People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists.

Within a semiparametric framework we propose a test of shape invariance of Engel curves, which is a necessary condition for base independence. Using Canadian family expenditure data for 1996 we reject shape invariance for the fuel and clothing share equations. ∗The first author would like to acknowledge SSHRC of Canada for financial support.

We present a theory of environmental bisimilarity for the delimited-control operators shift and reset. We consider two different notions of contextual equivalence: one that does not require the presence of a top-level control delimiter when executing tested terms, and another one, fully compatible with the original CPS semantics of shift and reset, that does. For each of them, we develop sound ...

We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence. While, at the outset, it might not be clear that this strategy should pay off, our ...

Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering, ≤B , are constructed. There is an analytic ideal on ù generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spa...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

The trace equivalence of BPP was shown to be undecidable by Hirshfeld. We show that the trace equivalence remains undecidable even if the number of labels is restricted to two. The undecidability result holds also for the simulation of two-label BPP processes. These results imply undecidability of some behavioral type systems for the π-calculus.

We describe the inner models with representatives in all equivalence classes of thin equivalence relations in a given projective pointclass of even level assuming projective determinacy. These models are characterized by their correctness and the property that they correctly compute the tree from the appropriate scale. The main lemma shows that the tree from a scale can be reconstructed in a ge...