Towards a Uniform Theory of Effectful State Machines

Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs' notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual language semantics for a number of known classes of machines/languages, including regular, context-free, recursively-enumerable and various subclasses of context free languages (e.g. deterministic and real-time ones). Moreover, our approach provides new generic techniques for studying the expressivity power of various machine-based models.Comment: final version accepted by TOC

Optimal infinite scheduling for multi-priced timed automata

This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules

Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata (without epsilon-transitions). We first show a general characterization of probabilistic bisimilarity in terms of two-player games, which naturally reduces checking bisimilarity of probabilistic labelled transition systems to checking bisimilarity of standard (non-deterministic) labelled transition systems. This reduction can be easily implemented in the framework of pPDA, allowing to use known results for standard (non-probabilistic) PDA and their subclasses. A direct use of the reduction incurs an exponential increase of complexity, which does not matter in deriving decidability of bisimilarity for pPDA due to the non-elementary complexity of the problem. In the cases of probabilistic one-counter automata (pOCA), of probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic process algebras (i.e., single-state pPDA) we show that an implicit use of the reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and 2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic versions. The bisimilarity problems for OCA and vPDA are known to have matching lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively); we show that these lower bounds also hold for fully probabilistic versions that do not use non-determinism

Behavioural Preorders on Stochastic Systems - Logical, Topological, and Computational Aspects

Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly. However, it is a notoriously difficult task to ensure that the software running on computers behaves correctly. One approach to ease this task is that of model checking, where a model of the system is made using some mathematical formalism. Requirements expressed in a formal language can then be verified against the model in order to give guarantees that the model satisfies the requirements. For many computer systems, time is an important factor. As such, we need our formalisms and requirement languages to be able to incorporate real time. We therefore develop formalisms and algorithms that allow us to compare and express properties about real-time systems. We first introduce a logical formalism for reasoning about upper and lower bounds on time, and study the properties of this formalism, including axiomatisation and algorithms for checking when a formula is satisfied. We then consider the question of when a system is faster than another system. We show that this is a difficult question which can not be answered in general, but we identify special cases where this question can be answered. We also show that under this notion of faster-than, a local increase in speed may lead to a global decrease in speed, and we take step towards avoiding this. Finally, we consider how to compare the real-time behaviour of systems not just qualitatively, but also quantitatively. Thus, we are interested in knowing how much one system is faster or slower than another system. This is done by introducing a distance between systems. We show how to compute this distance and that it behaves well with respect to certain properties.Comment: PhD dissertation from Aalborg Universit