A Chomsky-Schützenberger-Stanley type characterization of the class of slender context-free languages

Slender context-free languages have a complete algebraic characterization by L. Ilie in [13]. In this paper we give another characterization of this class of languages. In particular, using linear Dyck languages instead of unrestricted ones, we obtain a Chomsky-Schützenberger-Stanley type characterization of slender context-free languages

On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered

On the Generating Power of Regularly Controlled Bidirectional Grammars

RCB-grammars or regularly controlled bidirectional grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion. In addition, the application of these rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. In this paper the generating power of the derivation mode that uses right-occurrence rewriting (RO-mode) is determined. Furthermore, a new mode called RA is introduced, which is a better formalization of the intuitive idea of right-occurrence rewriting than the RO-mode. The RO- and RA-mode have the same generating power, viz. the corresponding RCB-grammars both generate the recursively enumerable languages. Consequently, providing RCB/RO-grammars with a time bound results in a less powerful grammar model

On the generating power of regularly controlled bidirection grammars

RCB-grammars or regularly controlled bidirectional grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion. In addition, the application of these\ud rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. In this paper the generating power of the derivation mode that uses right-occurrence rewriting (RO-mode) is determined. Furthermore, a new mode called RA is introduced, which is a better formalization of the intuitive idea of rightoccurrence rewriting than the RO-mode. The RO- and RA-mode have the same generating power, viz. the corresponding RCB-grammars both generate the recursively enumerable languages. Consequently, providing RCB/RO-grammars with a time bound results in a less powerful grammar model

2-Testability and Relabelings Produce Everything

AbstractWe show that grammar systems with communication by command and with extremely simple rewriting rules (in fact, only relabelings are needed) are able to generate all recursively enumerable languages. The result settles several open problems in the area of grammar systems. We also present the result in a general framework, without referring to grammar systems, obtaining a characterization of recursively enumerable languages from a new point of view

Grammars working on layered strings

We consider first an operation with strings and languages suggested by superposed windows on the computer screen (as well as by cryptographic systems of Richelieu type): we assume that the strings contain usual symbols as well as a transparent symbol. Superposing two strings (justified to left), we produce a new string consisting of the symbols observable from above. This operation is investigated as an abstract operation on strings, then it is used in building a variant of grammar systems with the component grammars working on the layers of an array of strings. Each grammar can rewrite only symbols in its layer which are observable from above. The language generated in this way consists of strings of the observable symbols, produced at the end of a derivation. The power of several variants of these generative mechanisms is investigated for the case of two layered strings. When a matrix-like control on the work of the component grammars is considered, then a characterization of recursively enumerable languages is obtained

Inductive Definition and Domain Theoretic Properties of Fully Abstract

A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF + "parallel conditional function"), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is new, in that it is given level-by-level in the finite type hierarchy. To prove full abstraction and non-dcpo domain theoretic properties of these models, a theory of computational strategies is developed. This is also an alternative and, in a sense, an analogue to the later game strategy semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong; and Nickau. In both cases of PCF and PCF^+ there are definable universal (surjective) functionals from numerical functions to any given type, respectively, which also makes each of these models unique up to isomorphism. Although such models are non-omega-complete and therefore not continuous in the traditional terminology, they are also proved to be sequentially complete (a weakened form of omega-completeness), "naturally" continuous (with respect to existing directed "pointwise", or "natural" lubs) and also "naturally" omega-algebraic and "naturally" bounded complete -- appropriate generalisation of the ordinary notions of domain theory to the case of non-dcpos.Comment: 50 page

On the dual post correspondence problem

The Dual Post Correspondence Problem asks whether, for a given word α, there exists a pair of distinct morphisms σ, τ, one of which needs to be non-periodic, such that σ(α) = τ(α) is satisfied. This problem is important for the research on equality sets, which are a vital concept in the theory of computation, as it helps to identify words that are in trivial equality sets only. Little is known about the Dual PCP for words α over larger than binary alphabets. In the present paper, we address this question in a way that simplifies the usual method, which means that we can reduce the intricacy of the word equations involved in dealing with the Dual PCP. Our approach yields large sets of words for which there exists a solution to the Dual PCP as well as examples of words over arbitrary alphabets for which such a solution does not exist