400 research outputs found
On better-quasi-ordering classes of partial orders
We provide a method of constructing better-quasi-orders by generalising a
technique for constructing operator algebras that was developed by Pouzet. We
then generalise the notion of -scattered to partial orders, and use our
method to prove that the class of -scattered partial orders is
better-quasi-ordered under embeddability. This generalises theorems of Laver,
Corominas and Thomass\'{e} regarding -scattered linear orders and
trees, countable forests and N-free partial orders respectively. In particular,
a class of countable partial orders is better-quasi-ordered whenever the class
of indecomposable subsets of its members satisfies a natural strengthening of
better-quasi-order.Comment: v1: 45 pages, 8 figures; v2: 44 pages, 11 figures, minor corrections,
fixed typos, new figures and some notational changes to improve clarity; v3:
45 pages, 12 figures, changed the way the paper is structured to improve
clarity and provide examples earlier o
Fair Testing
In this paper we present a solution to the long-standing problem of characterising the coarsest liveness-preserving pre-congruence with respect to a full (TCSP-inspired) process algebra. In fact, we present two distinct characterisations, which give rise to the same relation: an operational one based on a De Nicola-Hennessy-like testing modality which we call should-testing, and a denotational one based on a refined notion of failures. One of the distinguishing characteristics of the should-testing pre-congruence is that it abstracts from divergences in the same way as Milner¿s observation congruence, and as a consequence is strictly coarser than observation congruence. In other words, should-testing has a built-in fairness assumption. This is in itself a property long sought-after; it is in notable contrast to the well-known must-testing of De Nicola and Hennessy (denotationally characterised by a combination of failures and divergences), which treats divergence as catrastrophic and hence is incompatible with observation congruence. Due to these characteristics, should-testing supports modular reasoning and allows to use the proof techniques of observation congruence, but also supports additional laws and techniques. Moreover, we show decidability of should-testing (on the basis of the denotational characterisation). Finally, we demonstrate its advantages by the application to a number of examples, including a scheduling problem, a version of the Alternating Bit-protocol, and fair lossy communication channel
Indeterminateness and `The' Universe of Sets: Multiversism, Potentialism, and Pluralism
In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views
On path-based coalgebras and weak notions of bisimulation
It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of so-called silent actions is not yet fully developed. In this paper, we give a coalgebraic characterisation of branching (delay) bisimulation in the context of labelled transition systems (fully probabilistic systems). It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise the respected bisimulation relations in both cases
Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
We use the structure lattice, introduced in Part I, to undertake a systematic
study of the class consisting of compactly generated,
topologically simple, totally disconnected locally compact groups that are
non-discrete. Given , we show that compact open subgroups of
involve finitely many isomorphism types of composition factors, and do not
have any soluble normal subgroup other than the trivial one. By results of Part
I, this implies that the centraliser lattice and local decomposition lattice of
are Boolean algebras. We show that the -action on the Stone space of
those Boolean algebras is minimal, strongly proximal, and micro-supported.
Building upon those results, we obtain partial answers to the following key
problems: Are all groups in abstractly simple? Can a group in
be amenable? Can a group in be such that the
contraction groups of all of its elements are trivial?Comment: 82 page
A generic operational metatheory for algebraic effects
We provide a syntactic analysis of contextual preorder and equivalence for a polymorphic programming language with effects. Our approach applies uniformly across a range of algebraic effects, and incorporates, as instances: errors, input/output, global state, nondeterminism, probabilistic choice, and combinations thereof. Our approach is to extend Plotkin and Power’s structural operational semantics for algebraic effects (FoSSaCS 2001) with a primitive “basic preorder” on ground type computation trees. The basic preorder is used to derive notions of contextual preorder and equivalence on program terms. Under mild assumptions on this relation, we prove fundamental properties of contextual preorder (hence equivalence) including extensionality properties and a characterisation via applicative contexts, and we provide machinery for reasoning about polymorphism using relational parametricity
Partial Identification in Matching Models for the Marriage Market
We study partial identification of the preference parameters in models of
one-to-one matching with perfectly transferable utilities, without imposing
parametric distributional restrictions on the unobserved heterogeneity and with
data on one large market. We provide a tractable characterisation of the
identified set, under various classes of nonparametric distributional
assumptions on the unobserved heterogeneity. Using our methodology, we
re-examine some of the relevant questions in the empirical literature on the
marriage market which have been previously studied under the Multinomial Logit
assumption
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