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.     

The dynamic clusters method in nonhierarchical clustering

Given a finite setE R ⁿ, the problem is to find clusters (or subsets of similar points inE) and at the same time to find the most typical elements of this set. An original mathematical formulation is given to the problem. The proposed algorithm operates on groups of points, called samplings (samplings may be called multiple centers or cores); these samplings adapt and evolve into interesting clusters. Compared with other clustering algorithms, this algorithm requires less machine time and storage. We provide some propositions about nonprobabilistic convergence and a sufficient condition which ensures the decrease of the criterion. Some computational experiments are presented.     

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.     

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 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     

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.     

Sufficiency conditions for existence of an optimal feedback control in stochastic mechanics

In the framework of stochastic mechanics, the following problem is considered: in a set of admissible feedback controls v, with range inE ⁿ , find one minimizing the expectationE _sx { _s ^T L(t, (t), (t, (t)))dt + W _T ((T))} for all (s, x) [0,T) E ⁿ , whereL(t, x, ) = (/12)m ² – U(t, x) is the classical action integrand and is an-dimensional diffusion process in the weak sense, (see Bensoussan, 1982) with drift and diffusion coefficientD constant > 0.W _T andU are given real functions. Sufficiency conditions for the existence of such an optimal feedback control are given. Dedicated to George Leitmann Recommended by G.J. Olsder Presented at the Third Workshop on Control Mechanics in honor of George Leitmann, January 22–24, 1990, University of Southern California, Los Angeles, California (USA).     

Interpretations of open default theories in non-monotonic logics

It is shown that the translation of an open default into a modal formula x(L(x)LM ₁ (x)...LM _m (x)w(x)) gives rise to an embedding of open default systems into non-monotonic logics.     

Constructing sets of functions which have a givenF-cardinality

The termF-cardinality of (=F-card()) is introduced whereF: ^{n n} is a partial function and is a set of partial functionsf: ^{n n} . TheF-cardinality yields a lower bound for the worst-case complexity of computingF if only functionsf can be evaluated by the underlying abstract automaton without conditional jumps. This complexity bound isindependent from the oracles available for the abstract machine. Thus it is shown that any automaton which can only apply the four basic arithmetic operations needs (n logn) worst-case time to sortn numbers; this result is even true if conditional jumps witharbitrary conditions are possible. The main result of this paper is the following: Given a total functionF: ^{n n} and a natural numberk, it is almost always possible to construct a set such that itsF-cardinality has the valuek; in addition, can be required to be closed under composition of functionsf,g . Moreover, ifF is continuous, then consists of continuous functions.     

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.     

Modular visions: Referents, context and strategies for database open media works

The processes of constructing meaning in digital database environments entail a paradigm shift from previous models of audio-visual communication. Media emerging from the Electro-mechanical era (film/TV/video) present fixed spatio-temporal linearity and material conditions which objectify and render passive viewer and process. The problematic aspects of cinematic communication were addressed by Latin American filmmakers of the Third Cinema movement. Their concerns and approach presaged and assisted an understanding of the radical redefinition of audio-visual communication possible with digital databases. The conceptual and aesthetic aspirations of Third Cinema artists such as Julio Garcia Espinosa and Fernando Solanas were ultimately contradictory to linear media and find their fitting medium in digital modular construction. The materiality of database expression lacks an intrinsic temporal or spatial state and permits a more dynamic and multidirectional set of power relationships between author/s, piece, viewer/s. Other important referents for contextualising database art are modern art practitioners that rejected linear representational space and fractured the centrality of authorship. The author's own work, ...two, three, many Guevaras, an exploratory database environment, embraces the redefinition of process as artistic expression, the empowerment of interacting generative forces, and serves to illustrate the revolutionary potential of the new media.     

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.     

Sometime = always + recursion ≡ always on the equivalence of the intermittent and invariant assertions methods for proving inevitability properties of programs

Summary We propose and compare two induction principles called always and sometime for proving inevitability properties of programs. They are respective formalizations and generalizations of Floyd invariant assertions and Burstall intermittent assertions methods for proving total correctness of sequential programs whose methodological advantages or disadvantages have been discussed in a number of previous papers. Both principles are formalized in the abstract setting of arbitrary nondeterministic transition systems and illustrated by appropriate examples. The sometime method is interpreted as a recursive application of the always method. Hence always can be considered as a special case of sometime. These proof methods are strongly equivalent in the sense that a proof by one induction principle can be rewritten into a proof by the other one. The first two theorems of the paper show that an invariant for the always method can be translated into an invariant for the sometime method even if every recursive application of the later is required to be of finite length. The third and main theorem of the paper shows how to translate an invariant for the sometime method into an invariant for the always method. It is emphasized that this translation technique follows the idea of transforming recursive programs into iterative ones. Of course, a general translation technique does not imply that the original sometime invariant and the resulting always invariant are equally understandable. This is illustrated by an example.     

Hierarchy theorems for two-way finite state transducers

Summary For a family of languages , CAL() is defined as the family of images of under nondeterministic two-way finite state transducers, while FINITE · VISIT() is the closure of under deterministic two-way finite state transducers; CAL⁰()= and for n0, CAL ⁿ⁺¹()=CAL ⁿ (CAL()). For any semiAFL , if FINITE · VISIT() CAL(), then CAL ⁿ () forms a proper hierarchy and for every n0, FINITE · VISIT(CALⁿ()) CAL ⁿ⁺¹() FINITE · VISIT(CAL ⁿ⁺¹()). If is a SLIP semiAFL or a weakly k-iterative full semiAFL or a semiAFL contained in any full bounded AFL, then FINITE · VISIT() CAL() and in the last two cases, FINITE · VISIT(). If is a substitution closed full principal semiAFL and FINITE · VISIT(), then FINITE · VISIT() CAL(). If is a substitution closed full principal semiAFL generated by a language without an infinite regular set and ₁ is a full semiAFL, then is contained in CAL^m(₁) if and only if it is contained in ₁. Among the applications of these results are the following. For the following families , CAL ⁿ () forms a proper hierarchy: =INDEXED, =ETOL, and any semiAFL contained in CF. The family CF is incomparable with CAL ^m (NESA) where NESA is the family of one-way nonerasing stack languages and INDEXED is incomparable with CAL ^m (STACK) where STACK is the family of one-way stack languages.This work was supported in part by the National Science Foundation under Grants No. DCR74-15091 and MCS-78-04725     

How to find Steiner minimal trees in euclideand-space

This paper has two purposes. The first is to present a new way to find a Steiner minimum tree (SMT) connectingN sites ind-space,d >- 2. We present (in Appendix 1) a computer code for this purpose. This is the only procedure known to the author for finding Steiner minimal trees ind-space ford > 2, and also the first one which fits naturally into the framework of backtracking and branch-and-bound. Finding SMTs of up toN = 12 general sites ind-space (for anyd) now appears feasible.We tabulate Steiner minimal trees for many point sets, including the vertices of most of the regular and Archimedeand-polytopes with <- 16 vertices. As a consequence of these tables, the Gilbert-Pollak conjecture is shown to be false in dimensions 3–9. (The conjecture remains open in other dimensions; it is probably false in all dimensionsd withd 3, but it is probably true whend = 2.)The second purpose is to present some new theoretical results regarding the asymptotic computational complexity of finding SMTs to precision .We show that in two-dimensions, Steiner minimum trees may be found exactly in exponential time O(C ^N ) on a real RAM. (All previous provable time bounds were superexponential.) If the tree is only wanted to precision , then there is an (N/)^O(N)-time algorithm, which is subexponential if 1/ grows only polynomially withN. Also, therectilinear Steiner minimal tree ofN points in the plane may be found inN ^O(N) time.J. S. Provan devised an O(N ⁶/⁴)-time algorithm for finding the SMT of a convexN-point set in the plane. (Also the rectilinear SMT of such a set may be found in O(N ⁶) time.) One therefore suspects that this problem may be solved exactly in polynomial time. We show that this suspicion is in fact true—if a certain conjecture about the size of Steiner sensitivity diagrams is correct.All of these algorithms are for a real RAM model of computation allowing infinite precision arithmetic. They make no probabilistic or other assumptions about the input; the time bounds are valid in the worst case; and all our algorithms may be implemented with a polynomial amount of space. Only algorithms yielding theexact optimum SMT, or trees with lengths (1 + ) × optimum, where is arbitrarily small, are considered here.     

Complexity and computability of solutions to linear programming systems

Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal centered-cutoff algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By model approximation, both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral constraint contraction algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the imposed problem ignorance of past complexity research is deleterious to research progress on computability or efficiency of computation.This research was partly supported by Project NR047-071, ONR Contract N00014-80-C-0242, and Project NR047-021, ONR Contract N00014-75-C-0569, with the Center for Cybernetic Studies, The University of Texas at Austin.     

AI & Society and society

This article looks at the broadest implications of public acceptance of AI. A distinction is drawn between conscious belief in a technology, and organic belief where the technology is incorporated into an unconscious world model. The extent to which we feel threatened by AI's apparent denial of spirit is considered, along with a discussion of how people react to this threat. It is proposed that organic acceptance of AI models would lead to a rebirth of popular spiritual concepts as paradoxical as the New Age ideas that have their roots in the theories of physics. Finally the relevance of this speculation is discussed in terms of how it could impinge upon public acceptability of AI technology.     

On the Axioms of Scale Space Theory

We consider alternative scale space representations beyond the well-established Gaussian case that satisfy all reasonable axioms. One of these turns out to be subject to a first order pseudo partial differential equation equivalent to the Laplace equation on the upper half plane {(x, s) ^d × | s > 0}. We investigate this so-called Poisson scale space and show that it is indeed a viable alternative to Gaussian scale space. Poisson and Gaussian scale space are related via a one-parameter class of operationally well-defined intermediate representations generated by a fractional power of (minus) the spatial Laplace operator.     

Modal Pure Type Systems

We present a framework for intensional reasoning in typed -calculus. In this family of calculi, called Modal Pure Type Systems (MPTSs), a propositions-as-types-interpretation can be given for normal modal logics. MPTSs are an extension of the Pure Type Systems (PTSs) of Barendregt (1992). We show that they retain the desirable meta-theoretical properties of PTSs, and briefly discuss applications in the area of knowledge representation.