Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids

In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the interest of the finite power property to achieve partial solutions of this problem. We prove that the star problem is decidable in some trace monoid if and only if in the same monoid, it is decidable whether a recognizable language has the finite power property. Intermediary results allow us to give a shorter proof for the decidability of the two previous problems in every trace monoid without C4-submonoid. We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the finite power property, e.g., we show the decidability of these problems for recognizable languages which contain at most one non-connected trace. This article is published as Technical Report both at the Department of Computer Science at Dresden University of Technology and at the Laboratoire de ..

Modeling Soft State Protocols with SDL

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The Fiasco Kernel: Requirements Definition

Fiasco is a new implementation of the L4 microkernel interface for the x86 architecture. It is intended to be a drop-in replacement for L4/x86. Fiasco is intended to have good real-time properties, and it should be small, fast, embeddable, maintainable, and well-documented. It does not need to be portable, but it should be able to serve as a model for future L4 implementations. It will be distributed under a freeware (open-source) license. This document summarizes the preparations for the Fiasco implementation. It contains a definition of the problem which triggered the construction of Fiasco, a requirements definition, and pointers to documents containing further implementation prerequisites. Dresden University of Technology, Dept. of Computer Science, Operating Systems Group, D-01099 Dresden, Germany; Email: [email protected] Contents 1 Why a New µ-Kernel? 4 1.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The Solution . . . . . . . . . . ..

Pure and O-Substitution Pure and O-Substitution ∗

The basic properties of distributivity and deletion of pure and o-substitution are investigated. The obtained results are applied to show preservation of recognizability in a number of surprising cases. It is proved that linear and recognizable tree series are closed under o-substitution provided that the underlying semiring is commutative, continuous, and additively idempotent. It is known that, in general, pure substitution does not preserve recognizability (not even for linear target tree series), but it is shown that recognizable linear probability distributions (represented as tree series) are closed under pure substitution.