List Superstructures and Semantics of Iterators

Constraints formalize the dependencies in a physical world in terms of a logical relation among several unknowns. Constraint satisfaction methods allow efficient navigation of large search spaces to find an optimal solution that satisfies given constraints. This paper explores the application of constraint satisfaction methods to personalize generic information content with respect to a user-model. We present a constraint satisfaction based information personalization framework that (a) generates personalized information via the dynamic selection and synthesis of multiple information-snippets; and (b) ensures that the dynamically adapted personalized information is factually consistent. We present four constraint satisfaction methods that cumulatively work to maximize collaboration and minimize conflicts between a set of information-snippets in order to dynamically generate personalized information.

An efficient and reliable constrained genetic algorithm based load flow algorithm is developed. The components and the constraint satisfaction methods in the algorithm are presented. A nodal voltage differential technique and a gradient method are developed to accelerate the solution process in the algorithm. A method for dealing with generator reactive power limits is also developed. The new algorithm can determine multiple load flow solutions and can be used to determine the loadability limits of transmission systems. Its power is demonstrated through its applications to evaluate the loadability of the IEEE 30-, 57- and 118-node systems. Detailed results on the 30-node system are presented.

Given a first order language L, and a notion of a logic L w.r.t. L, we investigate the topological properties of the space of L-structures for L. We show that under a topology called the query topology which arises naturally in logic programming, the space of L-models (where L is a decent logic) of any sentence (set of clauses) in L may be regarded as a (closed, compact) T4-space. We then investigate the properties of maps from structures to structures. Our results allow us to apply various well-known results on the fixed-points of operators on topological spaces to the semantics of logic programming – in particular, we are able to derive necessary and sufficient topological conditions for the completion of covered general logic programs to be consistent. Moreover, we derive sufficient conditions guaranteeing the consistency of program completions, and for logic programs to be determinate. We also apply our results to characterize consistency of the unions of program completions.

Aczel's theory of hypersets provides an interesting alternative to the standard view of sets as inductively constructed, well-founded objects, thus providing a convienent formalism in which to consider non-well-founded versions of classically well-founded constructions, such as the “circular logic” of [3], This theory and ZFC are mutually interpretable; in particular, any model of ZFC has a canonical “extension” to a non-well-founded universe. The construction of this model does not immediately generalize to weaker set theories such as the theory of admissible sets. In this paper, we formulate a version of Aczel's antifoundation axiom suitable for the theory of admissible sets. We investigate the properties of models of the axiom system KPU−, that is, KPU with foundation replaced by an appropriate strengthening of the extensionality axiom. Finally, we forge connections between “non-wellfounded sets over the admissible set A” and the fragment LA of the modal language L∞.

Constraint solving techniques are frequently based on constraint propagation, a technique that can be seen as a specific form of deduction. Using constraint programming languages enhanced with constraint handling rules facilities, constraint propagation can be achieved just by applying deduction rules to constraints. The automatic generation of propagation rules has been recently investigated in the particular case of finite domains, when constraint satisfaction problems are based on predefined, explicitly given constraints. Due to its interest for practical applications, several solvers have been developed during the last decade for integrating finite domains into (constraint) logic programming. A possible way of integration is implemented using a unification algorithm to compute most general solutions of constraints. In this paper, we propose a mixed approach for designing finite domain constraints solvers: it consists in using a solver based on unification to improve the generation of propagation rules.

Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational complexity of all VCSPs for finite sets of cost functions over finite domains has been classified. Many natural optimisation problems, however, cannot be formulated as VCSPs over a finite domain. We initiate the systematic investigation of the complexity of infinite-domain VCSPs with piecewise linear homogeneous cost functions. Such VCSPs can be solved in polynomial time if the cost functions are improved by fully symmetric fractional operations of all arities. We show this by reducing the problem to a finite-domain VCSP which can be solved using the basic linear program relaxation. It follows that VCSPs for submodular PLH cost functions can be solved in polynomial time; in fact, we show that submodular PLH functions form a maximally tractable class of PLH cost functions.

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special cases of the constraint satisfaction problem (CSP), which is the problem of determining whether a set of constraints is satisfiable. In this paper we study the worst-case time complexity of NP-complete CSPs. Our main interest is in the CSP problem parameterized by a constraint language Gamma (CSP(Gamma)), and how the choice of Gamma affects the time complexity. It is believed that CSP(Gamma) is either tractable or NP-complete, and the algebraic CSP dichotomy conjecture gives a sharp delineation of these two classes based on algebraic properties of constraint languages. Under this conjecture and the ETH, we first rule out the existence of subexponential algorithms for finite domain NP-complete CSP(Gamma) problems. This result also extends to certain infinite-domain CSPs and structurally restricted CSP(Gamma) problems. We then begin a study of the complexity of NP-complete CSPs where one is allowed to arbitrarily restrict the values of individual variables, which is a very well-studied subclass of CSPs. For such CSPs with finite domain D, we identify a relation SD such that (1) CSP({SD}) is NP-complete and (2) if CSP(Gamma) over D is NP-complete and solvable in O(c^n) time, then CSP({SD}) is solvable in O(c^n) time, too. Hence, the time complexity of CSP({SD}) is a lower bound for all CSPs of this particular kind. We also prove that the complexity of CSP({SD}) is decreasing when |D| increases, unless the ETH is false. This implies, for instance, that for every c>1 there exists a finite-domain Gamma such that CSP(Gamma) is NP complete and solvable in O(c^n) time.

Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order logic theory on a given finite domain. First-Order Logic theories that admit polynomial-time WFOMC w.r.t domain cardinality are called domain liftable. We introduce the concept of lifted interpretations as a tool for formulating closed forms for WFOMC. Using lifted interpretations, we reconstruct the closed-form formula for polynomial-time FOMC in the universally quantified fragment of FO2, earlier proposed by Beame et al. We then expand this closed-form to incorporate cardinality constraints, existential quantifiers, and counting quantifiers (a.k.a C2) without losing domain-liftability. Finally, we show that the obtained closed-form motivates a natural definition of a family of weight functions strictly larger than symmetric weight functions.

The tractability conjecture for constraint satisfaction problems (CSPs) describes the constraint languages over a finite domain whose CSP can be solved in polynomial-time. The precise formulation of the conjecture uses basic notions from universal algebra. In this talk, we give a short introduction to the universal-algebraic approach to the study of the complexity of CSPs. Finally, we discuss attempts to generalise the tractability conjecture to large classes of constraint languages over infinite domains, in particular for constraint languages that arise in qualitative temporal and spatial reasoning.

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring. The PCSP significantly extends the standard decision CSP. The complexity of CSPs with a fixed constraint language on a finite domain has recently been fully classified, greatly guided by the algebraic approach, which uses polymorphisms — high-dimensional symmetries of solution spaces — to analyse the complexity of problems. The corresponding classification for PCSPs is wide open and includes some long-standing open questions, such as the complexity of approximate graph colouring, as special cases. The basic algebraic approach to PCSP was initiated by Brakensiek and Guruswami, and in this paper we significantly extend it and lift it from concrete properties of polymorphisms to their abstract properties. We introduce a new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem, and show that every PCSP with a fixed constraint language is equivalent to a problem of this form. This allows us to identify a ”measure of symmetry” that is well suited for comparing and relating the complexity of different PCSPs via the algebraic approach. We demonstrate how our theory can be applied by improving the state-of-the-art in approximate graph colouring: we show that, for any k≥ 3, it is NP-hard to find a (2k−1)-colouring of a given k-colourable graph.

SummaryThis paper describes a learning parallel constraint programming (CP) solver designed for solving CP problems with several instances on massively parallel computing platforms comprising multi‐core parallel machines or Many Integrated Cores. The CP solver proposed in this work is based on aPortfolioparallelization that employs a linear reward inaction learning algorithm in order to obtain the best possible performance for a large set of instances of the same problem. The linear reward inaction algorithm enables the prediction of the number of cores to be assigned to each search strategy based on previous experiments, reducing the computing time required to solve constraint satisfaction and optimization problems. The underlying principle of thePortfolioapproach is to runNsequential search strategies usingNcomputing cores (NToNPortfolio) where each core uses its own strategy in order to perform a search that is different from strategies used by the other cores. The first strategy that finds a solution stops all other strategies. The problem with theNToNPortfolioapproach is that the number of search strategies is very small compared with the current number of computing cores used by the parallel machines. However, using an internal parallelization for each search strategy, it is possible to runNparallel search usingPcomputing cores withP≫N(NToPPortfolio). ThisNToPPortfolioperforms suboptimally for solving different CP problems because many computing resources are wasted. To improve thisPortfoliomodel, an adaptiveNToPPortfoliowas proposed, which tries to privilege the strategy that is most likely to find a solution first in order to give it more computing cores than the other strategies. However, the main problem with the adaptivePortfoliois that it loses all the learned information at the end of each search; it is designed to solve just one CP problem. Furthermore, many computational resources are wasted by bothPortfoliosolvers, the non‐adaptive (NToNandNToP) and the adaptiveNToPPortfolio, when employed in some industrial projects, such as thePAJEROproject, which always solves different instances of the same CP problem. To minimize the amount of wasted resources and to learn the most efficient search strategies, we propose a new learningPortfoliosolver that uses a learning algorithm that configures automatically number of cores to each search. The performance obtained using the differentPortfoliosolvers is compared and illustrated by solving CP problems using as example the Google OR‐Tools solver. Copyright © 2016 John Wiley & Sons, Ltd.

An interpretation of lattice-valued logic, defined by Titani, in basic fuzzy logic, defined by Hájek, is presented. Moreover, Titani's axioms of lattice-valued set theory are interpreted in fuzzy set theory, as defined by the authors.

Mining maximal hyperclique pattern: A hybrid search strategy

This thesis introduces a well-ordering principle of type two, which we call the Bachmann-Howard principle. The main result states that the Bachmann-Howard principle is equivalent to the existence of admissible sets and thus to Pi^1_1-comprehension. This solves a conjecture of Rathjen and Montalban. The equivalence is interesting because it relates concrete notions from ordinal analysis to abstract notions from reverse mathematics and set theory. A type-one well-ordering principle is a map T which transforms each well-order X into another well-order T[X]. If T is particularly uniform then it is called a dilator (due to Girard). Our Bachmann-Howard principle transforms each dilator T into a well-order BH(T). The latter is a certain kind of fixed-point: It comes with an almost monotone collapse theta:T[BH(T)]->BH(T) (we cannot expect full monotonicity, since the order-type of T[X] may always exceed the order-type of X). The Bachmann-Howard principle asserts that such a collapsing structure exists. In fact we define three variants of this principle: They are equivalent but differ in the sense in which the order BH(T) is computed. On a technical level, our investigation involves the following achievements: a detailed discussion of primitive recursive set theory as a basis for set-theoretic reverse mathematics; a formalization of dilators in weak set theories and second-order arithmetic; a functorial version of the constructible hierarchy; an approach to deduction chains (Schutte) and beta-completeness (Girard) in a set-theoretic context; and a beta-consistency proof for Kripke-Platek set theory. Independently of the Bachmann-Howard principle, the thesis contains a series of results connected to slow consistency (introduced by S.-D. Friedman, Rathjen and Weiermann): We present a slow reflection statement and investigate its consistency strength, as well as its computational properties. Exploiting the latter, we show that instances of the Paris-Harrington principle can only have extremely long proofs in certain fragments of arithmetic.

Convex rough sets on finite domains