Extended macro grammars and stack controlled machines

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines

Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results

Complexity of Some Problems Concerning Varieties and Quasi-Varieties of Algebras

In this paper we consider the complexity of several problems involving finite algebraic structures. Given finite algebras A and B, these problems ask the following. (1) Do A and B satisfy precisely the same identities? (2) Do they satisfy the same quasi-identities? (3) Do A and B have the same set of term operations? In addition to the general case in which we allow arbitrary (finite) algebras, we consider each of these problems under the restrictions that all operations are unary and that A and B have cardinality two. We briefly discuss the relationship of these problems to algebraic specification theory

Secrecy-Preserving Reasoning Over Entailment Systems: Theory and Applications

Privacy, copyright, security and other concerns make it essential for many distributed web applications to support selective sharing of information while, at the same time, protecting sensitive knowledge. Secrecypreserving reasoning refers to the answering of queries against a knowledge base involving inference that uses sensitive knowledge without revealing it. We present a general framework for secrecy-preserving reasoning over arbitrary entailment systems. This framework enables reasoning with hierarchical ontologies, propositional logic knowledge bases (over arbitrary logics) and RDFS knowledge bases containing sensitive information that needs to be protected. We provide an algorithm that, given a knowledge base over an effectively enumerable entailment system, and a secrecy set over it, defines a maximally informative secrecypreserving reasoner. Secrecy-preserving mappings between knowledge bases that allow reusing reasoners across knowledge bases are introduced