Helmut Jürgensen

Outfix and infix codes and related classes of languages

A language L such that no word in L is a proper factor of another word in L is said to be an infix code. A language L such that no word in L can be obtained from another word in L by the cancellation of a proper factor is called an outfix code. We derive properties of infix and outfix codes which describe their relation to other classes of codes and which determine their combinatorial structures. In particular, we consider closure properties of these and related classes of codes, maximal codes within these classes, the syntactic monoids of such codes, and the connection of these codes with binary relations on the free monoid.

Randomness as an Invariant for Number Representations

We show that the usual positional representations of a real number are either random, in the sense of Martin-Lof, for all bases or not so for any base. Thus, randomness is an invariant of number representations. All our proofs are constructive.

Constructions for alternating finite automata

Alternation is a natural generalization of nondeterminism. The model of alternating finite automata was first introduced and studied by Chandra et al. in [2]. Although alternating finite automata are no more powerful than deterministic finite automata with respect to language recognition, special features of alternating finite automata may provide new approaches and techniques for solving theoretical and practical problems concerning regular languages. In this paper we present direct constructions for the usual language theoretic operations in terms of alternating finite automata. Moreover, we discuss minimization and direct transformations between alternating, non-deterministic, and deterministic finite automata.

A model for sequential machine testing and diagnosis

A mathematical framework for the testing and diagnosis of sequential machines is developed. A very general fault model is used in which a faulty machine is represented as a sequential machine, possibly with state and output sets different from those of the good machine. A deterministic finite automaton, called observer, describes the process by which one gains information from the observation of the responses to test sequences. It generalizes the work of Hennie on distinguishing and homing sequences, by modelling all the possible conclusions that could be drawn from observing the circuit under test. A nondeterministic acceptor is derived from the observer; it accepts diagnosing sequences and can also be used to generate test sequences. We then associate probabilities with this nondeterministic acceptor which, together with a stochastic source of input symbols, provides a probabilistic diagnoser. As a particular application we consider the testing and diagnosis of random-access memories by random test sequences. Our model generalizes the work by David et al. on the calculation of the length of a random test sequence required to guarantee that the probability of detection of a fault exceeds a prescribed threshold.

Accessible presentation of information for people with visual disabilities

Personal computers, palm top computers, media players and cell phones provide instant access to information from around the world. There are a wide variety of options available to make that information available to people with visual disabilities, so many that choosing one for use in any given context can often feel daunting to someone new to the field of accessibility. This paper reviews tools and techniques for the presentation of textual, graphic, mathematic and web documents through audio and haptic modalities to people with visual disabilities.

Relations on free monoids, their independent sets, and codes 1

Many classes of codes can be characterized as families of antichains with respect to partial orders on the free monoid or, in more general terms, as families of independent sets with respect to some binary relations. In this paper we investigate the general properties of this connection between families of sets and binary relations. This theory provides a framework in which known results about codes can be expressed elegantly and in which several new results are derived. Moreover, this theory can be generalized to relations of arbitrary finite arity in a very natural fashion. This allows us, for instance, to prove new hierarchy results. More importantly, however, this theory provides a new and profound insight into the mechanisms by which classes of codes are defined.

Is independence an exception

Abstract Godels incompleteness theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable statements of such a theory is dense and in many cases even corare.

Haptic emulation of games: haptic Sudoku for the blind

For blind persons, information is often presented through substitute media. We explore the possibility of emulating visual perception through haptic perception completely using a new haptic display and using games as a paradigm. We decsribe an implementation of Sudoku which utilizes the capabilities of the display: representing the full Sudoku square in its natural form; entering numbers and notes in the boxes of the square; emulating visual scanning for information through scanning by touch; interacting by finger movement (gestures). The only non-haptic component consists of sounds played to signal the outcome of actions. This demonstrates the advantages of the planar touch-sensitive refreshable haptic display when compared with other interaction modes for blind persons.

n-Prefix–suffix languages ∗

The combinatorial structure of n-prefix-suffix languages, called n-ps-codes in this paper, is investigated. An n-ps-code is a language, each of whose subsets of cardinality at most n is a prefix code or a suffix code.

Inference algorithms for developmental systems with cell lineages

An algorithmic formulation is presented for the inference procedure concerning lineage models. The problem is to find lineage rules from observed sequences of tree structures under the assumption that no interactions take place in the course of development and that sufficiently frequent observations are available at equal time intervals. The underlying structural pattern is taken to be a OL system, and the goal is to find propagating and deterministic OL schemes with minimal properties satifsying certain biological reliance criteria. Upper bounds have been found for the complexity of the inference algorithms.