Abstract.We study the problems of existence and construction of infinite schedules for finite weighted automata and one-clock weighted timed automata, subject to boundary constraints on the accumulated weight. More specifically, we consider automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource (e.g. energy). We ask the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints (e.g. remains between 0 and some given upper-bound). We also consider a game version of the above, where certain transitions may be uncontrollable.

Abstract. Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g. only for behaviours where a resource is always available (nonnegative accumulated weight), yet does not exceed a given maximum capacity. We extend energy games to a multiweighted and parameterized setting, allowing us to model systems with multiple quantitative aspects. We present reductions between Petri nets and multiweighted automata and among different types of multiweighted automata and identify new complexity and (un)decidability results for both one-and two-player games. We also investigate the tractability of an extension of multiweighted energy games in the setting of timed automata.

Stirling [1996Stirling [ , 1998 proved the decidability of bisimilarity on so-called normed pushdown processes. This result was substantially extended by Sénizergues [1998, 2005] who showed the decidability of bisimilarity for regular (or equational) graphs of finite out-degree; this essentially coincides with weak bisimilarity of processes generated by (unnormed) pushdown automata where the ε-transitions can only deterministically pop the stack. The question of decidability of bisimilarity for the more general class of so called Type -1 systems, which is equivalent to weak bisimilarity on unrestricted ε-popping pushdown processes, was left open. This was repeatedly indicated by both Stirling and Sénizergues. Here we answer the question negatively, that is, we show the undecidability of bisimilarity on Type -1 systems, even in the normed case.We achieve the result by applying a technique we call Defender's Forcing, referring to the bisimulation games. The idea is simple, yet powerful. We demonstrate its versatility by deriving further results in a uniform way. First, we classify several versions of the undecidable problems for prefix rewrite systems (or pushdown automata) as 0 1 -complete or 1 1 -complete. Second, we solve the decidability question for weak bisimilarity on PA (Process Algebra) processes, showing that the problem is undecidable and even 1 1 -complete. Third, we show 1 1 -completeness of weak bisimilarity for so-called parallel pushdown (or multiset) automata, a subclass of (labeled, place/transition) Petri nets.

Abstract. This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page

Formal methods is the term used to describe the specification and verification of software and software systems using mathematical logic. Various methodologies have been developed and incorporated into software tools. An important subclass is distributed systems. There are many books that look at particular methodologies for such systems, e.g. CSP, process algebra. This book offers a more balanced introduction for graduate students that describes the various approaches, their strengths and weaknesses, and when they are best used. Milner's CCS and its operational semantics are introduced, together with notions of behavioural equivalence based on bisimulation techniques and with variants of Hennessy-Milner modal logics. Later in the book, the presented theories are extended to take timing issues into account. The book has arisen from various courses taught in Iceland and Denmark and is designed to give students a broad introduction to the area, with exercises throughout.