Hybridization of institutions

Extended version including all proofsModal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to ‘universalize’ the hybridization idea. Following the lines of [DS07], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institution-independent level. The method extends arbitrary institutions with Kripke semantics (for multi-modalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL) deter- mines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features.Fundação para a Ciência e a Tecnologia (FCT

An Institution for Simple UML State Machines

We present an institution for UML state machines without hierarchical states. The interaction with UML class diagrams is handled via institutions for guards and actions, which provide dynamic components of states (such as valuations of attributes) but abstract away from details of class diagrams. We also study a notion of interleaving product, which captures the interaction of several state machines. The interleaving product construction is the basis for a semantics of composite structure diagrams, which can be used to specify the interaction of state machines. This work is part of a larger effort to build a framework for formal software development with UML, based on a heterogeneous approach using institutions.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1403.774

A Semantic Approach to Interpolation

Interpolation results are investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify more than twenty interpolation results for first-order logic and some for richer logics. A few of these results nontrivially generalize known interpolation results. All the others are new

Modular Construction of Modal Logics

We present a modular approach to defining logics for a wide variety of state-based systems. We use coalgebras to model the behaviour of systems, and modal logics to specify behavioural properties of systems. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular way. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems

Accelerating recurrent neural networks for gravitational wave experiments

This paper presents novel reconfigurable architectures for reducing the latency of recurrent neural networks (RNNs) that are used for detecting gravitational waves. Gravitational interferometers such as the LIGO detectors capture cosmic events such as black hole mergers which happen at unknown times and of varying durations, producing time-series data. We have developed a new architecture capable of accelerating RNN inference for analyzing time-series data from LIGO detectors. This architecture is based on optimizing the initiation intervals (II) in a multi-layer LSTM (Long Short-Term Memory) network, by identifying appropriate reuse factors for each layer. A customizable template for this architecture has been designed, which enables the generation of low-latency FPGA designs with efficient resource utilization using high-level synthesis tools. The proposed approach has been evaluated based on two LSTM models, targeting a ZYNQ 7045 FPGA and a U250 FPGA. Experimental results show that with balanced II, the number of DSPs can be reduced up to 42% while achieving the same IIs. When compared to other FPGA-based LSTM designs, our design can achieve about 4.92 to 12.4 times lower latency

Higher-Order Logic and Theorem Proving for Structured Specifications

In this paper we present the higher-order logic used in theorem-provers like the HOL system (see [GM 93]) or Isabelle HOL logic (see [Paul 94]) as an institution. Then we show that for maps of institutions into HOL that satisfy certain technical conditions we can reuse the proof system of the higher-order logic to reason about structured specifications built over the institutions mapped into HOL. We also show some maps of institutions underlying the CASL specification formalism (see [CASL 99]) into HOL that satisfy conditions needed for reusing proof systems