Searching minimax game trees under memory space constraint

Games such as CHESS, GO and OTHELLO can be represented by minimax game trees. Among various search procedures to solve such game trees,- and SSS^* are perhaps most well known. Although it is proved that SSS^* explores only a subset of the nodes explored by-, - is commonly believed to be faster in real applications, since it requires very little memory space and hence its storage management cost is low. Contrary to this folklore, however, this paper reports, using the OTHELLO game as an example, that SSS^* is much faster than-. It is also demonstrated that SSS^* can be modified to make the required memory space controllable to some extent, while retaining the high efficiency of the original SSS^*.This research was partially supported by the Ministry of Education, Science and Culture of Japan, under a Scientific Grant-in-Aid.     

Automatic surface reconstruction with alpha-shape method

In this paper, we present an algorithm for the reconstruction of piecewise linear surfaces from unorganized sample points with an improved -shape. Alpha-shape provides a nice mathematical definition of the shape of a set of points, but the selection of an value is tricky in surface reconstruction. F or solving this problem and the non-uniform distribution, we scale the ball according to the points density. The method discussed in this paper might be applied for surface reconstruction, and the process is fully automatic.     

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.     

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.     

A predicate transformer for the progress property ‘to-always’

The temporal property to-always has been proposed for specifying progress properties of concurrent programs. Although the to-always properties are a subset of the leads-to properties for a given program, to-always has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformerwta, derive some of its properties, and use it to define to-always. Proof rules for to-always are derived from the properties ofwta. We conclude by briefly describing two application areas, nondeterministic data flow networks and self-stabilizing systems where to-always properties are useful.     

A Mathematical Analysis of Pānini’s <Emphasis Type="Italic">Śivasūtras</Emphasis>

In Pninis grammar of Sanskrit one finds the ivastras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pninis way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, which are, however, implicitly given in the way a language clusters its phonological inventory. The key idea is to link the graph of the Hasse-diagram of the set of natural classes closed under intersection to ivastra-style representations of the classes. Moreover, the argument is so general that it allows one to decide for each set of sets whether it can be represented with Pninis method. Actually, Pnini had to modify the set of natural classes to define it by the ivastras (the segment h plays a special role). We show that this modification was necessary and, in fact, the best possible modification. We discuss how every set of classes can be modified in such a way that it can be defined in a ivastra-style representation.¹     

Reasoning about programs in continuation-passing style

Plotkin's _v -calculus for call-by-value programs is weaker than the -calculus for the same programs in continuation-passing style (CPS). To identify the call-by-value axioms that correspond to on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interesting in their own right. Using the new CPS transformation, we determine the precise language of CPS terms closed under -transformations, as well as the call-by-value axioms that correspond to the so-called administrative -reductions on CPS terms. Using the inverse mapping, we map the remaining and equalities on CPS terms to axioms on call-by-value terms. On the pure (constant free) set of -terms, the resulting set of axioms is equivalent to Moggi's computational -calculus. If the call-by-value language includes the control operatorsabort andcall-with-current-continuation, the axioms are equivalent to an extension of Felleisenet al.'s _v -C-calculus and to the equational subtheory of Talcott's logic IOCC.This article is a revised and extended version of the conference paper with the same title [42]. The technical report of the same title contains additional material.The authors were supported in part by NSF grant CCR 89-17022 and by Texas ATP grant 91-003604014.     

Deterministic polynomial-time quantum algorithms for Simon’s problem

D. R. Simon stated a problem, so-called Simons problem, whose computational complexity is in the class BQP but not in BPP, where is the function or oracle given in the problem. This result indicates that BPP may be strictly included in its quantum counterpart, BQP. Later, G. Brassard and P. Høyer showed that Simons problem and its extended version can be solved by a deterministic polynomial time quantum algorithm. That is, these problems are in the class EQP. In this paper, we show that Simons problem and its extended version can be deterministically solved in a simpler and more concrete way than that proposed by G. Brassard and P. Høyer.     

More Church–Rosser Proofs

The proofs of the Church–Rosser theorems for , , and reduction in untyped -calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle. For -reduction, both the standard proof and Takahashi's are given and compared. All proofs are based on a general theory of commutating relations that supports an almost geometric style of reasoning about confluence diagrams.     

Mathematical Analysis and Optimization of Infiltration Processes

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, and . The optimization problem associated with minimizing the infiltration time is also considered. Allowing and to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where and are treated as constants.     

Understanding Computer-based “Informated” Environments

The paper introduces the concept of Computer-based Informated Environments (CBIEs) to indicate an emergent form of work organisation facilitated by information technology. It first addresses the problem of inconsistent meanings of the informate concept in the literature, and it then focuses on those cases which, it is believed, show conditions of plausible informated environments. Finally, the paper looks at those factors that when found together contribute to building a CBIE. It makes reference to CBIEs as workplaces that comprise a non-technocentric perspective and questions whether CBIEs truly represent an anthropocentric route of information technology.     

A logical encoding of the π-calculus: model checking mobile processes using tabled resolution

We present MMC, a model checker for mobile systems specified in the style of the -calculus. MMCs development builds on that of XMC, a model checker for an expressive extension of Milners value-passing calculus implemented using the XSB tabled logic-programming engine. MMC addresses the salient issues that arise in the -calculus, including scope extrusion and intrusion and dynamic generation of new names to avoid name capture. We show that logic programming provides an efficient implementation platform for model checking -calculus specifications and can be used to obtain an exact encoding of the -calculuss transitional semantics. Moreover, MMC is easily extended to handle process expressions in the spi-calculus of Abadi and Gordon. Our experimental data show that MMC outperforms other known tools for model checking the -calculus.     

Finiteness in Infinite-Valued Łukasiewicz Logic

In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic _m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in _m. We also reduce the notion of logical consequence in to the same notion in a suitable finite set of finite-valued ukasiewicz logics. Finally, we define an analytic and internal sequent calculus for infinite-valued ukasiewicz logic.     

Fast Online Q(λ)

Q()-learning uses TD()-methods to accelerate Q-learning. The update complexity of previous online Q() implementations based on lookup tables is bounded by the size of the state/action space. Our faster algorithm's update complexity is bounded by the number of actions. The method is based on the observation that Q-value updates may be postponed until they are needed.     

Complex-Weighted One-Unit ‘Rigid-Bodies’ Learning Rule for Independent Component Analysis

Over the recent years, noticeable theoretical efforts have been devoted to the understanding of the role of networks' parameter spaces in neural learning. One of the contributions in this field concerns the study of weight-flows on Stiefel manifold, which is the natural parameter-space's algebraic-structure in some unsupervised (information-theoretic) learning task. An algorithm belonging to the class of learning equations generating Stiefel-flows is based on the rigid-body theory, introduced by the present Author in 1996. The aim of this Letter is to present an investigation on the capability of a complex-weighted neuron, trained by a rigid-bodies learning theory, with application to blind source separation of complex-valued independent signals for telecommunication systems.     

Computing Optimal Diameter-Bounded Polygon Partitions

The minimum -small partition problem is the problem of partitioning a given simple polygon into subpolygons, each with diameter at most , for a given > 0. This paper considers the version of this problem that disallows Steiner points. This problem is motivated by applications in mesh generation and collision detection. The main result in the paper is a polynomial-time algorithm that solves this problem, and either returns an optimal partition or reports the nonexistence of such a partition. This result contrasts with the recent NP-completeness result for the minimum -small partition problem for polygons with holes (C. Worman, 15th Canadian Conference on Computational Geometry, 2003). Even though the running time of our algorithm is a polynomial in the input size, it is prohibitive for most real applications and we seek faster algorithms that approximate an optimal solution. We first present a faster 2-approximation algorithm for the problem for simple polygons and then a near linear-time algorithm for convex polygons that produces, for any > 0, an (+)-small partition with no more polygons than in an optimal -small partition. We also present an exact polynomial-time algorithm for the minimum -small partition problem with the additional constraint that each piece in the partition be convex.     

The Claremont Shakespeare Authorship Clinic: How Severe Are the Problems?

Ward Elliott (from 1987) and Robert Valenza (from 1989) set out to the find the true Shakespeare from among 37 anti-Stratfordian Claimants. As directors of the Claremont Shakespeare Authorship Clinic, Elliott and Valenza developed novel attributional tests, from which they concluded that most Claimants are not-Shakespeare. From 1990-4, Elliott and Valenza developed tests purporting further to reject much of the Shakespeare canon as not-Shakespeare (1996a). Foster (1996b) details extensive and persistent flaws in the Clinic's work: data were collected haphazardly; canonical and comparative text-samples were chronologically mismatched; procedural controls for genre, stanzaic structure, and date were lacking. Elliott and Valenza counter by estimating maximum erosion of the Clinic's findings to include five of our 54 tests, which can amount, at most, to half of one percent (1998). This essay provides a brief history, showing why the Clinic foundered. Examining several of the Clinic's representative tests, I evaluate claims that Elliott and Valenza continue to make for their methodology. A final section addresses doubts about accuracy, validity and replicability that have dogged the Clinic's work from the outset.     

Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation

Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.Notation U ^ad set of admissible continuous design parameters - U _h ^ad set of admissible discrete design parameters - function fromU _h ^ad defining shape of body - _h function fromU _h ^ad defining approximated shape of body - vector of nodal values of _h - { _n} sequence of functions tending to - () domain defined by - K bulk modulus - shear modulus - penalty parameter for contact condition - V() space of virtual displacements in() - V _h(_h) finite element approximation ofV() - J cost functional - J _h discretized cost functional - J algebraic form ofJ _h - (u) stress tensor - e(u) strain tensor - K stiffness matrix - f force vector - b(q) term arising from nonlinear boundary conditions - q vector of nodal degrees of freedom - p vector of adjoint state variables - J Jacobian of isoparametric mapping - |J| determinant ofJ - N vector of shape function values on parent element - L matrix of shape function derivatives on parent element - G matrix of Cartesian derivatives of shape functions - X matrix of nodal coordinates of element - D matrix of elastic coefficients - B strain-displacement matrix - _P part of boundary where tractions are prescribed - _u part of boundary where displacements are prescribed - variable part of boundary - strain invariant     

Functional Estimation with Respect to a Threshold Parameter via Dynamic Split-and-Merge

We consider a class of stochastic models for which the performance measure is defined as a mathematical expectation that depends on a parameter , say (), and we are interested in constructing estimators of in functional form (i.e., entire functions of ), which can be computed from a single simulation experiment. We focus on the case where is a continuous parameter, and also consider estimation of the derivative (). One approach for doing that, when is a parameter of the probability law that governs the system, is based on the use of likelihood ratios and score functions. In this paper, we study a different approach, called split-and-merge, for the case where is a threshold parameter. This approach can be viewed as a practical way of running parallel simulations at an infinite number of values of , with common random numbers. We give several examples showing how different kinds of parameters such as the arrival rate in a queue, the probability that an arriving customer be of a given type, a scale parameter of a service time distribution, and so on, can be turned into threshold parameters. We also discuss implementation issues.     

Reduction and unification in lambda calculi with a general notion of subtype

Reduction, equality, and unification are studied for a family of simply typed -calculi with subtypes. The subtype relation is required to relate base types only to base types and to satisfy some order-theoretic conditions. Constants are required to have a least type, that is, no overloading. We define the usual and a subtype-dependent -reduction. These are related to a typed equality relation and shown to be confluent in a certain sense. We present a generic algorithm for preunification modulo -conversion and an arbitrary subtype relation. Furthermore it is shown that unification with respect to any subtype relation is universal.