The Algebraic Intersection Type Unification Problem

The algebraic intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the algebraic intersection type unification problem is decidable. We give the first nontrivial lower bound for the problem by showing (our main result) that it is exponential time hard. Furthermore, we show that this holds even under rank 1 solutions (substitutions whose codomains are restricted to contain rank 1 types). In addition, we provide a fixed-parameter intractability result for intersection type matching (one-sided unification), which is known to be NP-complete. We place the algebraic intersection type unification problem in the context of unification theory. The equational theory of intersection types can be presented as an algebraic theory with an ACI (associative, commutative, and idempotent) operator (intersection type) combined with distributivity properties with respect to a second operator (function type). Although the problem is algebraically natural and interesting, it appears to occupy a hitherto unstudied place in the theory of unification, and our investigation of the problem suggests that new methods are required to understand the problem. Thus, for the lower bound proof, we were not able to reduce from known results in ACI-unification theory and use game-theoretic methods for two-player tiling games

Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis

We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on combinatory logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation {\textemdash} is there a combinatory term e with type tau relative to an environment Gamma? {\textemdash} can be used to synthesize compositions. Here, Gamma represents the repository in the form of typed combinators, tau specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.Comment: In Proceedings ITRS 2012, arXiv:1307.784

Bounded Combinatory Logic

In combinatory logic one usually assumes a fixed set of basic combinators (axiom schemes), usually K and S. In this setting the set of provable formulas (inhabited types) is PSPACE-complete in simple types and undecidable in intersection types. When arbitrary sets of axiom schemes are considered, the inhabitation problem is undecidable even in simple types (this is known as Linial-Post theorem). k-bounded combinatory logic with intersection types arises from combinatory logic by imposing the bound k on the depth of types (formulae) which may be substituted for type variables in axiom schemes. We consider the inhabitation (provability) problem for k-bounded combinatory logic: Given an arbitrary set of typed combinators and a type tau, is there a combinatory term of type tau in k-bounded combinatory logic? Our main result is that the problem is (k+2)-EXPTIME complete for k-bounded combinatory logic with intersection types, for every fixed k (and hence non-elementary when k is a parameter). We also show that the problem is EXPTIME-complete for simple types, for all k. Theoretically, our results give new insight into the expressive power of intersection types. From an application perspective, our results are useful as a foundation for composition synthesis based on combinatory logic

The Intersection Type Unification Problem

The intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the unification problem is decidable. We give the first nontrivial lower bound for the problem by showing (our main result) that it is exponential time hard. Furthermore, we show that this holds even under rank 1 solutions (substitutions whose codomains are restricted to contain rank 1 types). In addition, we provide a fixed-parameter intractability result for intersection type matching (one-sided unification), which is known to be NP-complete. We place the intersection type unification problem in the context of unification theory. The equational theory of intersection types can be presented as an algebraic theory with an ACI (associative, commutative, and idempotent) operator (intersection type) combined with distributivity properties with respect to a second operator (function type). Although the problem is algebraically natural and interesting, it appears to occupy a hitherto unstudied place in the theory of unification, and our investigation of the problem suggests that new methods are required to understand the problem. Thus, for the lower bound proof, we were not able to reduce from known results in ACI-unification theory and use game-theoretic methods for two-player tiling games

Deciding Liveness in Component-Based Systems is NP-hard

Interaction systems are a formal model for component-based systems. Combining components via connectors to form more complex systems may give rise to deadlock situations. In a system that has been shown to be deadlock-free one can ask if a set of components is live. We present here a polynomial time reduction from 3-SAT to the question whether a set of components is live in a deadlock-free system

Establishing Properties of Interaction Systems

We exhibit sufficient conditions for generic properties of component based systems. The model we use to describe component based systems is the formalism of interaction systems. Because the state space explosion problem is encountered in interaction systems (i.e., an exploration of the state space gets unfeasible for a large number of components), we follow the guideline that these conditions have to be checkable efficiently (i.e., in time polynomial in the number of components). Further, the conditions are designed in such a way that the information gathered is reusable if a condition is not satisfied. Concretely, we consider deadlock-freedom and progress in interaction systems. We state a sufficient condition for deadlock-freedom that is based on an architectural constraint: We define what it means for an interaction system to be tree-like, and we derive a sufficient condition for deadlock-freedom of such systems. Considering progress, we first present a characterization of this property. Then we state a sufficient condition for progress which is based on a directed graph. We combine this condition with the characterization to point out one possibility to proceed if the graph-criterion does not yield progress. Both sufficient conditions can be checked efficiently because they only require the investigation of certain subsystems. Finally, we consider the effect that failure of some parts of the system has on deadlock-freedom and progress. We define robustness of deadlock-freedom respectively progress under failure, and we explain how the sufficient conditions above have to be adapted in order to be also applicable in this new situation

CALLISTO: towards reusability of a rocket stage: current status

JAXA, CNES and DLR have decided to cooperate to develop and fly a scaled reusable VTVL rocket stage called CALLISTO (Cooperative Action Leading to Launcher Innovation in Stage Toss - back Operations). This vehicle is paving the way for future reusable launch vehicles in Europe and in Japan. During phase B important progress in term of methods and operation philosophy specific to RLV have been made. Amongst other progresses, that will ease the development of future operational VTVL, in the domain of aerodynamic modelling, GNC landing leg deployment but also flight domain definitions are presented. These are concrete results which can at least partly be useful for other RLV projects

Genomic evolution of breast cancer metastasis and relapse

A.G.L. and J.H.R.F. were supported by a Cancer Research UK Program Grant to Simon Tavaré (C14303/A17197).Patterns of genomic evolution between primary and metastatic breast cancer have not been studied in large numbers, despite patients with metastatic breast cancer having dismal survival. We sequenced whole genomes or a panel of 365 genes on 299 samples from 170 patients with locally relapsed or metastatic breast cancer. Several lines of analysis indicate that clones seeding metastasis or relapse disseminate late from primary tumors, but continue to acquire mutations, mostly accessing the same mutational processes active in the primary tumor. Most distant metastases acquired driver mutations not seen in the primary tumor, drawing from a wider repertoire of cancer genes than early drivers. These include a number of clinically actionable alterations and mutations inactivating SWI-SNF and JAK2-STAT3 pathways.Publisher PDFPeer reviewe

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization.

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD