, we propose the notion of reducibility of symbols in term rewriting systems (TRSs). For a given algebraic specification, operation symbols can be classified on the basis of their denotations: the operation symbols for functions and those for constructors. In a model, each term constructed by using only constructors should denote an element, and functions are defined on sets formed by these elements. A term rewriting system provides operational semantics to an algebraic specification. Given a TRS, a term is called reducible if some rewrite rule can be applied to it. An irreducible term can be regarded as an answer in a sense. In this paper, we define the reducibility of operation symbols as follows: an operation symbol is reducible if any term containing the operation symbol is reducible. Non-trivial properties of context-sensitive rewriting, which is a simple restriction of rewriting, can be obtained by restricting the terms on the basis of variable occurrences, its sort, etc. We confirm the usefulness of the reducibility of operation symbols by applying them to behavioral specifications for proving the behavioral coherence property.     

Left-forbidding cooperating distributed grammar systems

A left-forbidding grammar, introduced in this paper, is a context-free grammar, where a set of nonterminal symbols is attached to each context-free production. Such a production can rewrite a nonterminal provided that no symbol from the attached set occurs to the left of the rewritten nonterminal in the current sentential form. The present paper discusses cooperating distributed grammar systems with left-forbidding grammars as components and gives some new characterizations of language families of the Chomsky hierarchy. In addition, it also proves that twelve nonterminals are enough for cooperating distributed grammar systems working in the terminal derivation mode with two left-forbidding components (including erasing productions) to characterize the family of recursively enumerable languages.     

Prescribed teams of grammars

We consider sets of grammars (calledteams) which process strings by cooperating together; a single derivation step in a team is done in such a way that each grammar in the set rewrites a symbol in the string. A cooperating grammar system with prescribed teams (CPT) consists of a finite number of teams. In a maximal rewriting mode, a team in a CPT can take a string for rewriting whenever it can make a derivation step on it; it keeps it and rewrites as long as it can, and once a string is obtained that cannot be rewritten by the team anymore it is returned and becomes available to all other teams.In this paper we investigate the power of CPT in the maximal and other rewriting modes. We establish the relationships of CPT with other models of grammars cooperating together and with various kinds of controlled grammars. We also solve some open problems from [6] and provide alternative proofs for some results from [6].The authors are indebted to Basic Research ASMICS II Working Group for supoort; the work of the first author has been also supported by the Alexander von Humboldt Foundation     

Simple restriction in context-free rewriting

Many rewriting systems with context-free productions and with controlled derivations have been studied. On one hand, these systems preserve the simplicity of applications of context-free productions and, on the other hand, they increase the generative power to cover more aspects of natural and programming languages. However, with λ-productions, many of these systems are computationally complete. It gives rise to a natural question of what are the simplest restrictions of the derivation process of context-free grammars to obtain the universal power. In this paper, we present such a simple restriction introducing so-called restricted context-free rewriting systems. These systems are context-free grammars with a function assigning a nonterminal coupled with + or − to each nonterminal. A production is applicable if it is applicable as a context-free production and if the symbol assigned to the left-hand side of the production is coupled with +, then this symbol has to appear in the sentential form, while if coupled with −, it must not appear in the sentential form. This restriction is simpler than most of the other restrictions, since the context conditions are assigned to nonterminals, not to productions, and their type is the simplest possible – a nonterminal.     

Evaluation properties of invariant polynomials

A polynomial invariant under the action of a finite group can be rewritten using generators of the invariant ring. We investigate the complexity aspects of this rewriting process; we show that evaluation techniques enable one to reach a polynomial cost.     

Visual discrimination on colour VDTs at two viewing distances

The paper describes a research study on visual discrimination of textual and graphic symbols on a visual display terminal (VDT) screen when viewed at eye-lo-screen distances of 61 cm and 152 cm (24 and 60 ins). Conducted as part of a development programme at McDonnell Douglas Corporation's St. Louis Aircraft Company for an Integrated Manufacturing Composites Centre (ICC), the study investigated symbol shapes, symbol sizes, symbol colours and background colours at the two viewing distances. The longer distance is representative of required placements of the VDTs at some manufacturing workstations to avoid interference with process or control equipment. Knowledge gained from the study was incorporated in the selection of the manufacturing computer information system (CIS) terminals.

All four treatments showed significant effects on visual discrimination at both viewing distances and, particularly at the 152 cm distance, the mix of symbol and background colours was highly significant. A black screen background colour with more luminous symbols such as orange, green, yellow provided much better visual discrimination at the extended viewing distance than less luminous symbols such as red and blue on a white background. Visual discrimination at the extended viewing distance, when compared with the shorter viewing distance and using symbols of equal size, was better than the loss in visual angle would suggest.

Sex and age (to age 65) did not significantly affect visual discrimination mean scores, but the variance among individuals in the 51-65 years age group was greater than for the younger age groups.

The visual discrimination scores for symbol sizes of 4 mm² were not significantly different from the 6 mm² symbols at the 61 cm viewing distance. The 4 mm² symbol size was therefore adequate for visual discrimination of standalone symbols at this distance. Although 8 mm symbols were not used in this study, projections from the data indicate that such symbol sizes at 152 cm would provide comparable discrimination scores to the 4 mm² at 61 cm.

Improved visual discrimination of standalone symbols occurs with gaps or changes in the angles of symbols, such as sets 'C' versus 'O' and 'Xl' versus'+'.     

Rotation invariant hand-drawn symbol recognition based on a dynamic time warping model

One of the major difficulties of handwriting symbol recognition is the high variability among symbols because of the different writer styles. In this paper, we introduce a robust approach for describing and recognizing hand-drawn symbols tolerant to these writer style differences. This method, which is invariant to scale and rotation, is based on the dynamic time warping (DTW) algorithm. The symbols are described by vector sequences, a variation of the DTW distance is used for computing the matching distance, and K-Nearest Neighbor is used to classify them. Our approach has been evaluated in two benchmarking scenarios consisting of hand-drawn symbols. Compared with state-of-the-art methods for symbol recognition, our method shows higher tolerance to the irregular deformations induced by hand-drawn strokes.     

Hierarchical Nominal Terms and Their Theory of Rewriting

Nominal rewriting introduced a novel method of specifying rewriting on syntax-with-binding. We extend this treatment of rewriting with hierarchy of variables representing increasingly 'meta-level' variables, e.g. in hierarchical nominal term rewriting the meta-level unknowns (representing unknown terms) in a rewrite rule can be 'folded into' the syntax itself (and rewritten). To the extent that rewriting is a mathematical meta-framework for logic and computation, and nominal rewriting is a framework with native support for binders, hierarchical nominal term rewriting is a meta-to-the-omega level framework for logic and computation with binders.     

Context-free like restrictions on selective rewriting

Selective substitution grammars based on ‘context-free’ productions form a possible framework for the study of ‘grammatically oriented’ formal language theory. Such grammars (with no control governing the composition of derivation steps) are studied in this paper. In particular we study the effect of various conditions on selectors (which define the way that rewriting is performed); those conditions are aimed to formalize the notion of ‘using information about the context’ during the rewriting process. Each of them captures a particular feature of a rewriting according to a context-free grammar or an EOS system (essentially a context-free grammar that can also rewrite terminal symbols). Some of those conditions yield characterizations of the class of context-free languages for other conditions the lower and upper bound on the language generating power are given. Also a natural notion of a class of ‘simple’ rewriting systems is introduced (pattern grammars) and it is demonstrated that they possess surprisingly high language generating power.     

Multi grammars

The theory of selective substitution grammars is an attempt to provide a common framework for a number of seemingly different rewriting systems. The core of a selective substitution grammar is its selector (language), which prescribes which occurrences of letters in a current sentential form must be rewritten. Three rudimentary forms of selectors, studied until now are sequential, parallel, and continuous selectors. This paper is concerned with building more involved selectors, starting with rudimentary ones and using operations of union and concatenation. The language generating power of several classes of rewriting systems obtained in this way is investigated.     

地形图点状符号的自动提取和识别

针对扫描地形图的点状符号, 提出了一种基于距离变换进行提取和识别的新方法. 首先优化分版图的提取结果, 根据弯曲密度和线划密度过滤掉非点状符号的线划, 利用加壳变换和蜕皮变换进行点状符号的图文分离. 然后根据加权距离函数来度量符号的全局特征, 由骨架线的一致性来度量符号的几何形状特征, 并结合这两个特征来识别点状符号. 最后, 提出了错切文字注记和线状要素注记的识别方法.     

On the power of magic

This paper considers the efficient evaluation of recursive queries expressed using Horn clauses. We define sideways information passing formally and show how a query evaluation algorithm may be defined in terms of sideways information passing and control. We then consider a class of information-passing strategies that suffices to describe most query evaluation algorithms in the database literature, and show that these strategies may always be implemented by rewriting a given program and evaluating the rewritten program bottom-up. We describe in detail several algorithms for rewriting a program. These algorithms generalize the counting and magic-sets algorithms to work with arbitrary programs. Safety and optimality of the algorithms are also considered.