Relativized polynomial hierarchies extending two levels

The existence of relativized polynomial hierarchies extending exactly two levels is shown. More precisely, oraclesX andY are constructed such thatNP(X) ₂ ^{P, X} = ₂ ^{P, X} and ₂ ^{P, Y} ₂ ^{P, Y} = ₂ ^{P, Y} . These results answer a question posed by Baker, Gill, and Solovay ([1]) and generalize their constructions of relativized polynomial hierarchies extending 0 resp. 1 level; i.e.,P(A) = NP(A) resp.P(B) NP(B) = coNP(B) for recursive oraclesA andB.     

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.     

A Delay-Averaged Logistic Model

For the equation x(t) = x(t) (1-(1/) _t-- ^t- x(u)du), > 0, > 0, > 0, conditions for the stability of a nonzero stationary solution under small perturbations are determined.     

Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of knowledge they contain (i.e., the level of support they provide) and in their ability to learn (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ Prolog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend Prolog with the necessity operator of modal logic. We develop a meta-interpreter realizing EBG for the extended language, Prolog, and provide examples of higher-order EBG.     

Two and three-quarter dimensional meshing facilitators

This paper presents generated enhancements for robust two and three-quarter dimensional meshing, including: (1) automated interval assignment by integer programming for submapped surfaces and volumes, (2) surface submapping, and (3) volume submapping. An introduction to the simplex method, an optimization technique of integer programming, is presented. Simplification of complex geometry is required for the formulation of the integer programming problem. A method of i-j unfolding is defined which explains how irregular geometry can be realigned into a simplified form that is suitable for submap interval assignment solutions. Also presented is the processes by which submapping eliminates the decomposition of surface geometry, through a pseudodecomposition process, producing suitable mapped meshes. The process of submapping involves the creation of interpolated virtual edges, user defined vertex types and i-j-k space traversals. The creation of interpolated virtual edges is the method by which submapping automatically subdivides surface geometry. The interpolated virtual edge is formulated according to an interpolation scheme using the node discretization of curves on the surface. User defined vertex types allow direct user control of surface decomposition and interval assignment by modifying i-j-k space traversals. Volume submapping takes the geometry decomposition to a higher level by using mapped virtual surfaces to eliminate decomposition of complex volumes.     

The conjoinability relation in Lambek calculus and linear logic

In 1958 J. Lambek introduced a calculusL of syntactic types and defined an equivalence relation on types: x y means that there exists a sequence x=x₁,...,x_n=y (n 1), such thatx _i x _i+1 or x_i+ x _i (1 i n). He pointed out thatx y if and only if there is joinz such thatx z andy z. This paper gives an effective characterization of this equivalence for the Lambeck calculiL andLP, and for the multiplicative fragments of Girard's and Yetter's linear logics. Moreover, for the non-directed Lambek calculusLP and the multiplicative fragment of Girard's linear logic, we present linear time algorithms deciding whether two types are equal, and finding a join for them if they are.The author was sponsored by project NF 102/62-356 (Structural and Semantic Parallels in Natural Languages and Programming Languages), funded by the Netherlands Organization for the Advancement of Research (N.W.O.).     

Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) K(₁... _N ) is attained, given the cost f( _i ) of a message ₁... _N . Various extremal relations between the message cost and the Kolmogorov complexity are also considered; in particular, the minimization problem for the function f( _i ) – K(₁... _N ) is studied. Here, is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.     

A Hyperbase for Binary Lattice Hyperidentities

We define an identity to be hypersatisfied by a variety V if, whenever the operation symbols of V, are replaced by arbitrary terms (of appropriate arity) in the operations of V, the resulting identity is satisfied by V in the usual sense. Whenever the identity is hypersatisfied by a variety V, we shall say that is a V hyperidentity. For example, the identity x + x y = x (x + y) is hypersatisfied by the variety L of all lattices. A proof of this consists of a case-by-case examination of { + , } {x, y, x y, x y}, the set of all binary lattice terms. In an earlier work, we exhibited a hyperbase ^L for the set of all binary lattice (or, equivalently, quasilattice) hyperidentities of type 2, 2. In this paper we provide a greatly refined hyperbase _L . The proof that _L is a hyperbase was obtained by using the automated reasoning program Otter 3.0.4.     

Finite canonical rewriting systems for congruences generated by concurrency relations

WhenC is a concurrency relation on alphabet , then ^*/= _C is a free partially commutative monoid. Here we show that it is decidable in polynomial time whether or not there exists a finite canonical rewriting systemR on such that the congruences _R ^* generated byR and = _C induced byC coincide. Further, in case such a systemR exists, one such system can be determined in polynomial time.     

Optimum design of Beck's column with a constraint on the static buckling load

The paper is concerned with optimization of a damped column subjected to a follower load. The aim is to determine the colum of least volume which has the same critical load as a uniform reference column. The stability analysis is based on the finite element method. The optimization problem is solved by sequential linear programming. By only including a constraint on the flutter load in the volume minimization, a very large volume reduction is possible but the static buckling load (by a pure conservative loading) becomes very small.In applications, it may be important that the optimal column also is capable of supporting a conservative load. Consequently, the volume is minimized with constraints on both the flutter load and the static buckling load. The constraint on the buckling loadp _b has the formp _b ^opt cp _b ⁰ , 0c1, where the upper index opt refers to the optimal design while the upper index 0 refers to the uniform initial design. It is found that, as the constantc approaches 1, the optimal column approaches the optimal Euler column of Tadjbakhsh and Keller (1962).Notation c slack parameter on the constraint on the static buckling load; defined by (9) - c _int,c _ext dimensionless internal and external damping parameters defined by (3) - d _j eigenvalue margin defined by (9) - d vector of time-independent nodal displacements and rotations - _e length of thee-th finite element - L total length of the column - vector of element lengths defined by (11) - m, m(x) mass distribution function - m _i design variables; the mass distribution function evaluated at the nodal points - upper and lower bounds on the design parameters - m design vector with elementsm _i - M mass matrix - N _e the number of finite elements used - p load parameter - Q load matrix - S stiffness matrix - t time - x distance along the column, measured from the clamped end - y lateral deflection of the column - y vector of nodal displacements and rotations - complex eigenvalue - b refers to buckling (static instability by conservative loading) - d refers to divergence (static instability by nonconservative loading) - f refers to flutter (dynamic instability by nonconservative loading)     

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.     

Representation of Algebraic Functions As Power and Fractional Power Series of Special Type

A Maple procedure is described by means of which an algebraic function given by an equation f(x y) = 0 can be expanded into a fractional power series (Puiseux series)

Automatic Extraction of Collocations From Korean Text

In this paper, we propose a statistical method to automaticallyextract collocations from Korean POS-tagged corpus. Since a large portion of language is represented by collocation patterns, the collocational knowledge provides a valuable resource for NLP applications. One difficulty of collocation extraction is that Korean has a partially free word order, which also appears in collocations. In this work, we exploit four statistics, frequency,randomness, convergence, and correlation' in order to take into account the flexible word order of Korean collocations. We separate meaningful bigrams using an evaluation function based on the four statistics and extend the bigrams to n-gram collocations using a fuzzy relation. Experiments show that this method works well for Korean collocations.     

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.     

On characterizations of recursively enumerable languages

Summary Geffert has shown that earch recursively enumerable languageL over can be expressed in the formL{h(x) ^–1 g(x)x in ⁺} ^* where is an alphabet andg, h is a pair of morphisms. Our purpose is to give a simple proof for Geffert's result and then sharpen it into the form where both of the morphisms are nonerasing. In our method we modify constructions used in a representation of recursively enumerable languages in terms of equality sets and in a characterization of simple transducers in terms of morphisms. As direct consequences, we get the undecidability of the Post correspondence problem and various representations ofL. For instance,L =(L ₀) ^* whereL ₀ is a minimal linear language and is the Dyck reductiona, A.     

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.     

A combinatorial property of EOL languages

Let be an alphabet and II its nontrivial binary partition. Each word over can uniquely be decomposed in subwords (called blocks) consisting of letters of II _i only,i {1,2}. LetK ^*.K has a long block property (with respect to II), abbreviated asLB-property, if there exists a functionf:N ⁺ N ⁺ such that for everyw K and every positive integerm the number of blocks of length at mostm inw is bounded byf(m). K has a clustered block property (with respect to II), abbreviated asCB-property, if there exists a positive integern _o and a growing functiong:N ⁺ N ⁺ such that for everyw K and for every positive integerm the blocks of length at mostm can be covered by at mostn _o segments of length at mostg(m).It is proved that aCB-property always implies aLB-property but not necessarily other way around. It is proved that an EOL language has aLB-property if and only if it has aCB-property.     

On a random Volterra integral equation

Summary Tsokos [12] showed the existence of a unique random solution of the random Volterra integral equation (*)x(t; ) = h(t; ) + _o ^t k(t, ; )f(, x(; )) d, where , the supporting set of a probability measure space (,A, P). It was required thatf must satisfy a Lipschitz condition in a certain subset of a Banach space. By using an extension of Banach's contraction-mapping principle, it is shown here that a unique random solution of (*) exists whenf is (, )-uniformly locally Lipschitz in the same subset of the Banach space considered in [12].     

Optimization and experimental investigations of stiffened, axially compressed CFRP-panels

Thin-walled, unstiffened and stiffened shell structures made of fibre composite materials are frequently applied due to their high stiffness/strength to weight ratios in all fields of lightweight constructions. One major design criterion of these structures is their sensitivity with respect to buckling failure when subjected to inplane compression and shear loads. This paper describes how the structural analysis program BEOS (Buckling of Eccentrically Orthotropic Sandwich shells) is combined with the optimization procedure SAPOP (Structural Analysis Program and Optimization Procedure) to produce a tool for designing optimum CFRP-panels against buckling. Experimental investigations are used to justify the described procedures.Nomenclature C, C _b material stiffness matrices (shell, beam stiffener) - f objective function - F _cr buckling load - g vector of inequality constraints - K,K _g , stiffness matrix, geometrical stiffness matrix, condensed stiffness matrix - n _s ,n _b vector of stress resultants (shell, beam stiffener) - N _x ,N _y ,N _xy membrane forces of the shell - P _x ,P _y ,P _xy membrane forces of the stiffener - r _x ,r _y ,r _xy radii of curvature - ⁿ n-dimensional Euclidean space - W strain energy - u, v, w deformations inx, y, z direction - x, y, z global coordinate system - x vector of design variables - y, z right-hand side, left-hand side eigenvector - variational symbol - _i ^k Kronecker's delta - e _s ,e _b strain vectors (shell, beam stiffener) - , _cr load factor, buckling load factor - , e total energy, external potential energy A (^) sign above a variable points out that this variable belongs to the prebuckling state.