Staircase visibility and computation of kernels

Let be some set of orientations, that is, . We consider the consequences of defining visibility based on curves that are monotone with respect to the orientations in . We call such curves -staircases. Two points p andq in a polygonP are said to -see each other if an -staircase fromp toq exists that is completely contained inP. The -kernel of a polygonP is then the set of all points which -see all other points. The -kernel of a simple polygon can be obtained as the intersection of all {}-kernels, with . With the help of this observation we are able to develop an algorithm to compute the -kernel of a simple polygon, for finite . We also show how to compute theexternal -kernel of a polygon in optimal time . The two algorithms are combined to compute the ( -kernel of a polygon with holes in time .This work was supported by the Deutsche Forschungsgemeinschaft under Grant No. Ot 64/5-4 and the Natural Sciences and Engineering Research Council of Canada and Information Technology Research Centre of Ontario.     

The computational complexity of recognizing permutation functions

Let be a finite field withq elements and a rational function over . No polynomial-time deterministic algorithm is known for the problem of deciding whetherf induces a permutation on . The problem has been shown to be in co-R co-NP, and in this paper we prove that it is inR NP and hence inZPP, and it is deterministic polynomial-time reducible to the problem of factoring univariate polynomials over . Besides the problem of recognizing prime numbers, it seems to be the only natural decision problem inZPP unknown to be inP. A deterministic test and a simple probabilistic test for permutation functions are also presented.     

Biologically Inspired Autonomous Rover Control

Robotic missions beyond 2013 will likely be precursors to a manned habitat deployment on Mars. Such missions require robust control systems for long duration activities. Current single rover missions will evolve into deployment of multiple, heterogeneous cooperating robotic colonies. This paper describes the map-making memory and action selection mechanism of BISMARC ( iologically nspired ystem for ap-based utonomous over ontrol) that is currently under development at the Jet Propulsion Laboratory in Pasadena, CA (Huntsberger and Rose, Neutral Networks, 11(7/8):1497–1510). BISMARC is an integrated control system for long duration missions involving robots performing cooperative tasks.     

Congruences et Automorphismes des Automates Finis

Summary We study a class of congruences of strongly connected finite automata, called the group congruences, which may be defined in this way: every element fixing any class of the congruence induces a permutation on this class. These congruences form an ideal of the lattice of all congruences of the automaton and we study the group associated with the maximal group congruence (maximal induced group) with respect to the Suschkevitch group of the transition monoid of . The transitivity equivalence of the subgroups of the automorphism group of are found to be the group congruences associated with regular groups, which form also in ideal of the lattice of congruences of . We then characterize the automorphism group of with respect to the maximal induced group. As an application, we show that, given a group G and an automaton , there exists an automaton whose automorphism group is isomorphic to G and such that the quotient by the automorphism congruence is .     

The Complexity of Learning According to Two Models of a Drifting Environment

We show that a bound on the rate of drift of the distribution generating the examples is sufficient for agnostic learning to relative accuracy , where c > 0 is a constant; this matches a known necessary condition to within a constant factor. We establish a sufficient condition for the realizable case, also matching a known necessary condition to within a constant factor. We provide a relatively simple proof of a bound of + on the sample complexity of agnostic learning in a fixed environment.     

On Projection Matrices $$\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, $$ and their Applications in Computer Vision

Projection matrices from projective spaces have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.     

Algorithmic properties of maximal orders in simple algebras over Q

This paper addresses an algorithmic problem related to associative algebras. We show that the problem of deciding if the index of a given central simple algebra over an algebraic number field isd, whered is a given natural number, belongs to the complexity classN P co N P. As consequences, we obtain that the problem of deciding if is isomorphic to a full matrix algebra over the ground field and the problem of deciding if is a skewfield both belong toN P co N P. These results answer two questions raised in [25]. The algorithms and proofs rely mostly on the theory of maximal orders over number fields, a noncommutative generalization of algebraic number theory. Our results include an extension to the noncommutative case of an algorithm given by Huang for computing the factorization of rational primes in number fields and of a method of Zassenhaus for testing local maximality of orders in number fields.     

Fast exponentiation using the truncation operation

Given an integerk, and anarbitrary integer greater than , we prove a tight bound of on the time required to compute with operations {+, –, *, /, ·, }, and constants {0, 1}. In contrast, when the floor operation is not available this computation requires (k) time. Using the upper bound, we give an time algorithm for computing log loga, for alln-bit integersa. This upper bound matches the lower bound for computing this function given by Mansour, Schieber, and Tiwari. To the best of our knowledge these are the first non-constant tight bounds for computations involving the floor operation.     

A Parallel Logarithmic Order Algorithm for General Multibody System Dynamics

A novel optimal order optimal resource parallel multibody algorithm with general system applicability is derived directly from the sequential recursive methods and the most recent developments in recursive constraint treatments. This new Recursive Coordinate Reduction Parallelism (RCRP) is the first optimal order parallel direct method with a sequential implementation that is exactly the efficient algorithm. Consequently, the RCRP sets new benchmarks for performance over a wide range of problem size and parallel resources. Comparisons to existing methods also demonstrate that the RCRP is presently the best general parallel method.     

Solving A\underline x =\underline b Using a Modified Conjugate Gradient Method Based on Roots of A

We consider the modified conjugate gradient procedure for solving A = in which the approximation space is based upon the Krylov space associated with A ^1/p and , for any integer p. For the square-root MCG (p=2) we establish a sharpened bound for the error at each iteration via Chebyshev polynomials in . We discuss the implications of the quickly accumulating effect of an error in in the initial stage, and find an error bound even in the presence of such accumulating errors. Although this accumulation of errors may limit the usefulness of this method when is unknown, it may still be successfully applied to a variety of small, almost-SPD problems, and can be used to jump-start the conjugate gradient method. Finally, we verify these theoretical results with numerical tests.     

Parallel computation of disease transforms

Distance transforms are an important computational tool for the processing of binary images. For ann ×n image, distance transforms can be computed in time (n) on a mesh-connected computer and in polylogarithmic time on hypercube related structures. We investigate the possibilities of computing distance transforms in polylogarithmic time on the pyramid computer and the mesh of trees. For the pyramid, we obtain a polynomial lower bound using a result by Miller and Stout, so we turn our attention to the mesh of trees. We give a very simple (logn) algorithm for the distance transform with respect to theL ₁-metric, an (log² n) algorithm for the transform with respect to theL -metric, and find that the Euclidean metric is much more difficult. Based on evidence from number theory, we conjecture the impossibility of computing the Euclidean distance transform in polylogarithmic time on a mesh of trees. Instead, we approximate the distance transform up to a given error. This works for anyL _k -metric and takes time (log³ n).This research was supported by the Deutsche Forschungsgemeinschaft under Grant Al 253/1-1, Schwerpunktprogramm Datenstrukturen und effiziente Algorithmen.     

Universal asynchronous iterative arrays of Mealy automata

Summary Asynchronous two-dimensional iterative arrays of automata will be introduced where the underlying automata are not of Moore-type but of Mealy-type. We will prove that there exists a Mealy automaton, , with only two states and one input and output for each of its four distinguished directions, such that any given Mealy-automaton can be realized by an iterative array with only for its component-machines. It is known that loop-free nets cannot be as powerful as Mealy automata; however, we will show that any Mealy automaton can be realized by a network, N, with very restrictive component machines, where no signal may pass a loop in N. Using this fact asynchronous iterative arrays can be built up with one component machine, such that any given Mealy automaton can be realized under the restriction that no signal passes a loop more than once. contains only four states and one input and output for each direction.     

Lower Bound Methods and Separation Results for On-Line Learning Models

We consider the complexity of concept learning in various common models for on-line learning, focusing on methods for proving lower bounds to the learning complexity of a concept class. Among others, we consider the model for learning with equivalence and membership queries. For this model we give lower bounds on the number of queries that are needed to learn a concept class in terms of the Vapnik-Chervonenkis dimension of , and in terms of the complexity of learning with arbitrary equivalence queries. Furthermore, we survey other known lower bound methods and we exhibit all known relationships between learning complexities in the models considered and some relevant combinatorial parameters. As it turns out, the picture is almost complete. This paper has been written so that it can be read without previous knowledge of Computational Learning Theory.     

A note on relativized log space

It is shown that there is a recursive oracleD such that, thereby answering an open question of Ladner and Lynch [5]. Here and denote the class of languages accepted in deterministic, respectively nondeterministic, space logn. This work was supported by NSF Grant MCS-8001963.     

The inf-sup condition for low order elements on anisotropic meshes

On a large class of two-dimensional anisotropic meshes, the infsup condition (stability) is proved for the triangular and quadrilateral finite element pairs suggested by Bernardi/Raugel and Fortin. As a consequence the pairs , and turn out to be stable independent of the aspect ratio of the elements. Both the visit of the first author in Valenciennes and the visit of the second author in Chemnitz were financed by the DFG (German Research Foundation), Sonderforschungsbereich 393.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

Tight Bounds on the Competitive Ratio on Accommodating Sequences for the Seat Reservation Problem

The unit price seat reservation problem is investigated. The seat reservation problem is the problem of assigning seat numbers on-line to requests for reservations in a train traveling through k stations. We are considering the version where all tickets have the same price and where requests are treated fairly, that is, a request which can be fulfilled must be granted.For fair deterministic algorithms, we provide an asymptotically matching upper bound to the existing lower bound which states that all fair algorithms for this problem are -competitive on accommodating sequences, when there are at least three seats.Additionally, we give an asymptotic upper bound of for fair randomized algorithms against oblivious adversaries.We also examine concrete on-line algorithms, First-Fit and Random for the special case of two seats. Tight analyses of their performance are given.     

Determination of the roots and of the global extremum of a lipschitz function

Conclusion The obvious deficiency of the method (1.3), (1.9) is the possible difficulty of the operation . In connection with this one can note that all the above given statements remain valid if the number is replaced by some positive lower bound of |f(t _k ,x)| on .In computational methods, the presence of the Lipschitz constant is considered as a deficiency. In connection with this we can note that the Lipschitz constant L can be replaced by any of its upper estimates. For example, for a differentiable function f(z) one can take .Translated from Kibernetika, No. 2, pp. 71–74, March–April, 1987.     

Structural properties for feasibly computable classes of type two

This paper treates classes in the polynomial hierarchy of type two, , that were first developed by Townsend as a natural extension of the Meyer-Stockmeyer polynomial hierarchy in complexity theory. For these classes, it is discussed whether each of them has the extension property and the three recursion-theoretic properties: separation, reduction, and pre-wellordering. This paper shows that every 0$$ " align="middle" border="0"> , lacks the pre-wellordering property by using a probabilistic argument on constant-depth Boolean circuits. From the assumption NP = coNP it follows by a pruning argument that has the separation and extension properties.