Showing papers on "Indexed language published in 2001"

A Characterization of Minimalist Languages

Abstract: In this paper we will fix the position of Minimalist Grammars as defined in Stabler (1997) in the hierarchy of formal languages. Michaelis (1998) has shown that the set of languages generated by Minimalist Grammars is a subset of the set of languages generated by Multiple Context-Free Grammars (Seki et al., 1991). In this paper we will present a proof showing the reverse. We thus conclude that Minimalist Grammars are weakly equivalent to Multiple Context-Free Grammars.

Automata arrays and context-free languages

Abstract: From a biological point of view automata arrays have been employed by John von Neumann in order to solve the logical problem of nontrivial self-reproduction. From a computer science point of view they are a model for massively parallel computing systems. Here we are dealing with automata arrays as acceptors for formal languages. Our focus of investigation concerns their capabilities to accept the classical linguistic languages. While there are simple relations to the regular and context-sensitive ones, here we shed some light on the relations to the context-free languages and some of their important subfamilies.

Security verification of programs with stack inspection

Abstract: Java development kit 1.2 provides a runtime access control mechanism which inspects a control stack to examine whether the program has appropriate access permissions. Guaranteeing that each execution of a program with stack inspection satisfies required security properties is desirable. Jensen et al. introduced a verification problem of deciding for a given program P and a given security property written in a temporal logic formula, whether every reachable state of P satisfies . They showed that the problem is decidable for the class of programs which do not contain mutual recursion. In this paper, we show that the set of state sequences of a program is always an indexed language and consequently the verification problem is decidable. Our result is stronger than Jensen's in that a security property can be specified by a regular language, whose expressive power is stronger than temporal logic, and in that a program can contain mutual recursion.

Valence Grammars with Target Sets

Abstract: We discuss an extension of valence grammars, where the value of a valid derivation is allowed to be an element of a given target set. We discuss closure properties of language families generated by such grammars. Moreover, we investigate the generative power of valence grammars with target sets over the groups Z k , over the monoids N k and over finite monoids. This way, we also prove a conjecture due to M. Jantzen stating that unordered vector languages can be characterized by grammars controlled by permutations of regular languages. Furthermore, we show that matrix languages are characterized by valence grammars with target sets over (arbitrary) finite monoids.

Languages recognized by a class of finite automata

Abstract: We consider automata defined by left multiplications in graph algebras, and describe all languages recognized by these automata in terms of combinatorial properties of words which belong to these languages, regular expressions and linear grammars defining these languages. This description is applied to investigate closure properties of the obtained family of languages.

Synthesizing noise-tolerant language learners

Abstract: An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephen's model of noisy data is empoloyed, in which, roughly, correct data crops up infintely often, and incorrect data only finitely often. Studied, then, is the synthesis from indices for r.e. classes and for indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The proofs of most of the positive resutls yield, as pleasant corollaries, strict subset-principle or tell-tale style characterization for the noise-tolerant learn-ability of the corresponding classes or families indexed.

A Descriptive Characterisation of Indexed Grammars

Abstract: Indexed grammars are shown to correspond to an existential monadic second-order logic over phrase structure trees, extended with a single existential quantifier ranging over a certain type of unary function. Indexed grammars are also shown to correspond to contingency grammars, a strengthening of context-free grammars that makes use of such unary functions.