1,472 research outputs found
Randomizations of models as metric structures
The notion of a randomization of a first order structure was introduced by
Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was
to form a new structure whose elements are random elements of the original
first order structure. In this paper we treat randomizations as continuous
structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the
earlier results show that the randomization of a complete first order theory is
a complete theory in continuous logic that admits elimination of quantifiers
and has a natural set of axioms. We show that the randomization operation
preserves the properties of being omega-categorical, omega-stable, and stable
On Roeckle-precompact Polish group which cannot act transitively on a complete metric space
We study when a continuous isometric action of a Polish group on a complete
metric space is, or can be, transitive. Our main results consist of showing
that certain Polish groups, namely and
, such an action can never be transitive (unless the
space acted upon is a singleton). We also point out "circumstantial evidence"
that this pathology could be related to that of Polish groups which are not
closed permutation groups and yet have discrete uniform distance, and give a
general characterisation of continuous isometric action of a Roeckle-precompact
Polish group on a complete metric space is transitive. It follows that the
morphism from a Roeckle-precompact Polish group to its Bohr compactification is
surjective
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
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