Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature

Synesthetic art through 3-D projection: The requirements of a computer-based supermedium

A computer-based form of multimedia art is proposed that uses the computer to fuse aspects of painting, sculpture, dance, music, film, and other media into a one-to-one synthesia of image and sound for spatially synchronous 3-D projection. Called synesthetic art, this conversion of many varied media into an aesthetically unitary experience determines the character and requirements of the system and its software. During the start-up phase, computer stereographic systems are unsuitable for software development. Eventually, a new type of illusory-projective supermedium will be required to achieve the needed combination of large-format projection and convincing real life presence, and to handle the vast amount of 3-D visual and acoustic information required. The influence of the concept on the author's research and creative work is illustrated through two examples

Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure

Towards Syntax-Aware Editors for Visual Languages

AbstractEditors for visual languages should provide a user-friendly environment supporting end users in the composition of visual sentences in an effective way. Syntax-aware editors are a class of editors that prompt users into writing syntactically correct programs by exploiting information on the visual language syntax. In particular, they do not constrain users to enter only correct syntactic states in a visual sentence. They merely inform the user when visual objects are syntactically correct. This means detecting both syntax and potential semantic errors as early as possible and providing feedback on such errors in a non-intrusive way during editing. As a consequence, error handling strategies are an essential part of such editing style of visual sentences.In this work, we develop a strategy for the construction of syntax-aware visual language editors by integrating incremental subsentence parsers into free-hand editors. The parser combines the LR-based techniques for parsing visual languages with the more general incremental Generalized LR parsing techniques developed for string languages. Such approach has been profitably exploited for introducing a noncorrecting error recovery strategy, and for prompting during the editing the continuation of what the user is drawing