Layered Fixed Point Logic

We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive specifications of properties. Two main theoretical contributions are a Moore Family result and a parametrized worst case time complexity result. We show that the logic and the associated solver can be used for rapid prototyping and illustrate a wide variety of applications within Static Analysis, Constraint Satisfaction Problems and Model Checking. In all cases the complexity result specializes to the worst case time complexity of the classical methods

Gate-controlled reversible rectifying behaviour in tunnel contacted atomically-thin MoS2_{2} transistor

Atomically-thin 2D semiconducting materials integrated into van der Waals heterostructures have enabled architectures that hold great promise for next generation nanoelectronics. However, challenges still remain to enable their full acceptance as compliant materials for integration in logic devices. Two key-components to master are the barriers at metal/semiconductor interfaces and the mobility of the semiconducting channel, which endow the building-blocks of ${pn}$ diode and field effect transistor. Here, we have devised a reverted stacking technique to intercalate a wrinkle-free h-BN tunnel layer between MoS$_{2}$ channel and contacting electrodes. Vertical tunnelling of electrons therefore makes it possible to suppress the Schottky barriers and Fermi level pinning, leading to homogeneous gate-control of the channel chemical potential across the bandgap edges. The observed unprecedented features of ambipolar ${pn}$ to ${np}$ diode, which can be reversibly gate tuned, paves the way for future logic applications and high performance switches based on atomically thin semiconducting channel.Comment: 23 pages, 5 main figures + 9 SI figure

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

On the Complexity of Temporal-Logic Path Checking

Given a formula in a temporal logic such as LTL or MTL, a fundamental problem is the complexity of evaluating the formula on a given finite word. For LTL, the complexity of this task was recently shown to be in NC. In this paper, we present an NC algorithm for MTL, a quantitative (or metric) extension of LTL, and give an NCC algorithm for UTL, the unary fragment of LTL. At the time of writing, MTL is the most expressive logic with an NC path-checking algorithm, and UTL is the most expressive fragment of LTL with a more efficient path-checking algorithm than for full LTL (subject to standard complexity-theoretic assumptions). We then establish a connection between LTL path checking and planar circuits, which we exploit to show that any further progress in determining the precise complexity of LTL path checking would immediately entail more efficient evaluation algorithms than are known for a certain class of planar circuits. The connection further implies that the complexity of LTL path checking depends on the Boolean connectives allowed: adding Boolean exclusive or yields a temporal logic with P-complete path-checking problem

2D Iterative MAP Detection: Principles and Applications in Image Restoration

The paper provides a theoretical framework for the two-dimensional iterative maximum a posteriori detection. This generalization is based on the concept of detection algorithms BCJR and SOVA, i.e., the classical (one-dimensional) iterative detectors used in telecommunication applications. We generalize the one-dimensional detection problem considering the spatial ISI kernel as a two-dimensional finite state machine (2D FSM) representing a network of the spatially concatenated elements. The cellular structure topology defines the design of the 2D Iterative decoding network, where each cell is a general combination-marginalization statistical element (SISO module) exchanging discrete probability density functions (information metrics) with neighboring cells. In this paper, we statistically analyse the performance of various topologies with respect to their application in the field of image restoration. The iterative detection algorithm was applied on the task of binarization of images taken from a CCD camera. The reconstruction includes suppression of the defocus caused by the lens, CCD sensor noise suppression and interpolation (demosaicing). The simulations prove that the algorithm provides satisfactory results even in the case of an input image that is under-sampled due to the Bayer mask

A Multispin Algorithm for the Kob-Andersen Stochastic Dynamics on Regular Lattices

The aim of the paper is to propose an algorithm based on the Multispin Coding technique for the Kob-Andersen glassy dynamics. We first give motivations to speed up the numerical simulation in the context of spin glass models [M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)], after defining the Markovian dynamics as in [W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993)] as well as the related interesting observables, we extend it to the more general framework of random regular graphs, listing at the same time some known analytical results [C. Toninelli, G. Biroli, D.S. Fisher, J. Stat. Phys. 120, 167 (2005)]. The purpose of this work is a dual one, firstly, we describe how bitwise operators can be used to build up the algorithm by carefully exploiting the way data are stored on a computer. Since it was first introduced [M. Creutz, L. Jacobs, C. Rebbi, Phys. Rev. D 20, 1915 (1979), C. Rebbi, R.H. Swendsen, Phys. Rev. D 21, 4094 (1980)], this technique has been widely used to perform Monte Carlo simulations for Ising and Potts spin systems, however, it can be successfully adapted to more complex systems in which microscopic parameters may assume boolean values. Secondly, we introduce a random graph in which a characteristic para- meter allows to tune the possible transition point. A consistent part is devoted to listing the numerical results obtained by running numerical simulations

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546