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.     

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.     

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.     

Nonterminal complexity of one-sided random context grammars

In the present paper, we study the nonterminal complexity of one-sided random context grammars. More specifically, we prove that every recursively enumerable language can be generated by a one-sided random context grammar with no more than ten nonterminals. An analogical result holds for thirteen nonterminals in terms of these grammars with the set of left random context rules coinciding with the set of right random context rules. Furthermore, we introduce the notion of a right random context nonterminal, defined as a nonterminal that appears on the left-hand side of a right random context rule. We demonstrate how to convert any one-sided random context grammar G to an equivalent one-sided random context grammar H with two right random context nonterminals. An analogical conversion is given in terms of (1) propagating one-sided random context grammars and (2) left random context nonterminals. In the conclusion, two open problems are stated.     

Rewriting systems with limited distance forbidding context

A random context production has a permitting and forbidding context. A symbol can be rewritten using such a production if all the permitting context symbols and no forbidding context symbol appear in the sentential string. In this paper we limit the effect of forbidding context symbols to be within a certain distance from the symbol to be rewritten. Outside this distance the forbidding context symbols do not influence the rewriting of a symbol. This restriction strictly increases the generating power of the rewriting system.

A further result of this paper is a “negative parallel” version of Penttonen's normal form.     

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.     

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.     

Unrestricted gapping grammars1

Since Colmerauer's introduction of metamorphosis grammars (MGs), with their associated type-O-like grammar rules, there has been a desire to allow more general rule formats in logic grammars. Gap symbols were added to the MG rule by Pereira, resulting in extraposition grammars (XGs). Gaps, which are referenced by gap symbols, are sequences of zero or more unspecified symbols which may be present anywhere in a sentence or in a sentential form. However, XGs imposed restrictions on the position of gap symbols and on the contents of gaps. With the introduction of gapping grammars (GGs) by Dahl, these restrictions were removed but the rule was still required to possess a nonterminal symbol as the first symbol on the left-hand side. This restriction is removed with the introduction of unrestricted gapping grammars. FIGG, a flexible implementation of gapping grammars, possesses a bottom-up parser which can process a large subset of unrestricted gapping grammars. It can be used to examine the usefulness of unrestricted GGs for describing phenomena of natural languages such as free word order and partially free word/constituent order. Unrestricted gapping grammars, as implemented in FIGG, can also be used to describe grammars (or metagrammars) that utilize the gap concept, such as Gazdar's generalized phrase structure grammars.     

Nonterminal complexity of tree controlled grammars

This paper studies the nonterminal complexity of tree controlled grammars. It is proved that the number of nonterminals in tree controlled grammars without erasing rules leads to an infinite hierarchy of families of tree controlled languages, while every recursively enumerable language can be generated by a tree controlled grammar with erasing rules and at most nine nonterminals.     

Syntactic complexity of scattered context grammars

The syntactic complexity of scattered context grammars with respect to the number of nonterminals is investigated. First, the family of the recursively enumerable languages is characterized by some basic operations, such as quotient and coding, over the languages generated by propagating scattered context grammars with four nonterminals. Then, a new method of achieving the characterization of the family of recursively enumerable languages by scattered context grammars is given; in fact, this family is characterized by scattered context grammars with only five nonterminals and a single erasing production. Finally, it is demonstrated that the number of nonterminals can be decreased by one in the present characterizations if scattered context grammars start their derivations from a word rather than a single symbol.     

A graph grammar programming style for recognition of music notation

Graph grammars are a promising tool for solving picture processing problems. However, the application of graph grammars to diagram recognition has been limited to rather simple analysis of local symbol configurations. This paper introduces the Build-Weed-Incorporate programming style for graph grammars and shows its application in determining the meaning of complex diagrams, where the interaction among physically distant symbols is semantically important. Diagram recognition can be divided into two stages: symbol recognition and high-level recognition. Symbol recognition has been studied extensively in the literature. In this work we assume the existence of a symbol recognizer and use a graph grammar to assemble the diagram's information content from the symbols and their spatial relationships. The Build-Weed-Incorporate approach is demonstrated by a detailed discussion of a graph grammar for high-level recognition of music notation. See Appendix A for an illustration of the terms for musical symbols used in this paper.     

Multipass precedence analysis

Summary This paper defines a hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family. The hierarchy is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family. The families of the hierarchy have properties analogous to those of the context free family, in particular, the new mechanism introduced is very suitable for parsing.A language in the n-th family is specified by a sequence of n — 1 labeled linear grammars and a context free grammar. By assuming that the reversals of the first n — 1 grammars and the last labeled linear grammar are precedence grammars, the concepts and parsing algorithm of Wirth and Weber extend to yield a parsing algorithm within the hierarchy. This considerably enhances the usefulness of the construction and allows much of the power of the context sensitive languages to become accessible in measured amounts for potential programming applications.     

Time-bounded controlled bidirectional grammars

We study regularly controlled bidirectional (RCB) grammars from the viewpoint of time-bounded grammars. RCB-grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. A time bound on such a grammar is a measure of its derivational complexity. For some families of time bounds and for some modes of derivation we establish closure properties and a normal form theorem. In addition parsing algorithms are given for some modes of derivation. We conclude with considering generalizations with respect to the family of control languages and the family of bounding functions..     

Graph grammars for evolutionary 3D design

A new interactive evolutionary 3D design system is presented. The representation is based on graph grammars, a fascinating and powerful formalism in which nodes and edges are iteratively rewritten by rules analogous to those of context-free grammars and shape grammars. The nodes of the resulting derived graph are labelled with Euclidean coordinates: therefore the graph fully represents a 3D beam design. Results from user-guided runs are presented, demonstrating the flexibility of the representation. Comparison with results using an alternative graph representation demonstrates that the graph grammar search space is more rich in organised designs. A set of numerical features are defined over designs. They are shown to be effective in distinguishing between the designs produced by the two representations, and between designs labelled by users as good or bad. The features allow the definition of a non-interactive fitness function in terms of proximity to target feature vectors. In non-interactive experiments with this fitness function, the graph grammar representation out-performs the alternative graph representation, and evolution out-performs random search.     

NTS languages are deterministic and congruential

A context-free grammar is said to be NTS if the set of sentential forms it generates is unchanged when the rules are used both ways. We prove here that such grammars generate deterministic languages which are finite unions of congruence classes. Moreover, we show that this family of languages is closed under reversal and intersection with regular sets. A forthcoming paper will prove that, for this class, the equivalence problem is decidable.     

On the structure of context-sensitive grammars

It is well known that the family of context-sensitive grammars generate languages which are not context-free and that it is undecidable whether a context-sensitive grammar generates a context-free language. However, the mechanism by which the use of context allows a non-context-free language to be generated is not well understood. In this paper we attempt to focus on this problem by surveying some of the results which speak to two questions: (i) What constraints can be placed on the form of the rules of context-sensitive grammars without restricting the weak generative capacity? (ii) What (nontrivial) constraints can be placed on the form of the rules of context-sensitive grammars such that only context-free languages will be generated?     

Finding Syntactic Structures from Human Motion Data

We present a new approach to motion rearrangement that preserves the syntactic structures of an input motion automatically by learning a context‐free grammar from the motion data. For grammatical analysis, we reduce an input motion into a string of terminal symbols by segmenting the motion into a series of subsequences, and then associating a group of similar subsequences with the same symbol. To obtain the most repetitive and precise set of terminals, we search for an optimial segmentation such that a large number of subsequences can be clustered into groups with little error. Once the input motion has been encoded as a string, a grammar induction algorithm is employed to build up a context‐free grammar so that the grammar can reconstruct the original string accurately as well as generate novel strings sharing their syntactic structures with the original string. Given any new strings from the learned grammar, it is straightforward to synthesize motion sequences by replacing each terminal symbol with its associated motion segment, and stitching every motion segment sequentially. We demonstrate the usefulness and flexibility of our approach by learning grammars from a large diversity of human motions, and reproducing their syntactic structures in new motion sequences.