This article focuses on three themes concerning determinism and indeterminism. The first theme is observational equivalence between deterministic and indeterministic models. Here I discuss several results about observational equivalence and present an argument on how to choose between deterministic and indeterministic models involving indirect evidence. The second theme is whether Newtonian phy...

We introduce the following notion of weak equivalence between shifts of nite type: two shifts of nite type S and T are equivalent if S = f ?1 (T) and T = g ?1 (S), where f (resp. g) is a sliding block map from A Z to B Z (resp. from B Z to A Z), where S A Z and T B Z. We give a necessary condition for this equivalence and we show how to decide the equivalence when the shifts are given by nite c...

There are continuum many ≤B-incomparable equivalence relations induced by a free, Borel action of a countable non-abelian free group – and hence, there are 20 many treeable countable Borel equivalence relations which are incomparable in the ordering of Borel reducibility

In this appendix we consider a procedure to assess quantitatively whether the expressive or strategic voting model is more appropriate for the state supreme court voting data used in this paper. As we remarked in the main text, for a given set of cases, the first-stage likelihood function for the votes is identical for both the expressive and strategic voting models, and in this sense the two m...

3 Logical Relation Proofs 15 3.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1 Properties of Step-Indexed Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 Approximation Yields Valid Semantic Objects . . . . . . . . . . . . . . . . . . . . . . 17 3.1.3 World Extension and Store Satisfaction Properties . . ...

We consider the problem of checking whether an implementation which contains parts with incomplete information is equivalent to a given full specification. We study implementations which are not completely specified, but contain boxes which are associated with incompletely specified functions (called Incompletely Specified Boxes or IS–Boxes). After motivating the use of implementations with Inc...

This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page http://www.brics.dk/∼srba/roadmap.