A test generation framework for quiescent real-time systems

We present an extension of Tretmans theory and algorithm for test generation for input-output transition systems to real-time systems. Our treatment is based on an operational interpretation of the notion of quiescence in the context of real-time behaviour. This gives rise to a family of implementation relations parameterized by observation durations for quiescence. We define a nondeterministic (parameterized) test generation algorithm that generates test cases that are sound with respect to the corresponding implementation relation. Also, the test generation is exhaustive in the sense that for each non-conforming implementation a test case can be generated that detects the non-conformance

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Labelled transition systems as a Stone space

A fully abstract and universal domain model for modal transition systems and refinement is shown to be a maximal-points space model for the bisimulation quotient of labelled transition systems over a finite set of events. In this domain model we prove that this quotient is a Stone space whose compact, zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree of bisimilarity such that image-finite labelled transition systems are dense. Using this compactness we show that the set of labelled transition systems that refine a modal transition system, its ''set of implementations'', is compact and derive a compactness theorem for Hennessy-Milner logic on such implementation sets. These results extend to systems that also have partially specified state propositions, unify existing denotational, operational, and metric semantics on partial processes, render robust consistency measures for modal transition systems, and yield an abstract interpretation of compact sets of labelled transition systems as Scott-closed sets of modal transition systems.Comment: Changes since v2: Metadata updat

The Complexity of Relating Quantum Channels to Master Equations

Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find it's form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P=NP: any efficiently computable criterion for Markovianity would imply P=NP; whereas a proof that P=NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.Comment: V1: 43 pages, single column, 8 figures. V2: titled changed; added proof-overview and accompanying figure; 50 pages, single column, 9 figure

Algorithmic problems in analysis of real time system specifications

I uppsatsen studeras representationen av William Shakespeares pjäs Hamlet i affischsammanhang. Ett antal Hamletaffischer från 1900-talet framtill 2008 beskrivs, tolkas och analyseras. Fokus ligger främst på det aktuella anslaget från 2008 års produktion på Dramaten i Stockholm. Bakgrunden innehåller kortare teoriavsnitt om klassisk och visuell retorik, bildstruktur, semiotik samt affischens historia och roll i dag. En kortare beskrivning av pjäsens handling ger en naturlig ingång till den kortare presentationen av samtliga affischer som följer. I analysen studeras Hamlet från 2008 i en djupare dimension, där en analysmodell av Roland Barthes tillämpas på ett detaljerat plan. Därefter följer en jämförande analys med tidigare affischer, vilket avslutningsvis följs av en sammanfattande diskussion kring tidigare affischer och hur dess framtida representation kan tänkas ta form.

Reachability of Communicating Timed Processes

We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata.Comment: Extended versio

Attribute Value Reordering For Efficient Hybrid OLAP

The normalization of a data cube is the ordering of the attribute values. For large multidimensional arrays where dense and sparse chunks are stored differently, proper normalization can lead to improved storage efficiency. We show that it is NP-hard to compute an optimal normalization even for 1x3 chunks, although we find an exact algorithm for 1x2 chunks. When dimensions are nearly statistically independent, we show that dimension-wise attribute frequency sorting is an optimal normalization and takes time O(d n log(n)) for data cubes of size n^d. When dimensions are not independent, we propose and evaluate several heuristics. The hybrid OLAP (HOLAP) storage mechanism is already 19%-30% more efficient than ROLAP, but normalization can improve it further by 9%-13% for a total gain of 29%-44% over ROLAP

A Primer on Reproducing Kernel Hilbert Spaces

Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geometry, associating with each geometric configuration a canonical overdetermined coordinate system. This coordinate system varies continuously with changing geometric configurations, making it well-suited for studying problems whose solutions also vary continuously with changing geometry. This primer can also serve as an introduction to infinite-dimensional linear algebra because reproducing kernel Hilbert spaces have more properties in common with Euclidean spaces than do more general Hilbert spaces.Comment: Revised version submitted to Foundations and Trends in Signal Processin