Some operators that preserve the locality of a pseudovariety of semigroups

It is shown that if V is a local monoidal pseudovariety of semigroups, then K(m)V, D(m)V and LI(m)V are local. Other operators of the form Z(m)(_) are considered. In the process, results about the interplay between operators Z(m)(_) and (_)*D_k are obtained.Comment: To appear in International Journal of Algebra and Computatio

Quantitative Timed Analysis of Interactive Markov Chains

Abstract This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2-player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering for-malisms such as AADL and dynamic fault trees. We provide algorithms for determining the extremal expected time of reaching a set of states, and the long-run average of time spent in a set of states. The prototypical tool Imca supports these algorithms as well as the synthesis of ε-optimal piecewise constant timed policies for timed reachability objectives. Two case studies show the feasibility and scalability of the algorithms.

Ordered monoids and J-trivial monoids

In this paper we give a new proof of the following result of Straubing and Thérien: every J -trivial monoid is a quotient of an ordered monoid satisfying the identity x <= 1

On a Uniform Framework for the Definition of Stochastic Process Languages

In this paper we show how Rate Transition Systems (RTSs) can be used as a unifying framework for the definition of the semantics of stochastic process algebras. RTSs facilitate the compositional definition of such semantics exploiting operators on the next state functions which are the functional counterpart of classical process algebra operators. We apply this framework to representative fragments of major stochastic process calculi namely TIPP, PEPA and IML and show how they solve the issue of transition multiplicity in a simple and elegant way. We, moreover, show how RTSs help describing different languages, their differences and their similarities. For each calculus, we also show the formal correspondence between the RTSs semantics and the standard SOS one