pinecone/core-2020-05-10-deduplication huggingface dataset:
Topological Queries in Spatial Databases

We studytopological queriesover two-dimensional spatial databases. First, we show that the topological properties of semi-algebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides aninvariantcharacterizing semi-algebraic regions up to homeomorphism. All topological queries on semi-algebraic regions can be answered by queries on the invariant whose complexity is polynomially related to the original. Also, we show that for the purpose of answering topological queries, semi-algebraic regions can always be represented simply as polygonal regions. We then study query languages for topological properties of two-dimensional spatial databases, starting from the topological relationships between pairs of planar regions introduced by Egenhofer. We show that the closure of these relationships under appropriate logical operators yields languages which arecompletefor topological properties. This provides a theoreticala posteriorijustification for the choice of these particular relationships. Unlike the point-based languages studied in previous work on constraint databases, our languages are region based—quantifiers range over regions in the plane. This yields a family of languages, whose complexity ranges fromNCto undecidable. Another type of completeness result shows that the region-based language of complexityNCexpresses precisely the same topological properties as well-known point-based languages
Temporal Connectives versus Explicit Timestamps to Query Temporal Databases

AbstractTemporal databases can be queried either by query languages working directly on a timestamp representation or by languages using an implicit access to time via temporal connectives. We study the differences in expressive power between these two approaches. First, we consider temporal and first-order logic. We show that future temporal logic is strictly less powerful than past–future temporal logic and also that there are queries expressible in first-order logic with explicit timestamps that are not expressible in extended temporal logic. Our proof technique is novel and based on communication complexity. Then, we consider extensions of first-order logic with fixpoints or while-loops. Again the explicit temporal version of these languages, using timestamps, is compared with an implicit one, using instructions for moving in time. We also compare the temporal versions of the fixpoint language with those of the while language
Answering Queries Using Limited External Query Processors

AbstractWhen answering queries using external information sources, the contents of the queries can be described by views. To answer a query, we must rewrite it using the set of views presented by the sources. When the external information sources also have the ability to answer some (perhaps limited) sets of queries that require performing operations on their data, the set of views presented by the source may be infinite (albeit encoded in some finite fashion). Previous work on answering queries using views has only considered the case where the set of views is finite. In order to exploit the ability of information sources to answer more complex queries, we consider the problem of answering conjunctive queries using infinite sets of conjunctive views. Our first result is that an infinite set of conjunctive views can be partitioned into a finite number of equivalence classes, such that picking one view from every nonempty class is sufficient to determine whether the query can be answered using the views. Second, we show how to compute the set of equivalence classes for sets of conjunctive views encoded by a datalog program. Furthermore, we extend our results to the case when the query and the views use the built-in predicates <, ⩽, =, and ≠, and they are interpreted over a dense domain. Finally, we extend our results to conjunctive queries and views with the built-in predicates <, ⩽, and = interpreted over the integers. In doing so we present a result of independent interest, namely, an algorithm to minimize such queries
Combining Fuzzy Information from Multiple Systems

AbstractIn a traditional database system, the result of a query is a set of values (those values that satisfy the query). In other data servers, such as a system with queries based on image content, or many text retrieval systems, the result of a query is a sorted list. For example, in the case of a system with queries based on image content, the query might ask for objects that are a particular shade of red, and the result of the query would be a sorted list of objects in the database, sorted by how well the color of the object matches that given in the query. A multimedia system must somehow synthesize both types of queries (those whose result is a set and those whose result is a sorted list) in a consistent manner. In this paper we discuss the solution adopted by Garlic, a multimedia information system being developed at the IBM Almaden Research Center. This solution is based on “graded” (or “fuzzy”) sets. Issues of efficient query evaluation in a multimedia system are very different from those in a traditional database system. This is because the multimedia system receives answers to subqueries from various subsystems, which can be accessed only in limited ways. For the important class of queries that are conjunctions of atomic queries (where each atomic query might be evaluated by a different subsystem), the naive algorithm must retrieve a number of elements that is linear in the database size. In contrast, in this paper an algorithm is given, which has been implemented in Garlic, such that if the conjuncts are independent, then with arbitrarily high probability, the total number of elements retrieved in evaluating the query is sublinear in the database size (in the case of two conjuncts, it is of the order of the square root of the database size). It is also shown that for such queries, the algorithm is optimal. The matching upper and lower bounds are robust, in the sense that they hold under almost any reasonable rule (including the standard min rule of fuzzy logic) for evaluating the conjunction. Finally, we find a query that is provably hard, in the sense that the naive linear algorithm is essentially optimal
Achilles and the Tortoise Climbing Up the Arithmetical Hierarchy

AbstractIn this paper we show how to construct for every setPof integers in the arithmetical hierarchy a dynamical system H with piecewise-constant derivatives such that deciding membership inPcan be reduced to solving the reachability problem between two rational points for H. The ability of such apparently simple dynamical systems, whose definition involves onlyrationalparameters, to “solve” highly unsolvable problems is closely related to Zeno's paradox, namely the ability to pack infinitely many discrete steps in a bounded interval of time
Deciding the Vapnik–Červonenkis Dimension is∑p3-complete

AbstractN. Linialet al.raised the question of how difficult the computation of the Vapnik–Červonenkis dimension of a concept class over a finite universe is. C. Papadimitriou and M. Yannakakis obtained a first answer using matrix representations of concept classes. However, this approach does not capture classes having exponential size, like monomials, which are encountered in learning theory. We choose a more natural representation, which leads us to redefine the VC DIMENSION problem. We establish that VC DIMENSION is∑p3-complete, thereby giving a rare natural example of a∑p3-complete problem
On the Learnability of Rich Function Classes

AbstractThe probably approximately correct (PAC) model of learning and its extension to real-valued function classes sets a rigorous framework based upon which the complexity of learning a target from a function class using a finite sample can be computed. There is one main restriction, however, that the function class have a finite VC-dimension or scale-sensitive pseudo-dimension. In this paper we present an extension of the PAC framework with which rich function classes with possibly infinite pseudo-dimension may be learned with a finite number of examples and a finite amount of partial information. As an example we consider learning a family of infinite dimensional Sobolev classes
Polynomial Time Approximation Schemes for Dense Instances of NP-Hard Problems

AbstractWe present a unified framework for designing polynomial time approximation schemes (PTASs) for “dense” instances of many NP-hard optimization problems, including maximum cut, graph bisection, graph separation, minimumk-way cut with and without specified terminals, and maximum 3-satisfiability. By dense graphs we mean graphs with minimum degreeΩ(n), although our algorithms solve most of these problems so long as the average degree isΩ(n). Denseness for nongraph problems is defined similarly. The unified framework begins with the idea ofexhaustive sampling:picking a small random set of vertices, guessing where they go on the optimum solution, and then using their placement to determine the placement of everything else. The approach then develops into a PTAS for approximating certainsmoothinteger programs, where the objective function and the constraints are “dense” polynomials of constant degree
The Computational Complexity of Some Problems of Linear Algebra

AbstractWe consider the computational complexity of some problems dealing with matrix rank. Let E, S be subsets of a commutative ring R. Let x1, x2, …, xt be variables. Given a matrix M=M(x1, x2, …, xt) with entries chosen from E∪{x1, x2, …, xt}, we want to determine maxrankS(M)=max(a1, a2, …, at)∈St rank M(a1, a2, …, at) and minrankS(M)=min(a1, a2, …, at)∈St rank M(a1, a2, …, at). There are also variants of these problems that specify more about the structure of M, or instead of asking for the minimum or maximum rank, they ask if there is some substitution of the variables that makes the matrix invertible or noninvertible. Depending on E, S, and which variant is studied, the complexity of these problems can range from polynomial-time solvable to random polynomial-time solvable to NP-complete to PSPACE-solvable to unsolvable. An approximation version of the minrank problem is shown to be MAXSNP-hard
Attractors of Linear Cellular Automata

AbstractIn this paper we study the asymptotic behavior of D-dimensional linear cellular automata over the ring Zm (D⩾1, m⩾2). In the first part of the paper we consider nonsurjective cellular automata (CA). We prove that, after a transient phase of length at most ⌊log2m⌋, the evolution of a linear nonsurjective cellular automata F takes place completely within a subspace YF. This result suggests that we can get valuable information on the long term behavior of F by studying its properties when restricted to YF. We prove that such study is possible by showing that the system (YF, F) is topologically conjugated to a linear cellular automata F* defined over a different ring Zm. In the second part of the paper, we study the attractor sets of linear cellular automata. Recently, Kurka has shown that CA can be partitioned into five disjoint classes according to the structure of their attractors. We present a procedure for deciding the membership in Kurka's classes for any linear cellular automata. Our procedure requires only gcd computations involving the coefficients of the local rule associated to the cellular automata
Creating Strong, Total, Commutative, Associative One-Way Functions from Any One-Way Function in Complexity Theory

AbstractRabi and Sherman presented novel digital signature and unauthenticated secret-key agreement protocols, developed by themselves and by Rivest and Sherman. These protocols use strong, total, commutative (in the case of multiparty secret-key agreement), associative one-way functions as their key building blocks. Although Rabi and Sherman did prove that associative one-way functions exist if P≠NP, they left as an open question whether any natural complexity-theoretic assumption is sufficient to ensure the existence of strong, total, commutative, associative one-way functions. In this paper, we prove that if P≠NP then strong, total, commutative, associative one-way functions exist
Algorithms for Matrix Groups and the Tits Alternative

AbstractTits has shown that a finitely generated matrix group either contains a nonabelian free group or has a solvable subgroup of finite index. We give a polynomial time algorithm for deciding which of these two conditions holds for a given finitely generated matrix group over an algebraic number field. Noting that many computational problems are undecidable for groups with nonabelian free subgroups, we investigate the complexity of problems relating to matrix groups with solvable subgroups of finite index. For such a groupG, we are able in polynomial time to compute a homomorphismφsuch thatφ(G) is a finite matrix group and the kernel ofφis solvable. If, in addition,Ghas a nilpotent subgroup of finite index, we obtain much stronger results. For such groups, we show how to effectively compute an encoding of elements ofGsuch that the encoding length of an element obtained as a product of length ⩽ℓ over the generators isO(logℓ) times a polynomial in the input length. This result is the best possible; it has been shown by Tits and Wolf that if a finitely generated matrix group does not have a nilpotent subgroup of finite index, then the number of group elements expressible as words of length ℓ over the generators grows ascℓfor some constantc>1 depending onG. For groups with abelian subgroups of finite index, we obtain a Las Vegas algorithm for several basic computational tasks, including membership testing and computing a presentation. This generalizes recent work of Beals and Babai, who give a Las Vegas algorithm for the case of finite groups, as well as recent work of Babai, Beals, Cai, Ivanyos, and Luks, who give a deterministic algorithm for the case of abelian groups
BPHSPACE(S)⊆DSPACE(S3/2)

AbstractWe prove that any language that can be recognized by a randomized algorithm (with possibly a two-sided error) that runs in spaceO(S) and always terminates can be recognized by deterministic algorithm running in spaceO(S3/2). This improves the best previously known result that such algorithms have deterministic spaceO(S2) simulations which, for one-sided error algorithms, follows from Savitch's theorem and, for two-sided error algorithms, follows by reduction to recursive matrix powering. Our result includes as a special case the result due to Nisan, Szemerédi, and Wigderson that undirected connectivity can be computed in spaceO(log3/2n). It is obtained via a new algorithm for repeated squaring of a matrix; we show how to approximate the 2rth power of ad×dmatrix in spaceO(r1/2logd), improving on the bound ofO(rlogd) that comes from the natural recursive algorithm. The algorithm employs Nisan's pseudorandom generator for space–bounded computation, together with some new techniques for reducing the number of random bits needed by an algorithm
An Exponential Lower Bound for the Size of Monotone Real Circuits

AbstractWe prove a lower bound, exponential in the eighth root of the input length, on the size of monotone arithmetic circuits that solve an NP problem related to clique detection. The result is more general than the famous lower bound of Razborov and Andreev, because the gates of the circuit are allowed to compute arbitrary monotone binary real-valued functions (including AND and OR). Our proof is relatively simple and direct and uses the method of counting bottlenecks. The generalization was proved independently by Pudlák using a different method, who also showed that the result can be used to obtain an exponential lower bound on the size of unrestricted cutting plane proofs in the propositional calculus
Synthesizers and Their Application to the Parallel Construction of Pseudo-Random Functions

AbstractA pseudo-random function is a fundamental cryptographic primitive that is essential for encryption, identification, and authentication. We present a new cryptographic primitive called pseudo-random synthesizer and show how to use it in order to get a parallel construction of a pseudo-random function. We show severalNC1implementations of synthesizers based on concrete intractability assumptions as factoring and the Diffie–Hellman assumption. This yields the first parallel pseudo-random functions (based on standard intractability assumptions) and the only alternative to the original construction of Goldreich, Goldwasser, and Micali. In addition, we show parallel constructions of synthesizers based on other primitives such as weak pseudo-random functions or trapdoor one-way permutations. The security of all our constructions is similar to the security of the underlying assumptions. The connection with problems in computational learning theory is discussed
Transforming Curves on Surfaces

AbstractWe describe an optimal algorithm to decide if one closed curve on a triangulated 2-manifold can be continuously transformed to another, i.e., if they are homotopic. SupposeC1andC2are two closed curves on a surfaceMof genusg. Further, supposeTis a triangulation ofMof sizensuch thatC1andC2are represented as edge–vertex sequences of lengthsk1andk2inT, respectively. Then, our algorithm decides ifC1andC2are homotopic inO(n+k1+k2) time and space, providedg≠2 ifMis orientable, andg≠3, 4 ifMis nonorientable. This implies as well an optimal algorithm to decide if a closed curve on a surface can be continuously contracted to a point. Except for three low genus cases, our algorithm completes an investigation into the computational complexity of two classical problems for surfaces posed by the mathematician Max Dehn at the beginning of this century. The novelty of our approach is in the application of methods from modern combinatorial group theory
The Learnability of Unions of Two Rectangles in the Two-Dimensional Discretized Space

AbstractWe study the problem of properly learning unions of two axis-parallel rectangles over the domain {0, n−1}2 in the on-line model with equivalence queries. When only O(logn) equivalence queries are allowed, this problem is one of the five interesting open problems proposed by W. Maass and G. Turán (Mach. Learning14, 1994, 251–269), regarding learning geometric concepts. In this paper, we design an efficient algorithm that properly learns unions of two rectangles over the domain {0, n−1}2 using O(log2n) equivalence queries
A Self-Stabilizing Algorithm for Detecting Fundamental Cycles in a Graph

AbstractThis paper presents a self-stabilizing algorithm for detecting a set of fundamental cycles of a connected undirected graph on an asynchronous distributed or network model of computation. The output of the algorithm is available in a distributed manner; i.e., when the algorithm terminates each node of the graph knows exactly how many fundamental cycles are passing through it and also a unique identifier for each of these fundamental cycles. The algorithm is resilient to transient faults and does not require initialization. It has been proved that the algorithm is correct and requires O(n2) time if the depth-first search spanning tree of the graph is known, or else it requires O(n3) time, where n is the number of nodes in the graph
A Technique for Proving Decidability of Containment and Equivalence of Linear Constraint Queries

AbstractWe develop a new technique based on counter machines to study the containment and equivalence of queries with linear constraints over integers Z, natural numbers N, rational numbers Q, and real numbers R. We show that the problems are dedicable in exponential space with an exponential time lower bound for conjunctive queries with linear constraints. For a subclass, called SQL-like conjunctive queries, the problems are shown to have a polynomial space upper bound. We also use the counter machine technique to show that for a syntactically restricted subclass of first-order queries with linear constraints over Z and N, the containment and equivalence problems are undecidable for finite databases but decidable for a subclass of finite databases
On the Decidability of Semilinearity for Semialgebraic Sets and Its Implications for Spatial Databases

AbstractSeveral authors have suggested using first-order logic over the real numbers to describe spatial database applications. Geometric objects are then described by polynomial inequalities with integer coefficients involving the coordinates of the objects. Such geometric objects are called semialgebraic sets. Similarly, queries are expressed by polynomial inequalities. The query language thus obtained is usually referred to as FO+poly. From a practical point of view, it has been argued that a linear restriction of this so-called polynomial model is more desirable. In the so-called linear model, geometric objects are described by linear inequalities and are called semilinear sets. The language of the queries expressible by linear inequalities is usually referred to as FO+linear. As part of a general study of the feasibility of the linear model, we show in this paper that semilinearity is decidable for semialgebraic sets. In doing so, we point out important subtleties related to the type of the coefficients in the linear inequalities used to describe semilinear sets. An important concept in the development of the paper is regular stratification. We point out the geometric significance, as well as its significance in the context of FO+linear and FO+poly computations. The decidability of semilinearity of semialgebraic sets has an important consequence. It has been shown that it is undecidable whether a query expressible in FO+poly is linear, i.e., maps spatial databases of the linear model into spatial databases of the linear model. It follows now that, despite this negative result, there exists a syntactically definable language precisely expressing the linear queries expressible in FO+poly
On the Complexity of Database Queries

AbstractWe revisit the issue of the complexity of database queries, in the light of the recent parametric refinement of complexity theory. We show that, if the query size (or the number of variables in the query) is considered as a parameter, then the relational calculus and its fragments (conjunctive queries, positive queries) are classified at appropriate levels of the so-called W hierarchy of Downey and Fellows. These results strongly suggest that the query size is inherently in the exponent of the data complexity of any query evaluation algorithm, with the implication becoming stronger as the expressibility of the query language increases. On the positive side, we show that this exponential dependence can be avoided for the extension of acyclic queries with ≠ (but not <) inequalities
Equivalence of Keyed Relational Schemas by Conjunctive Queries

AbstractThe concept of two schemas being equivalent is fundamental to database design, schema integration, and data model translation. An important notion of schema equivalence, query equivalence, was introduced by Atzeni et al., and used to evaluate the correctness of schema transformations. The logically equivalent notion of calculous equivalence, as well as three progressively more general notions of schema equivalence were introduced in 1984 by Hull, who showed that two schemas with no dependencies are equivalent (under all four notions of equivalence) if and only if they are identical (up to renaming and re-ordering of attributes and relations). Hull also conjectured that the same result holds for schemas with primary keys. In this work, we resolve the conjecture in the affirmative for the case of query equivalence based on mappings using conjunctive relational queries with equality selections