On Boolean closed full trios and rational Kripke frames

A Boolean closed full trio is a class of languages that is closed under the Boolean operations (union, intersection, and complementation) and rational transductions. It is well-known that the regular languages constitute such a Boolean closed full trio. It is shown here that every such language class that contains any non-regular language already includes the whole arithmetical hierarchy (and even the one relative to this language). A consequence of this result is that aside from the regular languages, no full trio generated by one language is closed under complementation. Our construction also shows that there is a fixed rational Kripke frame such that assigning an arbitrary non-regular language to some variable allows the definition of any language from the arithmetical hierarchy in the corresponding Kripke structure using multimodal logic

Reset machines

AbstractA reset tape has one read-write head which moves only left-to-right except that the head can be reset once to the left end and the tape rescanned; a multiple-reset machine has reset tapes as auxiliary storage and a one-way input tape. Linear time is no more powerful than real time for nondeterministic multiple-reset machines and so the family MULTI-RESET of languages accepted in real time by nondeterministic multiple-reset machines is closed under linear erasing. MULTI-RESET is closed under Kleene. It can be characterized as the smallest family of languages containing the regular sets and closed under intersection and linear-erasing homomorphic duplication or as the smallest intersection-closed semiAFL containing COPY = {ww | w in {a, b}∗}. A circular tape is read full-sweep from left-to-right only and then reset to the left, any number of times; a nonwriting circular tape cannot be altered after the first sweep. For nondeterministic machines operating in real time, multiple reset tapes, circular tapes or nonwriting circular tapes have the same power. Languages in MULTI-RESET can be accepted in real time by nondeterministic machines using only three reset tapes or using only one reset tape and one nonwriting circular tape

A meta-information structure for representing arguments in science text

The research for this thesis has been concerned with defining and demonstrating the existence of certain semantic elements in English natural language science text which can be called metainformation. Meta-information is described as being the organisational-, rather than the conceptual properties of an author's 'message' in text. Conceptual information is that subject-related output from a document which readers assimilate or synthesise with their current state-of-knowledge. Meta-information reflects the organisation or structural format used by an author to present conceptual information for transfer from text to readers. The example used here to demonstrate the existence of meta-information, is a format for the presentation of empirical argument in science text. At its most simplep a meta-informational element could be a report section-heading like, INTRODUCTION, which describes (we assume), the contents of the subsequent text. At a lower level of analysis the phrase, 'This paper describes contains some semantic inference that the complete statement is one of an introductory nature; thereforep such a statement could be labelled as one of INTRODUCTION for meta-informational purposes. A 'grammar' or set of meta-informational elements, has been developed as a means of identifying certain semantic aspects of text. This grammar is based on some experimental evidence and the consensus view of readers and writers of science text who produced what has been called a conventional format for empirical argument presentation. An initial set of rules for implementing this grammar have also been developed. The rules have been tested for replicability with positive results. Although analysis of full text hasshown deviation from a 'conventional argument structure readers' summaries of the same text conform to this structure. Thus, a model of the phenomenQn of information transfer from text to readers, which includes a structural transformation process based on the experimental results, has been built. A computer simulation is given to demonstrate the model in an inter-active program-user system designed to produce summaries of whole text. The thesis is that evidence exists for the presence of meta-information in science text and that if a grammar appropriate to the kind of output information required by users is built, highly structured text could be produced so that the process of information transfer is optimised