Controllability in partial and uncertain environments

© 2014 IEEE.Controller synthesis is a well studied problem that attempts to automatically generate an operational behaviour model of the system-to-be that satisfies a given goal when deployed in a given domain model that behaves according to specified assumptions. A limitation of many controller synthesis techniques is that they require complete descriptions of the problem domain. This is limiting in the context of modern incremental development processes when a fully described problem domain is unavailable, undesirable or uneconomical. Previous work on Modal Transition Systems (MTS) control problems exists, however it is restricted to deterministic MTSs and deterministic Labelled Transition Systems (LTS) implementations. In this paper we study the Modal Transition System Control Problem in its full generality, allowing for nondeterministic MTSs modelling the environments behaviour and nondeterministic LTS implementations. Given an nondeterministic MTS we ask if all, none or some of the nondeterministic LTSs it describes admit an LTS controller that guarantees a given property. We show a technique that solves effectively the MTS realisability problem and it can be, in some cases, reduced to deterministic control problems. In all cases the MTS realisability problem is in same complexity class as the corresponding LTS problem

Recognising Multidimensional Euclidean Preferences

Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as multidimensional unfolding, has applications in economics, psychometrics, marketing, and many other fields. We study the problem of deciding whether a given preference profile is d-Euclidean. For the one-dimensional case, polynomial-time algorithms are known. We show that, in contrast, for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard. We further show that some Euclidean preference profiles require exponentially many bits in order to specify any Euclidean embedding, and prove that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d > 1. We also study dichotomous preferencesand the behaviour of other metrics, and survey a variety of related work.Comment: 17 page

Bibliography on Realizability

AbstractThis document is a bibliography on realizability and related matters. It has been collected by Lars Birkedal based on submissions from the participants in “A Workshop on Realizability Semantics and Its Applications”, Trento, Italy, June 30–July 1, 1999. It is available in BibTEX format at the following URL: http://www.cs.cmu.edu./~birkedal/realizability-bib.html

Analysis of methods for extraction of programs from non-constructive proofs

The present thesis compares two computational interpretations of non-constructive proofs: refined A-translation and Gödel's functional "Dialectica" interpretation. The behaviour of the extraction methods is evaluated in the light of several case studies, where the resulting programs are analysed and compared. It is argued that the two interpretations correspond to specific backtracking implementations and that programs obtained via the refined A-translation tend to be simpler, faster and more readable than programs obtained via Gödel's interpretation. Three layers of optimisation are suggested in order to produce faster and more readable programs. First, it is shown that syntactic repetition of subterms can be reduced by using let-constructions instead of meta substitutions abd thus obtaining a near linear size bound of extracted terms. The second improvement allows declaring syntactically computational parts of the proof as irrelevant and that this can be used to remove redundant parameters, possibly improving the efficiency of the program. Finally, a special case of induction is identified, for which a more efficient recursive extracted term can be defined. It is shown the outcome of case distinctions can be memoised, which can result in exponential improvement of the average time complexity of the extracted program