Context-free text grammars

A text is a triple=(, ₁, ₂) such that is a labeling function, and ₁ and ₂ are linear orders on the domain of ; hence may be seen as a word (, ₁) together with an additional linear order ₂ on the domain of . The order ₂ is used to give to the word (, ₁) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.     

Unextendible Product Bases and Locally Unconvertible Bound Entangled States

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states _S and _T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision (S,T) > 0 such that for any LOCC protocol mapping _S into a probabilistic ensemble (p, ), the fidelity between _T and any possible final state satisfies F(_T, ) = 1 - (S,T).PACS: 03.65.Bz; 03.67.-a; 89.70+c.     

Duality in Quantum Information Geometry

Let H be a separable Hilbert space. We consider the manifold M consisting of density operators on H such that ^p is of trace class for some p (0, 1). We say M is nearby if there exists C > 1 such that C ^–1C. We show that the space of nearby points to can be furnished with the two flat connections known as the (±)-affine structures, which are dual relative to the BKM metric. We furnish M with a norm making it into a Banach manifold.     

Admissibility of Trajectories for Control Systems Related by Smooth Mappings

We examine the problem of relating a pair of nonlinear control systems by a smooth mapping between their state spaces that sends trajectories of one system onto trajectories of the other. This problem is fundamental to certain notions of hierarchical structure or state aggregation for control systems in which one wishes to relate a low-level, complex system, to a high-level, simpler system. Pappas, Lafferriere, and Sastry have recently introduced the concept of -related systems (where refers to the mapping between the systems state spaces) and have shown that this concept is equivalent to the property that sends trajectories of one system onto trajectories of the other. However, this equivalence does not address any regularity properties of the controls (such as measurability or piecewise smoothness). Thus, in principle, one is not allowed to work with specified admissible classes of trajectories generated by corresponding classes of admissible controls. In this paper we identify several situations in which one can be assured that -related systems do indeed send appropriately defined admissible trajectories of one system onto admissible trajectories of the other. Date received: August 7, 2002. Date revised: January 23, 2003.     

Random sequences in Fréchet spaces

This article deals with the generation of arbitrarily distributed sequences of random variables in a Fréchet space, using sequences ofcanonical random variables (c.r.v.)-i.e., independently uniformly distributed random variables taking real values in the unit interval [0, 1)-orcanonical random digits (c.r.d.)-i.e., independently uniformly distributed random variables taking integer values in some finite interval [0,B–1]. Two main results are established. First, that the members of a sequence of real random variables in [0, 1) are c.r.v. if and only if all the digits of all thebase- B digital representations of the members of the sequence are c.r.d. Secondly, that, given any sequence of random variables in a Fréchet space, there is a sequence of functions _n( ₁, ₂, ..., _n), forn=1, 2, 3,... (where ₁, ₂,..., _n,... are c.r.v.) which is distributed identically to.     

Automated Synthesis of Recursive Programs from a ∀∃ Logical Specification

The specification of a function is often given by a logical formula, called a -formula, of the following form: xy(x,y). More precisely, a specification is given in the context of a certain theory E and is stated by the judgment E xy (x,y).In this paper, we consider the case in which E is an equational theory. It is divided into two parts. In the first part, we develop a theory for the automated proof of such judgments in the initial model ofE . The validity in the initial model means that we consider not only equational theorems but also inductive ones. From our theory we deduce an automated method for the proof of a class of such judgments. In the second part, we present an automatedmethod for program synthesis. We show how the previous proof method can be used to generate a recursive program for a function f that satisfies a judgment E x (x, f(x)).We illustrate our method with the automated synthesis of some recursive programs on domains such as integers and lists. Finally, we describe our system LEMMA, which is an implementation in Common Lisp of these new methods.     

Logic Based Abstractions of Real-Time Systems

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called , n-equivalence, where is a set of actions and n is a natural number. It is proved that two transition systems are , n-equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in , and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set of actions and a natural number n, produces a reduced transition system , n-equivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving , n-equivalence.     

One Connection between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers

The language of standard propositional modal logic has one operator ( or ), that can be thought of as being determined by the quantifiers or , respectively: for example, a formula of the form is true at a point s just in case all the immediate successors of s verify .This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and generalized quantifiers: the combined generalized quantifier conditions of conservativity and extension correspond to the modal condition of invariance under generated submodels, and the modal condition of invariance under bisimulations corresponds to the generalized quantifier being a Boolean combination of and .     

Exact Linear Thermodynamic Evolution Equations from the Robertson Formalism

A linear evolution equation for a thermodynamic variable F, odd under time-reversal, is obtained from the exact equation derived by Robertson from the Liouville equation for the information-theoretic phase-space distribution. One obtains an exact expression for , the relaxation time for F. For very short , is time-independent for t > if C(t) F{exp(-i t)}Fo, the equilibrium time correlation, decays exponentially for t > . is the Liouville operator. So long as C(t) is such that decays rapidly to a steady-state value, the t limit of agrees with the fluctuation-dissipation theorem in applications to fluid transport.     

Minimization of norms and logarithmic norms by diagonal similarities

It is a commonly occurring problem to find good norms · or logarithmic norms (·) for a given matrix in the sense that they should be close to respectively the spectral radius (A) and the spectral abscissa (A). Examples may be the certification thatA is convergent, i.e. (A)A<1 or stable, i.e. (A)(A)<0. Often the ordinary norms do not suffice and one would like to try simple modifications of them such as using an ordinary norm for a diagonally transformed matrix. This paper treats this problem for some of the ordinary norms.

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Minimisierung von Normen und Logarithmischen Normen durch Diagonale Transformationen

Zusammenfassung Ein oft vorkommendes praktisches Problem ist die Konstruktion von guten Normen · und logarithmischen Normen (·) für eine gegebene MatrixA. Mit gut wird dann verstanden, daß A den Spektralradius (A)=max |₁| und (A) die Spektralabszisse (A)=max Re _i gut approximieren. Beispiele findet man für konvergente Matrizen wo (A)A<1 gewünscht ist, und für stabile Matrizen wo (A)(A)<0 zu zeigen ist. Wir untersuchen hier, wie weit man mit Diagonaltransformationen und dengewöhnlichsten Normen kommen kann.

     

On improving the accuracy of the Hough transform

The subject of this paper is very high precision parameter estimation using the Hough transform. We identify various problems that adversely affect the accuracy of the Hough transform and propose a new, high accuracy method that consists of smoothing the Hough arrayH(, ) prior to finding its peak location and interpolating about this peak to find a final sub-bucket peak. We also investigate the effect of the quantizations and ofH(, ) on the final accuracy. We consider in detail the case of finding the parameters of a straight line. Using extensive simulation and a number of experiments on calibrated targets, we compare the accuracy of the method with results from the standard Hough transform method of taking the quantized peak coordinates, with results from taking the centroid about the peak, and with results from least squares fitting. The largest set of simulations cover a range of line lengths and Gaussian zero-mean noise distributions. This noise model is ideally suited to the least squares method, and yet the results from the method compare favorably. Compared to the centroid or to standard Hough estimates, the results are significantly better—for the standard Hough estimates by a factor of 3 to 10. In addition, the simulations show that as and are increased (i.e., made coarser), the sub-bucket interpolation maintains a high level of accuracy. Experiments using real images are also described, and in these the new method has errors smaller by a factor of 3 or more compared to the standard Hough estimates.     

To the Metrical Rigidity of Binary Codes

A code C in the n-dimensional metric space E ⁿ over GF(2) is called metrically rigid if each isometry I : C E ⁿ can be extended to an isometry of the whole space E ⁿ . For n large enough, metrical rigidity of any length-n binary code that contains a 2-(n, k, )-design is proved. The class of such codes includes, for instance, all families of uniformly packed codes of large enough lengths that satisfy the condition d – 2, where d is the code distance and is the covering radius.     

The π-Calculus in Direct Style

We introduce a calculus which is a direct extension of both the and the calculi. We give a simple type system for it, that encompasses both Curry's type inference for the -calculus, and Milner's sorting for the -calculus as particular cases of typing. We observe that the various continuation passing style transformations for -terms, written in our calculus, actually correspond to encodings already given by Milner and others for evaluation strategies of -terms into the -calculus. Furthermore, the associated sortings correspond to well-known double negation translations on types. Finally we provide an adequate CPS transform from our calculus to the -calculus. This shows that the latter may be regarded as an assembly language, while our calculus seems to provide a better programming notation for higher-order concurrency. We conclude by discussing some alternative design decisions.     

Exact upper bounds of the probability of failure in a time interval in the case of incomplete information on the distribution function

Exact upper bounds are obtained for the probability F() - F(u), 0 < u < < , on the set of distribution functions F(x) of nonnegative random variables with unimodal density with an arbitrary mode m 0 and one or two fixed first moments.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 72–83, September–October 2004.     

ART1: Similarity Measures

This paper concerns with the ART1 (Adaptive Resonance Theory 1) in Neural Network. Important features of ART1 are similarity measure (criterion), vigilance parameter (), and their function to classify the input patterns. Experimental results show that the similarity measure as designed originally does not increase the number of categories with the increased value of but decreases, too. This is against the claim of stability-plasticity dilemma. A number of researchers have considered this and suggested alternative similarity measures. Here, we propose a new similarity criterion which eliminates this problem and also possesses the property of lowest list presentations needed for self stabilization of the network. We compare the results of different similarity criteria experimentally and present them in graphs. Analysis of the network under noisy environment is also carried out.     

Unification in partially commutative semigroups

Unification algorithms have been constructed for semigroups and commutative semigroups. This paper considers the intermediate case of partially commutative semigroups. We introduce classesN and of such semigroups and justify their use. We present an equation-solving algorithm for any member of the classN. This algorithm is relative to having an algorithm to determine all non-negative solutions of a certain class of diophantine equations of degree 2 which we call -equations. The difficulties arising when attempting to solve equations in members of the class are discussed, and we present arguments that strongly suggest that unification in these semigroups is undecidable.     

Maintaining the visibility map of spheres while moving the viewpoint on a circle at infinity

We investigate three-dimensional visibility problems for scenes that consist ofn non-intersecting spheres. The viewing point moves on a flightpath that is part of a circle at infinity given by a planeP and a range of angles {(t)¦t[01]} [02]. At timet, the lines of sight are parallel to the ray inP, which starts in the origin ofP and represents the angle(t) (orthographic views of the scene). We give an algorithm that computes the visibility graph at the start of the flight, all time parameters at which the topology of the scene changes, and the corresponding topology changes. The algorithm has running time0(n + k + p) logn), wheren is the number of spheres in the scene;p is the number of transparent topology changes (the number of different scene topologies visible along the flight path, assuming that all spheres are transparent); andk denotes the number of vertices (conflicts) which are in the (transparent) visibility graph at the start and do not disappear during the flight.The second author was supported by the ESPRIT II Basic Research Actions Program, under Contract No. 3075 (project ALCOM).     

Modelling structures in generic space, a condition for adaptiveness of monitoring cognitive agent

The adaptiveness of agents is one of the basic conditions for the autonomy. This paper describes an approach of adaptiveness forMonitoring Cognitive Agents based on the notion of generic spaces. This notion allows the definition of virtual generic processes so that any particular actual process is then a simple configuration of the generic process, that is to say a set of values of parameters. Consequently, generic domain ontology containing the generic knowledge for solving problems concerning the generic process can be developed. This lead to the design of Generic Monitoring Cognitive Agent, a class of agent in which the whole knowledge corpus is generic. In other words, modeling a process within a generic space becomes configuring a generic process and adaptiveness becomes genericity, that is to say independence regarding technology. In this paper, we present an application of this approach on Sachem, a Generic Monitoring Cognitive Agent designed in order to help the operators in operating a blast furnace. Specifically, the NeuroGaz module of Sachem will be used to present the notion of a generic blast furnace. The adaptiveness of Sachem can then be noted through the low cost of the deployment of a Sachem instance on different blast furnaces and the ability of NeuroGaz in solving problem and learning from various top gas instrumentation.     

The Relative Entropy of Entanglement of Schmidt Correlated States and Distillation

We show that a mixed state = _mna_mn|mn| can be realized by an ensemble of pure states {p_k, |_k} where . Employing this form, we discuss the relative entropy of entanglement of Schmidt correlated states. Also, we calculate the distillable entanglement of a class of mixed states. PACS: 03.67.-a; 03.65.Bz; 03.65.Ud     

Separating complexity classes related to bounded alternating ω-branching programs

We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of -branching programs, : , a semiring homomorphism, that generalizes ordinary branching programs, -branching programs [M2] andMOD _p-branching programs [DKMW].Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating -branching programs we are able to separate the corresponding complexity classesN _ba ,co-N _{ba ba} , andMOD _p - _ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.