Kleene algebra with domain

We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressiveness of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness; second, an algebraic reconstruction of propositional Hoare logic.Comment: 40 page

The theta-join as a join with theta

We present an algebra for the classical database operators. Contrary to most approaches we use (inner) join and projection as the basic operators. Theta joins result by representing theta as a database table itself and defining theta-join as a join with that table. The same technique works for selection. With this, (point-free) proofs of the standard optimisation laws become very simple and uniform. The approach also applies to proving join/projection laws for preference queries. Extending the earlier approach of [16], we replace disjointness assumptions on the table types by suitable consistency conditions. Selected results have been machine-verified using the CALCCHECK tool

Distribution-based bisimulation for labelled Markov processes

In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based bisimulations, our distribution bisimulation is weaker, but corresponds more closely to linear properties. We construct a logic and a metric to describe our distribution bisimulation and discuss linearity, continuity and compositional properties.Comment: Accepted by FORMATS 201

Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist

On Probabilistic Applicative Bisimulation and Call-by-Value λ\lambda-Calculi (Long Version)

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more surprisingly, full-abstraction only holds in a symmetric setting.Comment: 30 page

Multiwavelength Observations of the Hot DB Star PG 0112+104

We present a comprehensive multiwavelength analysis of the hot DB white dwarf PG 0112+104. Our analysis relies on newly-acquired FUSE observations, on medium-resolution FOS and GHRS data, on archival high-resolution GHRS observations, on optical spectrophotometry both in the blue and around Halpha, as well as on time-resolved photometry. From the optical data, we derive a self-consistent effective temperature of 31,300+-500 K, a surface gravity of log g = 7.8 +- 0.1 (M=0.52 Msun), and a hydrogen abundance of log N(H)/N(He) < -4.0. The FUSE spectra reveal the presence of CII and CIII lines that complement the previous detection of CII transitions with the GHRS. The improved carbon abundance in this hot object is log N(C)/N(He) = -6.15 +- 0.23. No photospheric features associated with other heavy elements are detected. We reconsider the role of PG 0112+104 in the definition of the blue edge of the V777 Her instability strip in light of our high-speed photometry, and contrast our results with those of previous observations carried out at the McDonald Observatory.Comment: 10 pages in emulateapj, 9 figures, accepted for publication in Ap

Domain and Antidomain Semigroups

Abstract. We axiomatise and study operations for relational domain and antidomain on semigroups and monoids. We relate this approach with previous axiomatisations for semirings, partial transformation semi-groups and dynamic predicate logic.

Park\u27s Tribolium Competition Experiments: A Non-equilibrium Species Coexistence Hypothesis

1. In this journal 35 years ago, P. H. Leslie, T. Park and D. B. Mertz reported competitive exclusion data for two Tribolium species. It is less well-known that they also reported \u27difficult to interpret\u27 coexistence data. We suggest that the species exclusion and the species coexistence are consequences of a stable coexistence two-cycle in the presence of two stable competitive exclusion equilibria. 2. A stage-structured insect population model for two interacting species forecasts that as interspecific interaction is increased there occurs a sequence of dynamic changes (bifurcations) in which the classic Lotka-Volterra-type scenario with two stable competitive exclusion equilibria is altered abruptly to a novel scenario with three locally stable entities; namely, two competitive exclusion equilibria and a stable coexistence cycle. This scenario is novel in that it predicts the competitive coexistence of two nearly identical species on a single limiting resource and does so under circumstances of increased interspecific competition. This prediction is in contradiction to classical tenets of competition theory

Lattice effects observed in chaotic dynamics of experimental populations

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discretestate models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discretestate models. We suggest that such lattice effects could be an important component of natural population fluctuations. The discovery that simple deterministic population models can display complex aperiodi