Descriptive complexity for pictures languages

This paper deals with logical characterizations of picture languages of any dimension by syntactical fragments of existential second-order logic. Two classical classes of picture languages are studied: - the class of "recognizable" picture languages, i.e. projections of languages defined by local constraints (or tilings): it is known as the most robust class extending the class of regular languages to any dimension; - the class of picture languages recognized on "nondeterministic cellular automata in linear time" : cellular automata are the simplest and most natural model of parallel computation and linear time is the minimal time-bounded class allowing synchronization of nondeterministic cellular automata. We uniformly generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of "recognizable" picture languages in existential monadic second-order logic. We state several logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata. They are the first machine-independent characterizations of complexity classes of cellular automata. Our characterizations are essentially deduced from normalization results we prove for first-order and existential second-order logics over pictures. They are obtained in a general and uniform framework that allows to extend them to other "regular" structures

Development and experimentation of LQR/APF guidance and control for autonomous proximity maneuvers of multiple spacecraft

http://dx.doi.org/10.1016/j.actaastro.2010.08.012This work introduces a novel control algorithm for close proximity multiple spacecraft autonomous maneuvers, based on hybrid linear quadratic regulator/artificial potential function (LQR/APF), for applications including autonomous docking, on-orbit assembly and spacecraft servicing. Both theoretical developments and experimental validation of the proposed approach are presented. Fuel consumption is sub-optimized in real-time through re-computation of the LQR at each sample time, while performing collision avoidance through the APF and a high level decisional logic. The underlying LQR/APF controller is integrated with a customized wall-following technique and a decision logic, overcoming problems such as local minima. The algorithm is experimentally tested on a four spacecraft simulators test bed at the Spacecraft Robotics Laboratory of the NAval Postgraduate School. The metrics to evaluate the control algorithm are: autonomy of the system in making decisions, successful completion of the maneuver, required time, and propellant consumption

Development and experimentation of LQR/APF guidance and control for autonomous proximity maneuvers of multiple spacecraft

http://dx.doi.org/10.1016/j.actaastro.2010.08.012This work introduces a novel control algorithm for close proximity multiple spacecraft autonomous maneuvers, based on hybrid linear quadratic regulator/artificial potential function (LQR/APF), for applications including autonomous docking, on-orbit assembly and spacecraft servicing. Both theoretical developments and experimental validation of the proposed approach are presented. Fuel consumption is sub-optimized in real-time through re-computation of the LQR at each sample time, while performing collision avoidance through the APF and a high level decisional logic. The underlying LQR/APF controller is integrated with a customized wall-following technique and a decision logic, overcoming problems such as local minima. The algorithm is experimentally tested on a four spacecraft simulators test bed at the Spacecraft Robotics Laboratory of the NAval Postgraduate School. The metrics to evaluate the control algorithm are: autonomy of the system in making decisions, successful completion of the maneuver, required time, and propellant consumption

Coordination using a Single-Writer Multiple-Reader Concurrent Logic Language

The principle behind concurrent logic programming is a set of processes which co-operate in monotonically constraining a global set of variables to particular values. Each process will have access to only some of the variables, and a process may bind a variable to a tuple containing further variables which may be bound later by other processes. This is a suitable model for a coordination language. In this paper we describe a type system which ensures the co-operation principle is never breached, and which makes clear through syntax the pattern of data flow in a concurrent logic program. This overcomes problems previously associated with the practical use of concurrent logic languages

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

On the Satisfiability of Temporal Logics with Concrete Domains

Temporal logics are a very popular family of logical languages, used to specify properties of abstracted systems. In the last few years, many extensions of temporal logics have been proposed, in order to address the need to express more than just abstract properties. In our work we study temporal logics extended by local constraints, which allow to express quantitative properties on data values from an arbitrary relational structure called the concrete domain. An example of concrete domain can be (Z, <, =), where the integers are considered as a relational structure over the binary order relation and the equality relation. Formulas of temporal logics with constraints are evaluated on data-words or data-trees, in which each node or position is labeled by a vector of data from the concrete domain. We call the constraints local because they can only compare values at a fixed distance inside such models. Several positive results regarding the satisfiability of LTL (linear temporal logic) with constraints over the integers have been established in the past years, while the corresponding results for branching time logics were only partial. In this work we prove that satisfiability of CTL* (computation tree logic) with constraints over the integers is decidable and also lift this result to ECTL*, a proper extension of CTL*. We also consider other classes of concrete domains, particularly ones that are \"tree-like\". We consider semi-linear orders, ordinal trees and trees of a fixed height, and prove decidability in this framework as well. At the same time we prove that our method cannot be applied in the case of the infinite binary tree or the infinitely branching infinite tree. We also look into extending the expressiveness of our logic adding non-local constraints, and find that this leads to undecidability of the satisfiability problem, even on very simple domains like (Z, <, =). We then find a way to restrict the power of the non-local constraints to regain decidability