pinecone/core-2020-05-10-deduplication huggingface dataset:
Comparison of Functional and Predicative Query Paradigms

AbstractIn the last decade many extensions of the relational model were proposed, and basic properties of the relational model were investigated in their contexts. In particular, the equivalence of calculus and algebra, and the relative expressive power of other related languages were explored. This paper investigates this subject in a general framework, independently of any specific data type constructors that may exist in specific models, with the goal of making explicit the conditions that enable translation between query languages. The framework is based on a combination the well-founded approach of deductive programs and the initial algebra approach of algebraic specifications. The latter does not support negation (i.e., disequations); hence our combination contributes to the theory of algebraic specifications. Given the framework, we present the predicative and functional approaches to database description and querying. The first leads to the calculus and deductive approaches, the second to several algebras and, also, to generalizations that allow restricted definition by equations. We extend the notions of domain independence to our framework. We then present various sufficient conditions for the calculus and (some) algebra to be equivalent. We also compare the expressive power of algebras and more general languages to several deductive languages, under stratified and well-founded semantics. Finally, we define safety conditions and prove similar results for safe versions of the languages
A Semideterministic Approach to Object Creation and Nondeterminism in Database Queries

AbstractWe introduce and study the concept of semideterminism. A non-deterministic, generic query is called semideterministic if any two possible results of the query to a database are isomorphic. Semideterminism is a generalization of determinacy, proposed by Abiteboul and Kanellakis in the context of object-creating query languages. The framework of semi-deterministic queries is less restrictive than that of the determinate queries and avoids the problem of copy elimination connected with determinacy. We argue that semideterminism is also interesting in its own right and show that it is natural and desirable, although hard to achieve in general. Nevertheless, we exhibit two major applications where semideterministic computations are possible. First, we show that there is a universal procedure to compute any semideterministic query in a semideterministic manner. Second, we show that the polynomial-time counting queries can be efficiently expressed semideterministically
Tie-Breaking Semantics and Structural Totality

AbstractWe address the question of when the structure of a Datalog program with negation guarantees the existence of a fixpoint. We propose a semantics of Datalog programs with negation, which we call the tie-breaking semantics. The tie-breaking semantics can be computed in polynomial time and results in a fixpoint whenever the rule-goal graph of the program has no cycle with an odd number of negative edges. We show that, in some well-defined sense, this is the most general fixpoint semantics of negation possible; in particular, we show that if a cycle with an odd number of negative edges is present, then the logic program is not structurally total, that is, it has an alphabetic variant which has no fixpoint semantics whatsoever. Determining whether a program is total is undecidable
On the Equivalence of Recursive and Nonrecursive Datalog Programs

AbstractWe study the problem of determining whether a given recursive Datalog program is equivalent to a given nonrecursive Datalog program. Since nonrecursive Datalog programs are equivalent to unions of conjunctive queries, we study also the problem of determining whether a given recursive Datalog program is contained in a union of conjunctive queries. For this problem, we prove doubly exponential upper and lower time bounds. For the equivalence problem, we prove triply exponential upper and lower time bounds
Knowledgebase Transformations

AbstractWe propose a language that expresses uniformly queries and updates on knowledgebases consisting of finite sets of relational structures. The language contains an operator that “inserts” arbitrary first-order sentences into a knowledgebase. The semantics of the insertion is based on the notion ofupdateformalized by Katsuno and Mendelzon in the context of belief revision theory. Our language can express, among other things, hypothetical queries and queries on recursively indefinite databases. The expressive power of our language lies between existential second-order and general second-order queries. The data complexity is in general within polynomial space, although it can be lowered toco-NPand to polynomial time by restricting the form of queries and updates
The Complexity of Querying Indefinite Data about Linearly Ordered Domains

AbstractIn applications dealing with ordered domains, the available data is frequently indefinite. While the domain is actually linearly ordered, only some of the order relations holding between points in the data are known. Thus, the data provides only a partial order, and query answering involves determining what holds under all the compatible linear orders. In this paper we study the complexity of evaluating queries in logical databases containing such indefinite information. We show that in this context queries are intractable even under the data complexity measure, but identify a number of PTIME subproblems. Data complexity in the case of monadic predicates is one of these PTIME cases, but for disjunctive queries the proof is nonconstructive, using well-quasi-order techniques. We also show that the query problem we study is equivalent to the problem of containment of conjunctive relational database queries containing inequalities. One of our result implies that the latter isΠp2-complete, solving an open problem of Klug (J. Assoc. Comput. Mach.35, No. 1 (1988), 146–160)
Reusing and Modifying Rulebases by Predicate Substitution

AbstractWe propose a method for reusing and modifying a deductive database. The need for such techniques occurs when new rulebased applications differ only slightly from existing ones or when an application is to be incrementally updated. Such techniques are particularly important when reprogramming is expensive or unreliable. In order to facilitate reuse, we extend deductive database systems by the concept ofpredicate substitution. In this way, during query evaluation, not only variables, but also predicates can be substituted. We provide a proof theory and a model theory for this language, including a fixpoint semantics. In addition, we show that substitution increases the expressive power of Datalog: not only does its data complexity increase from PTIME to EXPTIME, but substitution also allows large sets of Datalog rules to be succinctly expressed. In fact, finite rulebases with substitution can express infinite rulebases without substitutio
Breaking theΘ(nlog2n) Barrier for Sorting with Faults

AbstractIn this paper, we study the problem of constructing a sorting circuit, network, or PRAM algorithm that is tolerant to faults. For the most part, we focus on fault patterns that are random, i.e., where the result of each comparison is independently faulty with probability upper bounded by some constant. All previous fault-tolerant sorting circuits, networks, and parallel algorithms requireΩ(log2n) depth and/orΩ(nlog2n) comparisons to sort n items. In this paper, we construct: •a passive-fault-tolerant sorting circuit withO(nlognloglogn) comparators, thereby answering a question posed by Yao and Yao in 1985, •a reversal-fault-tolerant sorting network withO(nloglog23n) comparators, thereby answering a question posed by Assaf and Upfal in 1990, and •a deterministicO(logn)-stepO(n)-processor EREW PRAM fault-tolerant sorting algorithm, thereby answering a question posed by Feige, Peleg, Raghavan, and Upfal in 1990. The results are based on a new analysis of the AKS circuit, which uses a much weaker notion of expansion that can be preserved in the presence of faults. Previously, the AKS circuit was not believed to be fault-tolerant because the expansion properties that were believed to be crucial for the performance of the circuit are destroyed by random faults. Extensions of our results for worst-case faults are also presented
A Spectrum of Time–Space Trade-offs for Undirecteds-tConnectivity

AbstractWe present a family of randomized algorithms that enjoys a wide range of time–space trade-offs in deciding undirected S-T-connectivity. Our trade-offs cover the whole range between breadth first search and the random walk procedure of Aleliunaset al., and achieve a time-space product ofÕ(mn) (wherenis the number of vertices in the graph,mis the number of edges, andÕnotation is used in order to suppress logarithmic terms). Moreover, we obtain improved time–space trade-offs ofÕ(n2) for regular graphs. A convenient and informative way of expressing our trade-offs, that implies the trade-offs stated above, is asÕ((∑ni=1di)(∑ni=11/di)), wherediis the degree of vertexiin the input graph. In constructing our algorithms and analysing them, we build upon earlier work of Broderet al.(who achieved a time–space trade-off ofÕ(m2)), Barnes and Feige (who achieved a time–space trade-off ofÕ(m3/2n1/2)), and Aldous. In passing, we also improve previous results regarding the rate at which a random walk discovers new vertices in a graph
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations

AbstractWe prove the following about the Nearest Lattice Vector Problem (in anylpnorm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor isNP-hard. 2. If for someε>0 there exists a polynomial-time algorithm that approximates the optimum within a factor of 2log0.5−εn, then everyNPlanguage can be decided in quasi-polynomial deterministic time, i.e.,NP⊆DTIME(npoly(logn)). Moreover, we show that result 2 also holds for the Shortest Lattice Vector Problem in thel∞norm. Also, for some of these problems we can prove the same result as above, but for a larger factor such as 2log1−εnornε. Improving the factor 2log0.5−εntodimensionfor either of the lattice problems would imply the hardness of the Shortest Vector Problem inl2norm; an old open problem. Our proofs use reductions from few-prover, one-round interactive proof systems [FL], BG+], either directly, or through a set-cover problem
Efficient Out-of-Core Algorithms for Linear Relaxation Using Blocking Covers

AbstractWhen a numerical computation fails to fit in the primary memory of a serial or parallel computer, a so-called “out-of-core” algorithm, which moves data between primary and secondary memories, must be used. In this paper, we study out-of-core algorithms for sparse linear relaxation problems in which each iteration of the algorithm updates the state of every vertex in a graph with a linear combination of the states of its neighbors. We give a general method that can save substantially on the I/O traffic for many problems. For example, our technique allows a computer withMwords of primary memory to performT=Ω(M1/5) cycles of a multigrid algorithm for a two-dimensional elliptic solver over an n-point domain using onlyΘ(nT/M1/5) I/O transfers, as compared with the naive algorithm which requiresΩ(nT) I/O's. Our method depends on the existence of a “blocking” cover of the graph that underlies the linear relaxation. A blocking cover has the property that the subgraphs forming the cover have large diameters once a small number of vertices have been removed. The key idea in our method is to introduce a variable for each removed vertex for each time step of the algorithm. We maintain linear dependences among the removed vertices, thereby allowing each subgraph to be iteratively relaxed without external communication. We give a general theorem relating blocking covers to I/O-efficient relaxation schemes. We also give an automatic method for finding blocking covers for certain classes of graphs, including planar graphs andd-dimensional simplicial graphs with constant aspect ratio (i.e., graphs that arise from dividingd-space into “well-shaped” polyhedra). As a result, we can performTiterations of linear relaxation on anyn-vertex planar graph using onlyΘ(n+nTlgn/M1/4) I/O's or on anyn-noded-dimensional simplicial graph with constant aspect ratio using onlyΘ(n+nTlgn/MΩ(1/d)) I/O's
When Can We Sort ino(nlogn) Time?

AbstractWe define two conditions on a random access machine (RAM) with arithmetic and Boolean instructions and possible bounds on word and memory sizes. One condition asserts that we either restrict attention to short words or allow nonuniform programs. The second asserts that we either allow a large memory or a double-precision multiplication. Our main theorem shows that the RAM can sort ino(nlogn) time if and only if both of these conditions hold. This theorem breaks down into four upper bounds only one of which has been known before, and two lower bounds neither of which has been known
Learning an Intersection of a Constant Number of Halfspaces over a Uniform Distribution

AbstractWe present a polynomial-time algorithm to learn an intersection of a constant number of halfspaces inndimensions, over the uniform distribution on ann-dimensional ball. The algorithm we present in fact can learn an intersection of an arbitrary (polynomial) number of halfspaces over this distribution, if the subspace spanned by the normal vectors to the bounding hyperplanes has constant dimension. This generalizes previous results for this distribution, in particular a result of Baum who showed how to learn an intersection of two halfspaces defined by hyperplanes that pass through the origin. (His results also held for a variety of symmetric distributions.) Our algorithm uses estimates of second moments to find vectors in a low-dimensional “relevant subspace.” We believe that the algorithmic techniques studied here may be useful in other geometric learning applications. Our algorithm succeeds even in the presence of random noise, since the only use we make of the examples is to calculate the expectation of certain simple quantities
Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks

AbstractWe introduce a new method for proving explicit upper bounds on the VC dimension of general functional basis networks and prove as an application, for the first time, that the VC dimension of analog neural networks with the sigmoidal activation functionσ(y)=1/1+e−yis bounded by a quadratic polynomialO((lm)2) in both the numberlof programmable parameters, and the numbermof nodes. The proof method of this paper generalizes to much wider class of Pfaffian activation functions and formulas and gives also for the first time polynomial bounds on their VC dimension. We present also some other applications of our method
A Weak Version of the Blum, Shub, and Smale Model

AbstractWe propose a weak version of the Blum–Shub–Smale model of computation over the real numbers. In this weak model only a “moderate” usage of multiplications and divisions is allowed. The class of boolean languages recognizable in polynomial time is shown to be the complexity class P/poly. The main tool is a result on the existence of small rational points in semi-algebraic sets which is of independent interest. As an application, we generalize recent results of Siegelmann and Sontag on recurrent neural networks, and of Maass on feedforward nets. A preliminary version of this paper was presented at the1993 IEEE Symposium on Foundations of Computer Science. Additional results include: an efficient simulation of order-free real Turing machines by probabilistic Turing machines in the full Blum–Shub–Smale model; the strict inclusion of the real polynomial hierarchy in weak exponential time
On the Computation of Boolean Functions by Analog Circuits of Bounded Fan-In

AbstractWe consider the complexity of computing Boolean functions by analog circuits of bounded fan-in, i.e., by circuits of gates computing real-valued functions, either exactly or as sign-representation. Sharpupper boundsare obtained for the complexity of the most difficultn-variable function over certain bases (sign-representation by arithmetic circuits and exact computation by piecewise linear circuits). Bounds are given for the computational power gained by addingdiscontinuousgate functions andnondeterminism. We also prove explicitnonlinear lower boundsfor theformula sizeof analog circuits over bases containing addition, subtraction, multiplication, the sign function and all real constants
An Excursion to the Kolmogorov Random Strings

AbstractWe study the sets of resource-bounded Kolmogorov random strings:Rt={x|Ct(n)(x)⩾|x|} fort(n)=2nk. We show that the class of sets that Turing reduce toRthas measure 0 inEXPwith respect to the resource-bounded measure introduced by Lutz. From this we conclude thatRtis not Turing-complete forEXP. This contrasts with the resource-unbounded setting. ThereRis Turing-complete forco-RE. We show that the class of sets to whichRtbounded truth-table reduces, hasp2-measure 0 (therefore, measure 0 inEXP). This answers an open question of Lutz, giving a natural example of a language that is not weakly complete forEXPand that reduces to a measure 0 class inEXP. It follows that the sets that are ⩽pbbt-hard forEXPhavep2-measure 0
Counting Quantifiers, Successor Relations, and Logarithmic Space

AbstractGiven a successor relationS(i.e., a directed line graph), and given two distinguished pointssandt, the problem ORD is to determine whethersprecedestin the unique ordering defined byS. We show that ORD is L-complete (via quantifier-free projections). We then show that first-order logic with counting quantifiers, a logic that captures TC0over structures with a built-in total-ordering, cannot express ORD. Our original proof of this in the conference version of this paper employed an Ehrenfeucht–Fraı̈ssé Game for first-order logic with counting. Here we show how the result follows from a more general one obtained independently by Nurmonen. We then show that an appropriately modified version of the EF game is “complete” for the logic with counting in the sense that it provides a necessary and sufficient condition for expressibility in the logic. We observe that the L-complete problem ORD is essentially sparse if we ignore reorderings of vertices, a property which we term “pseudo-sparseness.” We then prove that there are no pseudo-sparse NP-complete properties (under P-time reductions) unless the polynomial time hierarchy collapses (toΣ3), revealing a structural property on which L and NP apparently differ
The Isomorphism Conjecture Holds and One-Way Functions Exist Relative to an Oracle

AbstractIn this paper we demonstrate an oracle relative to which there are one-way functions but every paddable 1-li-degree collapses to an isomorphism type, thus yielding a relativized failure of the Joseph–Young Conjecture [JY85]. We then use this result to construct an oracle relative to which the Isomorphism Conjecture is true but one-way functions exist, which answers an open question of Fenner, Fortnow, and Kurtz [FFK96]. Thus, there are now relativizations realizing every one of the four possible states of affairs between the Isomorphism Conjecture and the existence of one-way functions
Semantics vs Syntax vs Computations: Machine Models for Type-2 Polynomial-Time Bounded Functionals

AbstractThis paper investigates analogs of the Kreisel–Lacombe–Shoenfield Theorem in the context of the type-2 basic feasible functionals. We develop a direct, polynomial-time analog of effective operation in which the time bounding on computations is modeled after Kapron and Cook's scheme for their basic polynomial-time functionals. We show that if P=NP, these polynomial-time effective operations are strictly more powerful on R (the class of recursive functions) than the basic feasible functions. We also consider a weaker notion of polynomial-time effective operation where the machines computing these functionals have access to the computations of their procedural parameter, but not to its program text. For this version of polynomial-time effective operations, the analog of the Kreisel–Lacombe–Shoenfield is shown to hold—their power matches that of the basic feasible functionals on R
A Completeness Theorem for the Expressive Power of Higher-Order Algebraic Specifications

AbstractWe consider the expressive power of a general form of higher-order algebraic specification which allows constructors and hidden sorts and operations. We prove a completeness theorem which exactly characterises the expressiveness of such specifications with respect to the analytical hierarchy. In particular we show that for any countable signatureΣand minimalΣalgebraA,Ahas complexityΠ11if, and only if,Ahas a recursive second-order equational specification with constructors and hidden sorts and operators under higher-order initial semantics
On Fixed-Parameter Tractability and Approximability of NP Optimization Problems

AbstractFixed-parameter tractability of NP optimization problems is studied by relating it to approximability of the problems. It is shown that an NP optimization problem is fixed-parameter tractable if it admits a fully polynomial-time approximation scheme, or if it belongs to the class MAX SNP or to the class MIN F+Π1. This provides strong evidence that noW[1]-hard NP optimization problems belong to these optimization classes and includes a very large class of approximable optimization problems into the class of fixed-parameter tractable problems. Evidence is also demonstrated to support the current working hypothesis in the theory of fixed-parameter tractability
A Model of Interactive Teaching

AbstractPrevious teaching models in the learning theory community have been batch models. That is, in these models the teacher has generated a single set of helpful examples to present to the learner. In this paper we present an interactive model in which the learner has the ability to ask queries as in the query learning model of Angluin. We show that this model is at least as powerful as previous teaching models. We also show that anything learnable with queries, even by a randomized learner, is teachable in our model. In all previous teaching models, all classes shown to be teachable are known to be efficiently learnable. An important concept class that is not known to be learnable is DNF formulas. We demonstrate the power of our approach by providing a deterministic teacher and learner for the class of DNF formulas. The learner makes only equivalence queries and all hypotheses are also DNF formulas
Geometric Approach for Optimal Routing on a Mesh with Buses

AbstractThe architecture of “mesh of buses” is an important model in parallel computing. Its main advantage is that the additional broadcast capability can be used to overcome the main disadvantage of the mesh, namely its relatively large diameter. We show that the addition of buses indeed accelerates routing times. Furthermore, unlike in the “store and forward” model, the routing time becomes proportional to the network load, resulting in decreasing in routing time for a smaller number of packets. We consider 1–1 routing ofmpackets in ad-dimensional mesh withndprocessors andd·nd−1buses (one per row and column). The two standard models of accessing the buses are considered and compared: CREW, in which only one processor may transmit at any given time on a given bus, and the CRCW model, in which several processors may attempt to transmit at the same time (getting a noise signal as a result). We design a routing algorithm that routesmpackets in the CREW model inO(m1/d+n1/(d+1)) steps. This result holds form⩽n2d/3ford⩾3 and unconditionally ford=2. A matching lower bound is also proved. In the CRCW case we show an algorithm ofO(m1/dlogn) and a lower bound ofΩ(m1/d). It is shown that the difference between the models is essentially due to the improved capability of estimating threshold functions in the CRCW case