Uli Fahrenberg

In Science of Computer Programming

Abstract

Feature-based analysis of software product lines and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally done by translating to parity games, but also many quantitative model-checking problems can be reduced to (quantitative) games. As part of a program to make game-based model checking available for software product lines, we introduce featured reachability games, featured minimum reachability games, featured discounted games, featured energy games, and featured parity games. We show that all these admit optimal featured strategies, which project to optimal strategies for any product, and how to compute winners and values of such games in a family-based manner.

A Kleene theorem for higher-dimensional automata

By Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański

2022-09-06

In 33rd international conference on concurrency theory (CONCUR 2022)

Abstract

We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they recognise are precisely the rational subsumption-closed sets of interval pomsets. The rational operations include a gluing composition, for which we equip pomsets with interfaces. For our proof, we introduce HDAs with interfaces as presheaves over labelled precube categories and use tools inspired by algebraic topology, such as cylinders and (co)fibrations. HDAs are a general model of non-interleaving concurrency, which subsumes many other models in this field. Interval orders are used as models for concurrent or distributed systems where events extend in time. Our tools and techniques may therefore yield templates for Kleene theorems in various models and applications.

Posets with interfaces as a model for concurrency

By Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański

2022-06-30

In Information and Computation

Abstract

We introduce posets with interfaces (iposets) and generalise their standard serial composition to a new gluing composition. In the partial order semantics of concurrency, interfaces and gluing allow modelling events that extend in time and across components. Alternatively, taking a decompositional view, interfaces allow cutting through events, while serial composition may only cut through edges of a poset. We show that iposets under gluing composition form a category, which generalises the monoid of posets under serial composition up to isomorphism. They form a 2-category when a subsumption order and a lax tensor in the form of a non-commutative parallel composition are added, which generalises the interchange monoids used for modelling series-parallel posets. We also study the gluing-parallel hierarchy of iposets, which generalises the standard series-parallel one. The class of gluing-parallel iposets contains that of series-parallel posets and the class of interval orders, which are well studied in concurrency theory, too. We also show that it is strictly contained in the class of all iposets by identifying several forbidden substructures.