Decision Problems For Turing Machines

We answer two questions posed by Castro and Cucker, giving the exact complexities of two decision problems about cardinalities of omega-languages of Turing machines. Firstly, it is $D_2(\Sigma_1^1)$-complete to determine whether the omega-language of a given Turing machine is countably infinite, where $D_2(\Sigma_1^1)$ is the class of 2-differences of $\Sigma_1^1$-sets. Secondly, it is $\Sigma_1^1$-complete to determine whether the omega-language of a given Turing machine is uncountable.Comment: To appear in Information Processing Letter

Towards a Notion of Distributed Time for Petri Nets

We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks --- possibly one per place --- allowing a local timing as well as distributed time synchronisation. We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of processes of the respective models

A note on quantum algorithms and the minimal degree of epsilon-error polynomials for symmetric functions

The degrees of polynomials representing or approximating Boolean functions are a prominent tool in various branches of complexity theory. Sherstov recently characterized the minimal degree deg_{\eps}(f) among all polynomials (over the reals) that approximate a symmetric function f:{0,1}^n-->{0,1} up to worst-case error \eps: deg_{\eps}(f) = ~\Theta(deg_{1/3}(f) + \sqrt{n\log(1/\eps)}). In this note we show how a tighter version (without the log-factors hidden in the ~\Theta-notation), can be derived quite easily using the close connection between polynomials and quantum algorithms.Comment: 7 pages LaTeX. 2nd version: corrected a few small inaccuracie

Index to Library Trends Volume 38

published or submitted for publicatio

Fourth-order flows in surface modelling

This short article is a brief account of the usage of fourth-order curvature flow in surface modelling

A Sequent Calculus for Modelling Interferences

A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal with multisequent structures and has the cut-elimination property. Extensions are proposed that give first results concerning our objectives

Two Decades of Maude

This paper is a tribute to José Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech