Nondeterminism and boolean operations in pda's

There are nondeterministic context-free languages that cannot be expressed as a Boolean formula over deterministic context-free languages. The closure of the context-free languages under intersection does not yield closure under complementation.     

Two complementary operations inspired by the DNA hairpin formation: Completion and reduction

We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216–228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.     

Closure properties of linear context-free tree languages with an application to optimality theory

Context-free tree grammars, originally introduced by Rounds [Math. Systems Theory 4(3) (1970) 257–287], are powerful grammar devices for the definition of tree languages. The properties of the class of context-free tree languages have been studied for more than three decades now. Particularly important here is the work by Engelfriet and Schmidt [J. Comput. System Sci. 15(3) (1977) 328–353, 16(1) (1978) 67–99]. In the present paper, we consider a subclass of the class of context-free tree languages, namely the class of linear context-free tree languages. A context-free tree grammar is linear, if no rule permits the copying of subtrees. For this class of linear context-free tree languages we show that the grammar derivation mode, which is very important for the general class of context-free tree languages, is immaterial. The main result we present is the closure of the class of linear context-free tree languages under linear frontier-to-root tree transduction mappings. Two further results are the closure of this class under linear root-to-frontier tree transduction mappings and under intersection with regular tree languages.     

Recursive descent parsing for Boolean grammars

The recursive descent parsing method for the context-free grammars is extended for their generalization, Boolean grammars, which include explicit set-theoretic operations in the formalism of rules and which are formally defined by language equations. The algorithm is applicable to a subset of Boolean grammars. The complexity of a direct implementation varies between linear and exponential, while memoization keeps it down to linear. Supported by the Academy of Finland under grant 118540.     

Context-free graph grammars and concatenation of graphs

An operation of concatenation is defined for graphs. This allows strings to be viewed as expressions denoting graphs, and string languages to be interpreted as graph languages. For a class of string languages, is the class of all graph languages that are interpretations of languages from . For the classes REG and LIN of regular and linear context-free languages, respectively, . is the smallest class of graph languages containing all singletons and closed under union, concatenation and star (of graph languages). equals the class of graph languages generated by linear HR (= Hyperedge Replacement) grammars, and is generated by the corresponding -controlled grammars. Two characterizations are given of the largest class such that . For the class CF of context-free languages, lies properly inbetween and the class of graph languages generated by HR grammars. The concatenation operation on graphs combines nicely with the sum operation on graphs. The class of context-free (or equational) graph languages, with respect to these two operations, is the class of graph languages generated by HR grammars. Received 16 October 1995 / 18 September 1996     

Controlled bidirectional grammars

We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages.     

On sentential forms of context-free grammars

Summary There is no algorithm for deciding whether two linear context-free grammars generate the same sentential forms. The equivalence problem for propagatingOL-systems is undecidable. The finiteness problem forOL-systems is decidable.SF-languages, i.e., languages which equal the set of sentential forms of a context-free grammar, possess some of the properties of context-free languages but their family is not closed under any of the ordinary operations.     

Characterizations of regular and context-free matrices

The u-v theorem for context-free languages is extended to prove an intercalation theorem for the family of context-free matrix languages. A row-wise iteration factor theorem is proved for the families of regular and context-free matrix languages. Characterizations of regular and context-free matrix languages are given in terms of vertical regular sequences and simple operations on vertical regular sequences. Closure of regular and context-free matrix languages under array nondeterministic finite state transducer mappings is established and an image theorem proved. This is used to give another characterization of regular matrix languages. Further it is shown that the family of regular matrix languages is a principal abstract family of matrices (AFM). The effect of string control and array control on these families are examined.     

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.     

Büchi context-free languages

We define context-free grammars with Büchi acceptance condition generating languages of countable words. We establish several closure properties and decidability results for the class of Büchi context-free languages generated by these grammars. We also define context-free grammars with Müller acceptance condition and show that there is a language generated by a grammar with Müller acceptance condition which is not a Büchi context-free language.     

A strong pumping lemma for context-free languages

A context-free language is shown to be equivalent to a set of sentences describable by sequences of strings related by finite substitutions on finite domains, and vice-versa. As a result, a necessary and sufficient version of the Classic Pumping Lemma is established. This result provides a guaranteed method of proving that a language is not context-free when such is the case. An example is given of a language which neither the Classic Pumping Lemma nor Parikh's Theorem can show to be non-context-free, although Ogden's Lemma can. The main result also establishes {aⁿba^mn} as a language which is not in the Boolean closure of deterministic context-free languages.     

On a family of L languages resulting from systolic tree automata

Recent work on systolic tree automata has given rise to a rather natural subfamily of EOL languages, referred to as systolic EOL languages in this paper. Systolic EOL languages possess some remarkable properties. While their family contains (because of its closure under Boolean operations) intuitively quite complicated languages, it still has decidable equivalence problem. Especially interesting is the fact that similar decision problems for slightly more general families lead to the celebrated open problems concerning Z-rational power series.     

Several properties of array languages

The languages generated by connected and disconnected array grammars are studied. We define substitutions of array languages, and we study closure properties of classes of array languages under substitutions. A characterization by means of substitutions for connected context-free array languages and a Kleene-like theorem for regular array languages are given.     

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.     

Tree controlled grammars

Languages are studied which can be generated by context-free grammars under a single simple restriction which must be satisfied by its derivation trees. Using tree controlled grammars (TC grammars for short) all unambigous and some inherently ambigous context-free languages, and also some non context-free languages can be parsed in timeO(n ²). The classes of regular, linear, context-free, EOL, ETOL and type 0 languages can be characterized in a natural manner using TC grammars. A context-free generator for all type 0 languages is exhibited. Some normal forms for TC grammars are established but it is shown that many common normal forms (e. g. Greibach normal form) cannot be obtained for TC grammars in general.     

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.     

A decidability result for deterministic ω context-free languages

It is shown that the problem whether an effectively given deterministic ω-context-free language is in the family of all closures of deterministic context-free languages is decidable.     

Pseudo-inversion: closure properties and decidability

We consider a pseudo-inversion operation inspired by biological events, such as DNA sequence transformations, where only parts of a string are reversed. We define the pseudo-inversion of a string \(w = uxv\) to be the set of all strings \(v^Rxu^R\), where \(uv \ne \lambda \) and consider the operation from a formal language theoretic viewpoint. We show that regular languages are closed under the pseudo-inversion operation whereas context-free languages are not. Furthermore, we study the iterated pseudo-inversion operation and show that the iterated pseudo-inversion of a context-free language is recognized by a nondeterministic reversal-bounded multicounter machine. Finally, we introduce the notion of pseudo-inversion-freeness and examine closure properties and decidability problems for regular and context-free languages. We demonstrate that pseudo-inversion-freeness is decidable in polynomial time for regular languages and undecidable for context-free languages.     

Genetic programming over context-free languages with linear constraints for the knapsack problem: first results

In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling complementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.     

Recursive generation of local adjunct languages

The local adjunct grammars and languages have been introduced by Joshi, Kosaraju, and Yamada in response to linguistic considerations. These grammars differ fundamentally from the Chomsky phrase-structure grammars, and they generate a distinct class of languages.In this paper, it is shown that the local adjunct languages are actually closely related to the regular and context-free languages, despite the entirely different form of definition. The adjunct languages are obtained by closure of the finite set of strings under the set operations of union, product, and a new operation, iterated adjunction. This method of generating adjunct languages is of exactly the same form as that of the regular sets (closure under union, product, and Kleene star) and a more recent characterization of the CFL's derived independently by several authors. In fact, iterated adjunction is obtained by a natural modification of the iterated substitution operation used to generate the CFL's.The material in this paper has appeared in part in the author's Ph.D. dissertation at the University of Pennsylvania, Philadelphia, PA, August, 1972.