On the Degree of Extension of Some Models Defining Non-Regular Languages

This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results regarding the degree on non-regularity of a context-free grammar as well as the degree of extension of finite automata over groups. Finally, we consider a similar measure for the finite automata with translucent letters and present some preliminary results. This measure could be considered for many mechanisms that extend a less expressive one.Comment: In Proceedings AFL 2023, arXiv:2309.0112

Automata with One-way Jumping Mode (Algebraic system, Logic, Language and Related Areas in Computer Sciences II)

Recently, new types of non-sequential machine models have been introduced and studied, such as jumping automata and one-way jumping automata. We study the abilities and limitations of automata with these two jumping modes of tape heads with respect to how they affect the class of accepted languages. We give several methods to determine whether a language is accepted by a machine with jumping mode. We also consider relationships among the classes of languages defined by the new machines and their classical counterparts

Proceedings of the 2008 Oxford University Computing Laboratory student conference.

This conference serves two purposes. First, the event is a useful pedagogical exercise for all participants, from the conference committee and referees, to the presenters and the audience. For some presenters, the conference may be the first time their work has been subjected to peer-review. For others, the conference is a testing ground for announcing work, which will be later presented at international conferences, workshops, and symposia. This leads to the conference's second purpose: an opportunity to expose the latest-and-greatest research findings within the laboratory. The fourteen abstracts within these proceedings were selected by the programme and conference committee after a round of peer-reviewing, by both students and staff within this department

Sweep Complexity Revisited

We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having skipped some of the symbols. The class of languages accepted by these machines strictly includes the regular class and constant sweep complexity allows exactly the acceptance of regular languages. However, we show that there exist machines with higher than constant complexity still only accepting regular languages and that in general the sweep complexity of an automaton does not distinguish between accepting regular and non-regular languages. We establish separation results for asymptotic classes defined by this complexity measure and give a surprising exponential/logarithmic relation between factors of certain inputs which can be verified by such machines.Comment: 12 pages, 8 figure

Java Generics are Turing Complete

This paper describes a reduction from the halting problem of Turing machines to subtype checking in Java. It follows that subtype checking in Java is undecidable, which answers a question posed by Kennedy and Pierce in 2007. It also follows that Java's type checker can recognize any recursive language, which improves a result of Gill and Levy from 2016. The latter point is illustrated by a parser generator for fluent interfaces