logical analysis of numerical data logical analysis of data lad is a methodology developed since the late eighties aimed at discovering hidden structural information in data sets lad was originally developed for analyzing binary data by using the theory of partially defined boolean functions an extension of lad for the analysis of numerical data sets is achieved through the process of binarization consisting in the replacement of each numerical variable by binary indicator variables each showing whether the value of the original variable is above or below a certain level binarization was successfully applied to the analysis of a variety of real life data sets this paper develops the theoretical foundations of the binarization process studying the combinatorial optimization problems related to the minimization of the number of binary variables to provide an algorithmic framework for the practical solution of such problems we construct compact linear integer programming formulations of them we develop polynomial time algorithms for some of these minimization problems and prove np hardness of others

analysis of a unilateral contact problem taking into account adhesion and friction abstract in this paper we investigate a contact problem between a viscoelastic body and a rigid foundation when both the effects of the irreversible adhesion and of the friction are taken into account we describe the adhesion phenomenon in terms of a damage surface parameter according to fremond s theory and we model unilateral contact by signorini conditions and friction by a nonlocal coulomb law all the constraints on the internal variables as well as the contact and the friction conditions are rendered by means of subdifferential operators whence the highly nonlinear character of the resulting pde system our main result states the existence of a global in time solution to a suitable variational formulation of the related cauchy problem it is proved by an approximation procedure combined with time discretization

a computational method for frictional contact problem using finite element method a numerical procedure is developed for the solution of the two dimensional frictional contact problems with coulomb s law of friction the formulation for this procedure is reduced to a complementarity problem the contact region is separated into stick and slip regions and the contact stress can be solved systematically by applying the solution technique of the complementarity problem

on the desirability of acyclic database schemes a class of database schemes called acychc was recently introduced it is shown that this class has a number of desirable properties in particular several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity in addition several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given and a smaple algorithm for determining acychclty is presented also given are several eqmvalent characterizations of those sets m of multivalued dependencies such that m is the set of murlvalued dependencies that are the consequences of a given join dependency several characterizations for a conflict free in the sense of lien set of muluvalued dependencies are provided

on an iterative method for variational inequalities a number of numerical solutions are presented as examples of a new iterative method for variational inequalities the iterative method is based on the reduction of variational inequalities to the wiener hopf equations for obstacle problems the convergence is guaranteed inw 1 p spaces forp 2 the examples presented are one and two dimensional obstacle problems in cases when the greens function is known but the method is very general

uncovering trees in constraint networks abstract this paper examines the possibility of removing redundant information from a given knowledge base and restructuring it in the form of a tree to enable efficient problem solving routines we offer a novel approach that guarantees removal of all redandancies that hide a tree structure we develop a polynomial time algorithm that given an arbitrary binary constraint network either extracts by edge removal a precise tree representation from the path consistent version of the network or acknowledges that no such tree can be extracted in the latter case a tree is generated that may serve as an approximation to the original network

iterative methods for linear complementarity problems with upperbounds on primary variables this paper is concerned with iterative methods for the linear complementarity problem lcp of findingx and y in rn such thatc dx y 0 b x 0 andxt c dx y yt b x 0 whenb 0 this is the lcp m q withm l 0d t which is in turn equivalent to a linear variational inequality over a rectangle this type of problem arises for example from quadratic programming qp problems with upper and lower bounds ifd is symmetric and from multicommodity market equilibrium problems with institutional price controls imposed ifd is not necessarily symmetric iterative methods for the lcp m q with symmetricm are well developed and studied using qp applications for nonsymmetric cases withm being either an h matrix with positive diagonals or a z matrix there exists a robust iterative method with guaranteed convergence this paper extends this algorithm so that the lcp m q withm l 0d t which is neither symmetric nor an h matrix with positive diagonals nor a z matrix can be processed when onlyd notm satisfies such properties the case whered is nonsymmetric is explicitly discussed

the inverse satisfiability problem we study the complexity of telling whether a set of bit vectors represents the set of all satisfying truth assignments of a boolean expression of a certain type we show that the problem is conp complete when the expression is required to be in conjunctive normal form with three literals per clause 3cnf we also prove a dichotomy theorem analogous to the classical one by schaefer stating that unless p np the problem can be solved in polynomial time if and only if the clauses allowed are all horn or all anti horn or all 2cnf or all equivalent to equations modulo two

learning possibilistic graphical models from data graphical models especially probabilistic networks like bayes networks and markov networks are very popular to make reasoning in high dimensional domains feasible since constructing them manually can be tedious and time consuming a large part of recent research has been devoted to learning them from data however if the dataset to learn from contains imprecise information in the form of sets of alternatives instead of precise values this learning task can pose unpleasant problems in this paper we survey an approach to cope with these problems which is not based on probability theory as the more common approaches like e g expectation maximization but uses the possibility theory as the underlying calculus of a graphical model we provide semantic foundations of possibilistic graphical models explain the rationale of possibilistic decomposition as well as the graphical representation of decompositions of possibility distributions and finally discuss the main approaches to learn possibilistic graphical models from data

optimal compression of propositional horn knowledge bases complexity and approximation abstract horn formulae play a prominent role in artificial intelligence and logic programming in this paper we investigate the problem of optimal compression of propositional horn production rule knowledge bases the standard approach to this problem consisting in the removal of redundant rules from a knowledge base leads to an irredundant but not necessarily optimal knowledge base we prove here that the number of rules in any irredundant horn knowledge base involving n propositional variables is at most n 1 times the minimum possible number of rules therefore the quadratic time transformation of an arbitrary horn production rule base to an equivalent irredundant and prime one presented in 9 provides a reasonable approximation algorithm in order to formalize the optimal compression problem we define a boolean function of a knowledge base as being the function whose set of true points is the set of models of the knowledge base in this way the optimal compression of production rule knowledge bases becomes a problem of boolean function minimization in this paper we prove that the minimization of horn functions i e boolean functions associated to horn knowledge bases is np complete

a regression type problem let x 1 x n be random vectors that take values in a compact set in r d d 1 2 let y 1 y n be random variables the responses which conditionally on x 1 x 1 x n x n are independent with densities f y x i b x i i l n assuming that lies in a sup norm compact space of real valued functions an l 1 consistent estimator of is constructed via empirical measures the rate of convergence of the estimator of the estimator to the true parameter depends on kolmogorov s entropy of

a quasistatic frictional problem with normal compliance a friction and contact problem will be considered for an elastic solid body which under the influence of volume and surface forces is in contact with a rigid foundation

logical analysis of binary data with missing bits we model a given pair of sets of positive and negative examples each of which may contain missing components as a partially defined boolean function with missing bits pbmb t f where email protected 0 1 n and email protected 0 1 n and stands for a missing bit then we consider the problem of establishing a boolean function an extension f 0 1 n 0 1 belonging to a given function class c such that f is true respectively false for every vector in t respectively in f this is a fundamental problem encountered in many areas such as learning theory pattern recognition example based knowledge bases logical analysis of data knowledge discovery and data mining in this paper depending upon how to deal with missing bits we formulate three types of extensions called robust consistent and most robust extensions for various classes of boolean functions such as general positive horn threshold decomposable and k dnf the complexity of the associated problems are then clarified some of them are solvable in polynomial time while the others are np hard

network based heuristics for constraint satisfaction problems abstract many ai tasks can be formulated as constraint satisfaction problems csp i e the assignment of values to variables subject to a set of constraints while some csps are hard those that are easy can often be mapped into sparse networks of constraints which in the extreme case are trees this paper identifies classes of problems that lend themselves to easy solutions and develops algorithms that solve these problems optimally the paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree structured csps the advice is generated by simplifying the pending subproblems into trees counting the number of consistent solutions in each simplified subproblem and comparing these counts to decide among the choices pending in the original problem

the complexity of minimal satisfiability problems a dichotomy theorem for a class of decision problems is a result asserting that certain problems in the class are solvable in polynomial time while the rest are np complete the first remarkable such dichotomy theorem was proved by schaefer in 1978 it concerns the class of generalized satisfiability problems sat s whose input is a cnf s formula i e a formula constructed from elements of a fixed set s of generalized connectives using conjunctions and substitutions by variables here we investigate the complexity of minimal satisfiability problems min sat s where s is a fixed set of generalized connectives the input to such a problem is a cnf s formula and a satisfying truth assignment the question is to decide whether there is another satisfying truth assignment that is strictly smaller than the given truth assignment with respect to the coordinate wise partial order on truth assignments minimal satisfiability problems were first studied by researchers in artificial intelligence while investigating the computational complexity of propositional circumscription the question of whether dichotomy theorems can be proved for these problems was raised at that time but was left open we settle this question affirmatively by establishing a dichotomy theorem for the class of all min sat s problems where s is a finite set of generalized connectives we also prove a dichotomy theorem for a variant of min sat s in which the minimization is restricted to a subset of the variables whereas the remaining variables may vary arbitrarily this variant is related to extensions of propositional circumscription and was first studied by cadoli moreover we show that similar dichotomy theorems hold also when some of the variables are assigned constant values finally we give simple criteria that tell apart the polynomial time solvable cases of these minimal satisfiability problems from the np complete ones

a posteriori error estimation of h p finite element approximations of frictional contact problems abstract dynamic and static frictional contact problems are described using the normal compliance law on the contact boundary dynamic problems are recast into quasistatic problems by time discretization an a posteriori error estimator is developed for a nonlinear elliptic equation of corresponding static or quasistatic problems the a posteriori error estimator is applied to a frictionless case and extended to frictional contact problems also an adaptive strategy is introduced and h p finite element meshes are obtained through a procedure based on a priori and a posteriori error estimations numerical examples are given to support the theoretical results

tractable constraints on ordered domains abstract finding solutions to a constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted in this paper we identify a restricted set of contraints which gives rise to a class of tractable problems this class generalizes the notion of a horn formula in propositional logic to larger domain sizes we give a polynomial time algorithm for solving such problems and prove that the class of problems generated by any larger set of constraints is np complete

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

theory and approximation of quasistatic frictional contact problems abstract a variational formulation of a class of quasistatic frictional contact problems is derived for which a compliant interface model of the contact surface is assumed proof of existence and uniqueness of solutions is given finite element approximations of a regularized version of the fractional problem are developed and a priori error estimates are derived the theory is implemented and used to solve representative test problems of frictional contact the numerical simulations show that frictional stress distributions can be very sensitive to load histories and surface properties of contact interfaces

fundamental study the multiple facets of the canonical direct unit implicational basis the notion of dependencies between attributes arises in many areas such as relational databases data analysis data mining formal concept analysis knowledge structures formalization of dependencies leads to the notion of so called full implicational systems or full family of functional dependencies which is in one to one correspondence with the other significant notions of closure operator and of closure system an efficient generation of a full implicational system or a closure system can be performed from equivalent implicational systems and in particular from the bases for such systems for example the so called canonical basis this paper shows the equality between five other bases originating from different works and satisfying various properties in particular they are unit implicational systems the three main properties of this unique basis are the directness canonical and minimal properties whence the name canonical direct unit implicational basis given to this unit implicational system the paper also gives a nice characterization of this canonical basis and makes precise its link with the prime implicants of the horn function associated to a closure operator it concludes that it is necessary to compare more closely related works made independently and with a different terminology in order to take advantage of the really new results in these works

on random variational inequalities abstract in this paper we consider a random variational inequality an existence theorem for a unique solution of a random variational inequality is proved which includes the results of noor lions and stampacchia several special cases which can be obtained from our results are also discussed

generalized nash games and quasi variational inequalities abstract a generalized nash game is an n person noncooperative game with nondisjoint strategy sets other names for this game form include social equilibria and pseudo nash games this paper explores both the qualitative and quantitative properties of such games through the use of quasi variational inequality theory several interesting relationships between the variational and quasi variational inequality forms of this class of games are described and the practical implementation of generalized nash games are explored at length

error free and best fit extensions of partially defined boolean functions abstract in this paper we address a fundamental problem related to the induction of boolean logic given a set of data represented as a set of binary truen vectors or positive examples and a set of falsen vectors or negative examples we establish a boolean function or an extension f so thatfis true resp false in every given true resp false vector we shall further require that such an extension belongs to a certain specified class of functions e g class of positive functions class of horn functions and so on the class of functions represents our a priori knowledge or hypothesis about the extensionf which may be obtained from experience or from the analysis of mechanisms that may or may not cause the phenomena under consideration the real world data may contain errors e g measurement and classification errors might come in when obtaining data or there may be some other influential factors not represented as variables in the vectors in such situations we have to give up the goal of establishing an extension that is perfectly consistent with the given data and we are satisfied with an extensionfhaving the minimum number of misclassifications both problems i e the problem of finding an extension within a specified class of boolean functions and the problem of finding a minimum error extension in that class will be extensively studied in this paper for certain classes we shall provide polynomial algorithms and for other cases we prove their np hardness

reasoning with models we develop a model based approach to reasoning in which the knowledge base is represented as a set of models satisfying assignments rather than a logical formula and the set of queries is restricted we show that for every propositional knowledge base kb there exists a set of characteristic models with the property that a query is true in kb if and only if it is satisfied by the models in this set we characterize a set of functions for which the model based representation is compact and provides efficient reasoning these include cases where the formula based representation does not support efficient reasoning in addition we consider the model based approach to abductive reasoning and show that for any propositional kb reasoning with its model based representation yields an abductive explanation in time that is polynomial in its size some of our technical results make use of the monotone theory a new characterization of boolean functions recently introduced the notion of restricted queries is inherent in our approach this is a wide class of queries for which reasoning is efficient and exact even when the model based representation kb provides only an approximate representation of the domain in question moreover we show that the theory developed here generalizes the model based approach to reasoning with horn expressions and captures even the notion of reasoning with horn approximations

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

general contact boundary conditions and the analysis of frictional systems abstract general factional systems i e solid bodies interacting by contact forces are investigated and variational formulations are presented following recent ideas general contact boundary conditions are formulated using the notions of subdifferentials and generalized gradients

on minimal constraint networks in a minimal binary constraint network every tuple of a constraint relation can be extended to a solution the tractability or intractability of computing a solution to such a minimal network was a long standing open question dechter conjectured this computation problem to be np hard we prove this conjecture we also prove a conjecture by dechter and pearl stating that for k 2 it is np hard to decide whether a single constraint can be decomposed into an equivalent k ary constraint network we show that this holds even in case of bi valued constraints where k 3 which proves another conjecture of dechter and pearl finally we establish the tractability frontier for this problem with respect to the domain cardinality and the parameter k

an error estimate for the signorini problem with coulomb friction approximated by finite elements the present paper is concerned with the unilateral contact model and the coulomb friction law in linear elastostatics we consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area the chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the contact zone a convenient discrete contact and friction condition is introduced in order to perform a convergence study we finally obtain a first a priori error estimate under the assumptions ensuring the uniqueness of the solution to the continuous problem

rates of convergence of minimum distance estimators and kolmogorov s entropy on construit des estimateurs robustes et on montre que le taux de convergence resultant depend naturellement d une fonction entropie

on the hardness of approximate reasoning abstract many ai problems when formalized reduce to evaluating the probability that a propositional expression is true in this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability we consider various methods used in approximate reasoning such as computing degree of belief and bayesian belief networks as well as reasoning techniques such as constraint satisfaction and knowledge compilation that use approximation to avoid computational difficulties and reduce them to model counting problems over a propositional domain we prove that counting satisfying assignments of propositional languages is intractable even for horn and monotone formulae and even when the size of clauses and number of occurrences of the variables are extremely limited this should be contrasted with the case of deductive reasoning where horn theories and theories with binary clauses are distinguished by the existence of linear time satisfiability algorithms what is even more surprising is that as we show even approximating the number of satisfying assignments i e approximating approximate reasoning is intractable for most of these restricted theories we also identify some restricted classes of propositional formulae for which efficient algorithms for counting satisfying assignments can be given

on functional dependencies in q horn theories this paper studies functional dependencies in q horn theories and discusses their use in knowledge condensation we introduce compact model based representations of q horn theories analyze the structure of functional dependencies in q horn theories and show that every minimal functional dependency in a q horn theory can be expressed either by a single term or by a single clause we also prove that the set of all minimal functional dependencies in is quasi acyclic we then develop polynomial time algorithms for recognizing whether a given functional dependency holds in a q horn theory which is represented either by a q horn cnf or as the q horn envelope of a set of models finally we show that every q horn theory has a unique condensation and can be condensed in polynomial time

double horn functions abstract in this paper we define double horn functions which are the boolean functions f such that both f and its complement i e negation f are horn and investigate their semantical and computational properties double horn functions embody a balanced treatment of positive and negative information in the course of the extension problem of partially defined boolean functions pdbfs where a pdbf is a pair t f of disjoint sets t f 0 1 n of true and false vectors respectively and an extension of t f is a boolean function f that is compatible with t and f we derive syntactic and semantic characterizations of double horn functions and determine the number of such functions the characterizations are then exploited to give polynomial time algorithms i that recognize double horn functions from horn dnfs disjunctive normal forms and ii that compute the prime dnf from an arbitrary formula as well as its complement and its dual furthermore we consider the problem of determining a double horn extension of a given pdbf we describe a polynomial time algorithm for this problem and moreover an algorithm that enumerates all double horn extensions of a pdbf with polynomial delay however finding a shortest double horn extension in terms of the size of a formula representing it is shown to be intractable

a complete classification of the complexity of propositional abduction abduction is the process of explaining a given query with respect to some background knowledge for instance p is an explanation for the query q given the knowledge p rightarrow q this problem is well known to have many applications particularly in artificial intelligence ai and has been widely studied from both an ai and a complexity theoretic point of view in this paper we completely classify the complexity of propositional abduction in schaefer s famous framework we consider the case where knowledge bases are taken from a class of formulas in generalized conjunctive normal form this means that the propositional formulas considered are conjunctions of constraints taken from a fixed finite language we show that according to the properties of this language deciding whether at least one explanation exists is either polynomial np complete or sigma 2 mathrm p complete our results are stated for a query consisting of a single positive literal and for assumption based solutions i e the solutions must be formed upon a distinguished subset of the variables that is part of the input we show however that our results can be interpreted dually for negative queries and thus also for unrestricted positive or negative queries

quasi variational inequalities and applications to the traffic equilibrium problem discussion of a paradox abstract this paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of a quasi variational inequality it is shown that the solving procedure proposed by maugeri 1987 with respect to the fixed demands model is also available when the equilibrium problem with elastic demands is expressed in terms of a quasi variational inequality a numerical example is presented to illustrate the computational procedure and to discuss a paradox moreover a theorem that ensures the existence of a solution of the quasi variational inequality is exhibited

the complexity of conservative valued csps we study the complexity of valued constraint satisfaction problems vcsps parametrized by a constraint language a fixed set of cost functions over a finite domain an instance of the problem is specified by a sum of cost functions from the language and the goal is to minimize the sum under the unique games conjecture the approximability of finite valued vcsps is well understood see raghavendra 2008 however there is no characterization of finite valued vcsps let alone general valued vcsps that can be solved exactly in polynomial time thus giving insights from a combinatorial optimization perspective we consider the case of languages containing all possible unary cost functions in the case of languages consisting of only 0 valued cost functions i e relations such languages have been called conservative and studied by bulatov 2003 2011 and recently by barto 2011 since we study valued languages we call a language conservative if it contains all finite valued unary cost functions the computational complexity of conservative valued languages has been studied by cohen et al 2006 for languages over boolean domains by deineko et al 2008 for 0 1 valued languages a k a max csp and by takhanov 2010a for 0 valued languages containing all finite valued unary cost functions a k a min cost hom we prove a schaefer like dichotomy theorem for conservative valued languages if all cost functions in the language satisfy a certain condition specified by a complementary combination of stp and mjn multimorphisms then any instance can be solved in polynomial time via a new algorithm developed in this article otherwise the language is np hard this is the first complete complexity classification of general valued constraint languages over non boolean domains it is a common phenomenon that complexity classifications of problems over non boolean domains are significantly harder than the boolean cases the polynomial time algorithm we present for the tractable cases is a generalization of the submodular minimization problem and a result of cohen et al 2008 our results generalize previous results by takhanov 2010a and a subset of results by cohen et al 2006 and deineko et al 2008 moreover our results do not rely on any computer assisted search as in deineko et al 2008 and provide a powerful tool for proving hardness of finite valued and general valued languages

general nonlinear variational inequalities abstract the fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities several special cases which can be obtained from our main result are also discussed

ordered binary decision diagrams as knowledge bases we consider the use of ordered binary decision diagrams obdds as a means of realizing knowledge bases and show that from the view point of space requirement the obdd based representation is more efficient and suitable in some cases compared with the traditional cnf based and or model based representations we then present polynomial time algorithms for the two problems of testing whether a given obdd represents a unate boolean function and of testing whether it represents a horn function

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

theory revision with queries horn read once and parity formulas a theory in this context is a boolean formula it is used to classify instances or truth assignments theories can model real world phenomena and can do so more or less correctly the theory revision or concept revision problem is to correct a given roughly correct concept this problem is considered here in the model of learning with equivalence and membership queries a revision algorithm is considered efficient if the number of queries it makes is polynomial in the revision distance between the initial theory and the target theory and polylogarithmic in the number of variables and the size of the initial theory the revision distance is the minimal number of syntactic revision operations such as the deletion or addition of literals needed to obtain the target theory from the initial theory efficient revision algorithms are given for horn formulas and read once formulas where revision operators are restricted to deletions of variables or clauses and for parity formulas where revision operators include both deletions and additions of variables we also show that the query complexity of the read once revision algorithm is near optimal

operations and evaluation measures for learning possibilistic graphical models one focus of research in graphical models is how to learn them from a dataset of sample cases this learning task can pose unpleasant problems if the dataset to learn from contains imprecise information in the form of sets of alternatives instead of precise values in this paper we study an approach to cope with these problems which is not based on probability theory as the more common approaches like e g expectation maximization but uses possibility theory as the underlying calculus of a graphical model since the search methods employed in a learning algorithm are relatively independent of the underlying uncertainty or imprecision calculus we focus on evaluation measures or scoring functions

sensitivity analysis framework for variational inequalities in this paper a sensitivity analysis framework is developed for variational inequalities the perturbed solution to a parametric variational inequality problem is shown to be continuous and directionally differentiable under appropriate second order and regularity assumptions moreover this solution is once continuously differentiable if strict complementarity also holds

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

closure properties of constraints many combinatorial search problems can be expressed as constraint satisfaction problems and this class of problems is known to be np complete in general in this paper we investigate the subclasses that arise from restricting the possible constraint types we first show that any set of constraints that does not give rise to an np complete class of problems must satisfy a certain type of algebraic closure condition we then investigate all the different possible forms of this algebraic closure property and establish which of these are sufficient to ensure tractability as examples we show that all known classes of tractable constraints over finite domains can be characterized by such an algebraic closure property finally we describe a simple computational procedure that can be used to determine the closure properties of a given set of constraints this procedure involves solving a particular constraint satisfaction problem which we call an indicator problem

auxiliary problems and algorithm for a system of generalized variational like inequality problems in this paper we consider a system of generalized variational like inequality problems sgvlip involving nondifferentiable terms and its related auxiliary problems in real hilbert spaces an existence theorem for auxiliary problems is established further by exploiting this theorem an algorithm for the sgvlip is constructed furthermore we prove the existence of a unique solution of sgvlip and discuss the convergence analysis of the algorithm the technique and results presented in this paper generalize and unify the corresponding techniques and results given in m a noor general nonlinear variational inequalities j math anal appl 126 1987 78 84 m a noor general variational inequalities appl math lett 1 1988 119 122 m a noor mixed variational like inequalities commun appl nonlinear anal 1 4 1994 63 75

first order lub approximations characterization and algorithms one of the major approaches to approximation of logical theories is the upper and lower bounds approach introduced by selman and kautz 1991 1996 in this paper we address the problem of lowest upper bound lub approximation in a general setting we characterize lub approximations for arbitrary target languages both propositional and first order and describe algorithms of varying generality and efficiency for all target languages proving their correctness we also examine some aspects of the computational complexity of the algorithms both propositional and first order show that they can be used to characterize properties of whole families of resolution procedures discuss the quality of approximations and relate lub approximations to other approaches existing in the literature which are not typically seen in the approximation framework and which go beyond the knowledge compilation perspective that led to the introduction of lubs

on computing all abductive explanations from a propositional horn theory abduction is a fundamental mode of reasoning with applications in many areas of ai and computer science the computation of abductive explanations is an important computational problem which is at the core of early systems such as the atms and clause management systems and is intimately related to prime implicate generation in propositional logic many algorithms have been devised for computing some abductive explanation and the complexity of the problem has been well studied however little attention has been paid to the problem of computing multiple explanations and in particular all explanations for an abductive query we fill this gap and consider the computation of all explanations of an abductive query from a propositional horn theory or of a polynomial subset of them our study pays particular attention to the form of the query ranging from a literal to a compound formula to whether explanations are based on a set of abducible literals and to the representation of the horn theory either by a horn conjunctive normal form cnf or model based in terms of its characteristic models for these combinations we present either tractability results in terms of polynomial total time algorithms intractability results in terms of nonexistence of such algorithms unless p e np or semi tractability results in terms of solvability in quasi polynomial time established by polynomial time equivalence to the problem of dualizing a monotone cnf expression our results complement previous results in the literature and refute a longstanding conjecture by selman and levesque they elucidate the complexity of generating all abductive explanations and shed light on related problems such as generating sets of restricted prime implicates of a horn theory the algorithms for tractable cases can be readily applied for generating a polynomial subset of explanations in polynomial time

3d unsteady navier stokes problem with memory and subdifferential boundary condition abstract we consider a mathematical model which describes the motion of a 3d unsteady fluid flow governed by the navier stokes system and subjected to mixed boundary conditions with a given velocity on one part of the boundary and nonlinear slip conditions with a memory term reminiscent of coulomb s friction law on the other part we establish first some regularity properties and estimates for a simplified model then we prove the existence of a solution to our problem by using a successive approximation technique and compactness arguments based on helly s theorem for the velocity field

tree clustering for constraint networks research note abstract the paper offers a systematic way of regrouping constraints into hierarchical structures capable of supporting search without backtracking the method involves the formation and preprocessing of an acyclic database that permits a large variety of queries and local perturbations to be processed swiftly either by sequential backtrack free procedures or by distributed constraint propagation processes

rates of convergence of estimates kolmogorov s entropy and the dimensionality reduction principle in regression l 1 optimal minimum distance estimators are provided for a projection pursuit regression type function with smooth functional components that are either additive or multiplicative in the presence of or without interactions the obtained rates of convergence of the estimate to the true parameter depend on kolmogorov s entropy of the assumed model and confirm stone s heuristic dimensionality reduction principle rates of convergence are also obtained for the error in estimating the derivatives of a regression type function

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

structure identification in relational data this paper presents several investigations into the prospects for identifying meaningful structures in empirical data namely structures permitting effective organization of the data to meet requirements of future queries we propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability using this framework we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a cnf theory with desirable topology and if the answer is positive identifying the desired decomposition finally we address the problem of expressing a given relation as a horn theory and if this is impossible finding the best k horn approximation to the given relation we show that both problems can be solved in time polynomial in the length of the data

on a class of variational inequalities in this paper we introduce and study a new unified and general class of variational inequalities we derive the general error estimates for the finite element solutions of variational inequalities it has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities several special cases which can be obtained from the general results are also discussed

horn approximations of empirical data abstract formal ai systems traditionally represent knowledge using logical formulas sometimes however a model based representation is more compact and enables faster reasoning than the corresponding formula based representation the central idea behind our work is to represent a large set of models by a subset of characteristic models more specifically we examine model based representations of horn theories and show that there are large horn theories that can be exactly represented by an exponentially smaller set of characteristic models we show that deduction based on a set of characteristic models requires only polynomial time as it does using horn theories more surprisingly abduction can be performed in polynomial time using a set of characteristic models whereas abduction using horn theories is np complete finally we discuss algorithms for generating efficient representations of the horn theory that best approximates a general set of models

horn extensions of a partially defined boolean function given a partially defined boolean function pdbf t f we investigate in this paper how to find a horn extension f 0 1 n mapsto 0 1 which is consistent with t f where t subseteq 0 1 n denotes a set of true boolean vectors or positive examples and f subseteq 0 1 n denotes a set of false boolean vectors or negative examples given a pdbf t f it is known that the existence of a horn extension can be checked in polynomial time as there are many horn extensions however we consider those extensions f which have maximal and minimal sets t f of the true vectors of f respectively for a pdbf t f there always exists the unique maximal i e maximum horn extension but there are in general many minimal horn extensions we first show that a polynomial time membership oracle can be constructed for the maximum extension even if its disjunctive normal form dnf can be very long our main contribution is to show that checking if a given horn dnf represents a minimal extension and generating a horn dnf of a minimal horn extension can both be done in polynomial time we also can check in polynomial time if a pdbf t f has the unique minimal horn extension however the problems of finding a horn extension f with the smallest t f and of obtaining a horn dnf whose number of literals is smallest are both np hard

on some existence and uniqueness results in contact problems with nonlocal friction the workwe present is a mathematical study of signorini s problem with friction i e the problem of equilibrium of a linearly elastic body in contact with a rigid foundation until recently the questions of existence and uniqueness of solutions to such problems were open recently two ideas have appeared which have led to some positive results the first presented by netas jarusek haslinger 11 involves a concept of small friction and provides for the development of an existence result for a very special case of a uniformly loaded infinite strip the second established by duvaut 5 is based on the idea of a nonlocal friction law which enables one to establish an existence result for any friction and also to establish uniqueness for small friction in this paper we present some new results in this direction and a new proof of a non local existence theory our approach differs considerably from the proof outlined in 5 instead of using fixed point arguments we develop a theory of perturbed variational inequalities the origin of which can be found in 9 and establish a generalization for the class of nonlinear variational inequalities characterizing the non local signorini problem this approach should prove to be very useful in studies of approximations of friction prohlems

merit functions and error bounds for generalized variational inequalities we consider the generalized variational inequality and construct certain merit functions associated with this problem in particular those merit functions are everywhere nonnegative and their zero sets are precisely solutions of the variational inequality we further use those functions to obtain error bounds i e upper estimates for the distance to solutions of the problem

a note on general algorithm for variational inequalities in this note we introduce and study a new general strongly quasivariational inequality problem which includes as special cases a number of known classes of variational inequalities studied previously by many authors in this field a general and unified iterative algorithm for finding the approximate solution to this problem is constructed by the projection method we prove the existence of the solution for this problem and the convergence of the iterative sequence generated by this algorithm

a lower bound on the error in nonparametric regression type problems let x1 y1 xn yn be a sample denote the conditional density of ylxi xi as f ylxi 0 xi and 0 an element of a metric space 9 d a lower bound is provided for the d error in estimating 0 the order of the bound depends on the local behavior of the kullback information of the conditional density as an application we consider the case where 1 is the space of q smooth functions on 0 i d metrized with the lr distance 1 r oo

two results on solution uniqueness and multiplicity for the linear elastic friction problem with normal compliance abstract this study is concerned with the frictional contact problem governed by the normal compliance law in linear elasticity the paper presents two contributions dealing with the stationary problem we first obtain improved bounds ensuring the uniqueness of a solution second we exhibit examples in which infinitely many solutions to the problem exist