Precedence-regular grammars

A new class of grammars (precedence-regular grammars) is obtained as a proper extension of the class of weak precedence grammars. A parsing algorithm is described for this class of grammars, using Domolki's algorithm. Finally a criterion is obtained to decide whether a given context-free grammar belongs to this class.     

LL(k)-PARSING OF COUPLED-CONTEXT-FREE GRAMMARS

Coupled-context-free grammars are a natural generalization of context-free grammars obtained by combining nonterminals to corresponding parentheses which can only be substituted simultaneously. Refering to the generative capacity of the grammars we obtain an infinite hierarchy of languages that comprises the context-free languages as the first and all the languages generated by TAGs as the second element. Here, we present a generalization of the context-free LL(k) -notion onto coupled-context-free grammars, which leads to a characterization of subclasses of coupled-context-free grammars–and in this way of TAGs as well–which can be parsed in linear time. The parsing procedure described works incrementally so that it can be used for on-line parsing of natural language. Examples show that important elements of the tree-adjoining languages can be generated by LL(k )-coupled-context-free grammars.     

A hierarchy of uniquely parsable grammar classes and deterministic acceptors

We introduce a new class of grammars called uniquely parsable grammars (UPGs). A UPG is a kind of phrase structure grammar having a restricted type of rewriting rules, where parsing can be performed without backtracking. We show that, in spite of such restriction to the rules, UPGs are universal in their generating ability. We then define three subclasses of UPGs. They are M-UPGs (monotonic UPGs), RC-UPGs (UPGs with right-terminating and context-free-like rules), and REG-UPGs (regular UPGs). It is proved that the generating abilities of the classes of M-UPGs, RC-UPGs, and REG-UPGs are exactly characterized by the classes of deterministic linear-bounded automata, deterministic pushdown automata, and deterministic finite automata, respectively. Especially, the class of RC-UPGs gives a very simple grammatical characterization of the class of deterministic context-free languages. Thus, these four classes form a deterministic counterpart of the classical Chomsky hierarchy. Received August 30, 1995 / May 13, 1996     

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.     

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.     

Abstract families of context-free grammars

An abstract family of grammars (AFG) may be defined as a class of grammars for which the corresponding class of languages forms an abstract family of languages (AFL) as defined by Ginsburg and Greibach. The derivation bounded grammars of Ginsburg and Spanier is an example of an AFG which is properly included in the class of all context-free grammars (also AFG). The main result is that there exist two distinct infinite hierarchies of AFG which exhaust the derivation bounded AFG such that the AFL associated with the kth member of one of these AFG hierarchies is properly included in the AFL associated with the k-lst member of that same hierarchy. Each hierarchy is shown to be strongly incomparable to the other; that is, the first member of each generates some language not generated by a fixed but arbitrary member of the other. We designate these hierarchies as the hierarchies of left and right dominant grammars (languages)     

Operator precedence and the visibly pushdown property

Floyd?s operator precedence grammars and languages (FG, FL) are a classical subclass of deterministic context-free (DCF) grammars and languages. We prove that several recently introduced language families motivated by the needs of model checking and of specifying XML-like languages are proper subsets of FL. The main cases considered include visibly pushdown languages (VPL) and balanced languages (BALAN), which are characterized by restricted precedence relations. FL have all the closure properties available for regular languages and generally viewed as necessary for application to model checking: reversal, prefixing and suffixing, concatenation, Kleene star, and boolean operations. All but the last results are new, and some require complex proofs, due to the necessary changes of syntax structure. Thus FL are the largest known subfamily of DCF having the same closure properties as VPL. FG, unlike VPL grammars, which are intended for abstract syntax modelling, are structurally adequate to specify real programming languages.     

The complexity of the membership problem for some extensions of context-free languagest†

The time and tape complexity of some families of languages defined in the literature by altering methods of generation by context-free grammars is considered. Specifically; it is shown that the following families of languages can be recognized by deterministic multitape Turing machines either in polynomial time or within (log n)² tape:

1) the context independent developmental (EOL) languages;

2) the simple matrix languages;

3) the languages generated by derivation restricted state grammars.:

4) the languages generated by linear context-free grammars with certain non-regular control sets;

5) the languages generated by certain classes of vector grammars.

In fact, these languages are of the same tape complexity as context-free languages. Other results indicate the complexity of EDOL languages and the effects on complexity of applying the homomorphic replication operator to regular and context-free languages.     

The language intersection problem for non-recursive context-free grammars

We prove that, given as input two context-free grammars, deciding non-emptiness of intersection of the two generated languages is PSPACE-complete if at least one grammar is non-recursive. The problem remains PSPACE-complete when both grammars are non-recursive and deterministic. Also investigated are generalizations of the problem to several context-free grammars, of which a certain number are non-recursive.     

Spinal-Formed Context-Free Tree Grammars

In this paper we introduce a restricted model of context-free tree grammars called spine grammars, and study their formal properties including considerably simple normal forms. Recent research on natural languages has suggested that formalisms for natural languages need to generate a slightly larger class of languages than context-free grammars, and for that reason tree adjoining grammars have been widely studied relating them to natural languages. It is shown that the class of string languages generated by spine grammars coincides with that of tree adjoining grammars. We also introduce acceptors called linear pushdown tree automata, and show that linear pushdown tree automata accept exactly the class of tree languages generated by spine grammars. Linear pushdown tree automata are obtained from pushdown tree automata with a restriction on duplicability for the pushdown stacks. Received May 29, 1998, and in revised form April 27, 1999, and in final form May 10, 1999.     

On the generative power of sequential and parallel programmed graph grammars

Programmed graph grammars are formally introduced and their generative power is investigated. Programmed graph grammars differ from other approaches to graph grammars in the so-called control diagram which controls the application order of productions. Restricting the form of the productions of a programmed graph grammar we get several classes of graph languages. These are compared mutually as well as with the hierarchy introduced by Nagl [18]. For unrestricted and monotone productions corresponding classes of graph languages coincide, while the class of context free programmed graph languages is properly contained in the class of context free graph languages in the sense of [18].     

The Generating Power of Total Deterministic Tree Transducers

Attributed tree transducers are abstract models used to study properties of attribute grammars. One abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input, instead of derivation trees of a context-free grammar. In this paper we show that with respect to the generating power this isnotan abstraction; i.e., we show that attributed tree transducers and attribute grammars generate the same class of term (or tree) languages. To prove this, a number of results concerning the generating power of top-down tree transducers are established, which are interesting in their own. We also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes. The latter result is achieved by proving a hierarchy of classes of tree languages generated by context-free hypergraph grammars with respect to their rank.     

A NEW AUTOMATON MODEL FOR TAGS: 2-SA

In this paper, we introduce and define a new class of automata (pushdown automata with n stacks, abbreviated as n-SA). The ultimate aim is to give a new characterization of LCRFL, the class of languages accepted by a linear context-free rewriting system (LCFRS). In particular, we introduce 2-SA as a new automaton model for tree-adjoining grammars (TAG). In the simplest cases (0-SA and 1-SA), the languages that are accepted by the automata are the regular and context-free languages respectively. A more complex case is the case of a 2-SA which accepts TALs. The n-SA creates an infinite hierarchy of languages and it seems that this hierarchy corresponds to others in the class LCFRL. The 2-SA corresponds closely to the EPDA (embedded pushdown automaton, an automaton model equivalent to TAGs). Unlike the EPDA, which allows push operations "below the top stack," an n-SA allows push and pop operations only on the top of their (multiple) stacks. So n-SA trade simpler operations against an also simpler but expanded storage structure.     

Context-free languages over infinite alphabets

In this paper we introduce context-free grammars and pushdown automata over infinite alphabets. It is shown that a language is generated by a context-free grammar over an infinite alphabet if and only if it is accepted by a pushdown automaton over an infinite alphabet. Also the generated (accepted) languages possess many of the properties of the ordinary context-free languages: decidability, closure properties, etc.. This provides a substantial evidence for considering context-free grammars and pushdown automata over infinite alphabets as a natural extension of the classical ones. Received November 27, 1995 / March 4, 1997     

Formes de langages et de grammaires

Summary This paper is devoted to the study of context-free languages over infinite alphabets. This work can be viewed as a new attempt to study families of grammars, replacing the usual grammar forms and giving a new point of view on these questions. A language over an infinite alphabet or I-language appears as being a model for a family of usual languages; an interpretation is an homomorphism from the infinite alphabet to any finite alphabet. Using this notion of interpretation we can associate to each family of I-languages an image, called its shadow, which is a family of usual languages.The closure properties of families, generalizing to infinite alphabets the family of context-free languages, lead to define rational transductions between infinite alphabets or I-transductions, and then, families of I-languages closed under I-transductions, or I-cones. We study here relations between the closure properties of a family of I-languages and these of its shadow. As a result, we obtain that any union closed rational cone of context-free languages, principal or not, is the shadow of a principal I-cone.This work leads to new results about the classical theory of context-free languages. For instance, we prove that any principal rational cone of context-free languages can be generated by a context-free language, whose grammar has only 6 variables. This work also leads to more general considerations about the adequacy of some generating devices to the generated languages. It appears that the context-free grammars are fair, in a sense that we define, for generating context-free languages but that non-expansive context-free grammars are not for generating non-expansive context-free languages. This point of view raises a number of questions.     

A class of linearly parsable graph grammars

Summary Specializing an existing graph grammar model we look in detail at node context-free graph grammars. With a slight generalization the parse trees for context-free Chomsky grammars can be used to describe derivations of these graph grammars.As shown already in former works the precedence graph grammars are defined as a subclass of context-free graph grammars by certain algebraic restrictions on the form of the rules. Then we can prove that every precedence grammar is unambiguous and additionally the reduction process in such a grammar read as replacement system is finite.The most important aim in defining the predence relations was a simple parsing method. This is realized because it is shown that the syntactic analysis for precedence graph grammars can be done in a time which linearly depends on the size of the input graph.The whole method has been implemented and a documentation is available.     

An infinite hierarchy of intersections of context-free languages

The class of languages expressible as the intersection ofk context-free languages is shown to be properly contained within the class of languages expressible as the intersection ofk + 1 context-free languages. Hence an infinite hierarchy of classes of languages is exhibited between the class of context-sensitive languages and the class of context-free languages.     

A representation of trees by languages I

A tree can be represented by a language consisting of a suitable coding of its finite branches. We investigate this representation and derive a number of reductions between certain equivalence problems for context-free tree grammars and recursive program schemes and the (open) equivalence problem for DPDA's. This is the first part of this work: it is devoted to technical results on prefix-free languages and strict deterministic grammars. Application to context-free tree grammars will be published in the second part.     

Leftist Grammars and the Chomsky Hierarchy

Leftist grammars are characterized in terms of rules of the form a → ba and cd → d, without distinction between terminals and nonterminals. They were introduced by Motwani et al. [13], where the accessibility problem for some general protection system was related to these grammars. This protection system was originally proposed in [4] and [15] in the context of Java virtual worlds. The accessibility problem is formulated in the form "Can object p gain (illegal) access to object q by a series of legal moves (as prescribed by the policy)?" The membership problem for leftist grammar is decidable [13], which implies decidability of the accessibility problem for the appropriate protection system. We study relationships between language classes defined by various types of leftist grammars and classes of the Chomsky hierarchy. We show that general leftist grammars can define languages which arenot context free, answering in the negative a question from [13]. Moreover, we study some restricted variants of leftist grammars and relate them to regular, deterministic context-free, and context-free languages.