Characterization of quantum states in predicative logic

We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of random first order domain and find a characterization of pure states in predicative logic and mixed states in propositional logic, due to a focusing condition. We discuss the role of first order variables and the related contextuality, in terms of sequents.Comment: 14 pages, Boston, IQSA10, to appea

A new separation result for Euler-Lagrange-like systems

This paper presents a separation result for some global stabilization via output feedback of a class of quadratic-like nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and unboundedness observability on the other hand. They allow to design, for any domain of output initial condition, a dynamic output feedback controller achieving global stability. As an example, these conditions are shown to be satisfied by so-called Euler-Lagrange systems, for which a tracking output feedback control law is thus proposed

Basic Logic and Quantum Entanglement

As it is well known, quantum entanglement is one of the most important features of quantum computing, as it leads to massive quantum parallelism, hence to exponential computational speed-up. In a sense, quantum entanglement is considered as an implicit property of quantum computation itself. But...can it be made explicit? In other words, is it possible to find the connective "entanglement" in a logical sequent calculus for the machine language? And also, is it possible to "teach" the quantum computer to "mimic" the EPR "paradox"? The answer is in the affirmative, if the logical sequent calculus is that of the weakest possible logic, namely Basic logic. A weak logic has few structural rules. But in logic, a weak structure leaves more room for connectives (for example the connective "entanglement"). Furthermore, the absence in Basic logic of the two structural rules of contraction and weakening corresponds to the validity of the no-cloning and no-erase theorems, respectively, in quantum computing.Comment: 10 pages, 1 figure,LaTeX. Shorter version for proceedings requirements. Contributed paper at DICE2006, Piombino, Ital

A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

A multimicro system for high performance control applications

A computing architecture based on digital signal processors (DSPs) is presented for high-performance control applications. This computing system efficiently handles heavy computational loads, which typically arise when controlled plants have fast and nonlinear dynamics. In fact, general purpose computer are not a cheap nor convenient solution in those cases. The system is designed upon the structure of a hierarchical controller and it consists of a "decision" level consisting of a general purpose HOST computer and an "actuator" level (DSPs), directly connected to the plant. The synchronization and the real-time communications between the HOST and a DSP are implemented by two memory banks alternatively connected to the HOST and the DSP . A complete transparency and a minimum overhead result for the tasks running on the DSP. The system has been tested in a high demanding robotics application

An architecture for high performance control using digital signal processing chips

Increasingly demanding industrial applications require fast and cheap computing tools for real-time control. For example, high performance industrial robotics would benefit from fast and cheap computing, but fast structures are generally expensive and dedicated to particular tasks [ 1,2,3]. Another example which requires fast computing is the control of electrical transients of ac motors, where complex numerical computations must be carried out within times like 1 ms [4]. A recent paper described implementation of a self-tuning controller which uses a digital signal processing chip for rapid calculations [5]. For many control applications there is a natural hierarchical structure so that algorithms devoted to simple tasks are placed at the lowest level (for example, controlling a robot axis or determining the switching time of a static converter), whereas complex tasks are at the high levels, forming a pyramidal control structure which reflects the multilevel structure described by Mesarovic [6].I n such a structure, tasks are usually repetitive and involve rapid manipulation of data, directly derived from the measurements of sensors, while high-level tasks are done over larger time intervals with more complex algorithms. This paper describes a computing structure taking into account the hierarchical considerations above. The architecture consists of a high level general purpose computer (HOST) and up to eight digital signal processors (DSPs) which can be interfaced with the controlled plant(s). The high-level computer is either a work station or an advanced personal computer with sufficient memory space (RAM and mass memory), equipped with peripherals for implementation of user-friendly interface and with the ability to communicate with other computers, perhaps in a local network. The synchronization and the real-time communications between the HOST and a DSP are implemented by the two memory bank alternatively switched between the HOST and the DSP. A complete transparency and a minimum overhead result for the tasks running on the DSP

A new separation result for a class of quadratic-like systems with application to Euler-Lagrange models

A separation result for some kind of global stabilization via output feedback of a class of nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and some unboundedness observability on the other hand is presented. They allow to design, for any domain of output initial condition, some dynamic output feedback controller achieving global stability. It is also highlighted how disturbance attenuation can further be achieved on the same basis. As an example, the proposed conditions are shown to be satis7ed by the class of so-called Euler–Lagrange systems, for which a tracking output feedback control law is thus proposed