信息与控制最新文献

Database relations with incomplete information are considered. The no-information interpretation of null values is adopted, due to its characteristics of generality and naturalness. Coherently with the framework and its motivation, two meaningful classes of integrity constraints are studied: (a) functional dependencies, which have been widely investigated in the classical relational theory and (b) constraints on null values, which control the presence of nulls in the relations. Specifically, three types of constraints on null values are taken into account (nullfree subschemes, existence constraints, disjunctive existence constraints), and the interaction of each of them with functional dependencies is studied. In each of the three cases, the inference problem is solved, the complexity of the algorithms for its solution analyzed, and the existence of a complete axiomatization discussed.

The aggregation problem is to design an inferential agent that makes intelligent use of the theories offered by a team of inductive inference machines working in a common environment. The present paper formulates several versions of the aggregation problem and investigates them from a recursion theoretic point of view.

The following problem is considered: given a linked list of length n, compute the distance from each element of the linked list to the end of the list. The problem has two standard deterministic algorithms: a linear time serial algorithm, and an O(log n) time parallel algorithm using n processors. We present new deterministic parallel algorithms for the problem. Our strongest results are (1) O(log n log* n) time using n/(log n log* n) processors (this algorithm achieves optimal speed-up); (2) O(log n) time using n log^(k)n/log n processors, for any fixed positive integer k. The algorithms apply a novel “random-like” deterministic technique. This technique provides for a fast and efficient breaking of an apparently symmetric situation in parallel and distributed computation.

For on-line recognition of the words in an arbitrary linear context-free language, there are known tight bounds on the time required by a deterministic multitape Turing machine. In terms of word length n, the time need never be worse than some constant times n², even if only one worktape is available; and there is a linear context-free language that requires at least time proportional to n²/log n, no matter how many worktapes are available. Using Kolmogorov's notion of descriptional complexity as a tool, we present a simple proof of the latter result.

Node label controlled (NLC) grammars are graph grammars (operating on node labeled undirected graphs) which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only. They define (possibly infinite) languages of undirected node labeled graphs (or, if we just omit the labels, languages of unlabeled graphs). Here we consider a restriction of NLC grammars, so-called boundary NLC (BNLC) grammars, distinguished by the property that whenever in a graph already generated two nodes may be rewritten, then these nodes are not adjacent. The graph languages generated by this type of grammars are called BNLC languages. Although we show that this restriction leads to a smaller class of languages, still enough generative power remains to define interesting graph languages. For example, trees, complete bipartite graphs, maximal outerplanar graphs, k-trees, graphs of bandwidth ⩽k, graphs of cyclic bandwidth ⩽k, graphs of binary tree bandwidth ⩽k, graphs of cutwidth ⩽k (always for a fixed positive integer k) turn out all to be BNLC languages. We prove a number of normal forms for BNLC grammars and then we indicate their usefulness by various applications. In particular, we show that for connected graphs of bounded degree the membership problem for BNLC languages is solvable in deterministic polynomial time.

This paper considers a number of arithmetic theories and shows how the strength of these theories relates to certain open problems in complexity theory concerning the polynomial-time hierarchy. These results are proved quite generally and hold for a wide class of subrecursive hierarchies. They can be used to characterize certain properties of functions provable in these theories.

The notion of the complexity of performing an inductive inference is defined. Some examples of the tradeoffs between the complexity of performing an inference and the accuracy of the inferred result are presented. An axiomatization of the notion of the complexity of inductive inference is developed and several results are presented which both resemble and contrast with results obtainable for the axiomatic computational complexity of recursive functions.

Our main aim is to present the connection between λ-calculus and Cartesian closed categories both in an untyped and purely syntactic setting. More specifically we establish a syntactic equivalence theorem between what we call categorical combinatory logic and λ-calculus with explicit products and projections, with β and η-rules as well as with surjective pairing. “Combinatory logic” is of course inspired by Curry's combinatory logic, based on the well-known S, K, I. Our combinatory logic is “categorical” because its combinators and rules are obtained by extracting untyped information from Cartesian closed categories (looking at arrows only, thus forgetting about objects). Compiling λ-calculus into these combinators happens to be natural and provokes only n log n code expansion. Moreover categorical combinatory logic is entirely faithful to β-reduction where combinatory logic needs additional rather complex and unnatural axioms to be. The connection easily extends to the corresponding typed calculi, where typed categorical combinatory logic is a free Cartesian closed category where the notion of terminal object is replaced by the explicit manipulation of applying (a function to its argument) and coupling (arguments to build datas in products). Our syntactic equivalences induce equivalences at the model level. The paper is intended as a mathematical foundation for developing implementations of functional programming languages based on a “categorical abstract machine,” as developed in a companion paper (Cousineau, Curien, and Mauny, in “Proceedings, ACM Conf. on Functional Programming Languages and Computer Architecture,” Nancy, 1985).

In this paper we present techniques that result in $O\left(\sqrt{n}\right)$ time algorithms for computing many properties and functions of an n-node forest stored in an $\sqrt{n}\times \sqrt{n}$ mesh of processors. Our algorithms include computing simple properties like the depth, the height, the number of descendents, the preorder (resp. postorder, inorder) number of every node, and a solution to the more complex problem of computing the Minimax value of a game tree. Our algorithms are asymptotically optimal since any nontrivial computation will require $\Omega \left(\sqrt{n}\right)$ time on the mesh. All of our algorithms generalize to higher dimensional meshes.