Related papers: Bisimilarity is not Borel
We initiate the effective metric structure theory of Keisler randomizations. We show that a classical countable structure $\mathcal{M}$ has a decidable presentation if and only if its Borel randomization $\mathcal{M}^{[0,1)}$ has a…
We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
We prove a number of results motivated by global questions of uniformity in computability theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of…
We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism),…
We study the complexity with respect to Borel reducibility of the relations of isometry and isometric embeddability between ultrametric Polish spaces for which a set $D$ of possible distances is fixed in advance. These are, respectively, an…
We provide time lower bounds for sequential and parallel algorithms deciding bisimulation on labeled transition systems that use partition refinement. For sequential algorithms this is $\Omega((m \mkern1mu {+} \mkern1mu n ) \mkern-1mu \log…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E is essentially…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
We define some natural notions of strong and weak Borel Ramsey properties for countable Borel equivalence relations and show that they hold for a countable Borel equivalence relation if and only if the equivalence relation is smooth. We…
We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility hierarchy, comparing and contrasting it with…
Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
We study the nature of applicative bisimilarity in $\lambda$-calculi endowed with operators for sampling from continuous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide…
We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in Desharnais [*] does not…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…