efficient tests for top down termination of logical rules considered is the question of whether top down prolog like evaluation of a set of logical rules can be guaranteed to terminate the nail system is designed to process programs consisting of logical rules and to select for each fragment of the program the best from among many possible strategies for its evaluation in the context of such a system it is essential that termination tests be fast thus the uniqueness property of logical rules is introduced this property is satisfied by many of the common examples of rules and is easily recognized for rules with this property a set of inequalities whose satisfaction is sufficient for termination of the rules can be generated in polynomial time then a polynomial test for satisfaction of constraints generated by this process is given

ranking paths in stochastic time dependent networks abstract in this paper we address optimal routing problems in networks where travel times are both stochastic and time dependent in these networks the best route choice is not necessarily a path but rather a time adaptive strategy that assigns successors to nodes as a function of time nevertheless in some particular cases an origin destination path must be chosen a priori since time adaptive choices are not allowed unfortunately finding the a priori shortest path is an np hard problem in this paper we propose a solution method for the a priori shortest path problem and we show that it can be easily extended to the ranking of the first k shortest paths our method exploits the solution of the time adaptive routing problem as a relaxation of the a priori problem computational results are presented showing that under realistic distributions of travel times and costs our solution methods are effective and robust

output feedback control of nonlinear systems using direct adaptive fuzzy neural controller in this paper a direct adaptive fuzzy neural output feedback controller dafoc for a class of uncertain nonlinear systems is developed under the constraint that only the system output is available for measurement an output feedback control law and an update law are derived for on line tuning the weighting factors of the dafoc by using strictly positive real lyapunov theory the stability of the closed loop system compensated by the dafoc can be verified moreover the proposed overall control scheme guarantees that all signals involved are bounded and the output of the closed loop system asymptotically tracks the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

finding the k best policies in a finite horizon markov decision process abstract directed hypergraphs represent a general modelling and algorithmic tool which have been successfully used in many different research areas such as artificial intelligence database systems fuzzy systems propositional logic and transportation networks however modelling markov decision processes using directed hypergraphs has not yet been considered in this paper we consider finite horizon markov decision processes mdps with finite state and action space and present an algorithm for finding the k best deterministic markov policies that is we are interested in ranking the first k deterministic markov policies in non decreasing order using an additive criterion of optimality the algorithm uses a directed hypergraph to model the finite horizon mdp it is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time with respect to the input data representing the mdp using different additive optimality criteria

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

technical communique further result on a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems in kim et al 1997 a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems automatica 33 8 1539 1543 authors present an excellent neural network nn observer for a class of nonlinear systems however the output error equation in their paper is strictly positive real spr which is restrictive assumption for nonlinear systems in this note by introducing a vector b 0 and lyapunov equation the observer design is obtained without requiring the spr condition thus our observer can be applied to a wider class of systems

on line algorithms for satisfiability problems with uncertainty in this paper the problem of the on line satisfiability of a horn formula with uncertainty is addressed we show how to represent a significant class of formulae by weighted directed hypergraphs and we present two algorithms that solve the on line sat problem and find a minimal interpretation for the formula working on the dynamic hypergraph representation these algorithms make increasing assumptions on the formula and we will find that the second one solves the on line sat problem with a total time linear in the size of the formula matching the optimal result for boolean horn formulae

succinctness and tractability of closure operator representations it is widely known that closure operators on finite sets can be represented by sets of implications also known as inclusion dependencies as well as by formal contexts in this article we consider these two representation types as well as generalizations of them extended implication sets and context families we discuss the mutual succinctness of these four representations and the tractability of certain operations used to compare and modify closure operators

algorithms for k meet semidistributive lattices in this paper we consider k meet semidistributive lattices and we are interested in the computation of the set colored poset associated to an implicational base the parameter k is of interest since for any finite lattice l there exists an integer k for which l is k meet semidistributive when k 1 they are known as meet semidistributive lattices we first give a polynomial time algorithm to compute an implicational base of a k meet semidistributive lattice from its associated colored poset in other words for a fixed k finding a minimal implicational base of a k meet semidistributive lattice l from a context fca literature of l can be done not just in output polynomial time which is open in the general case but in polynomial time in the size of the input this result generalizes that in 26 second we derive an algorithm to compute a set colored poset from an implicational base which is based on the enumeration of minimal transversals of a hypergraph and turns out to be in polynomial time for k meet semidistributive lattices 13 20 finally we show that checking whether a given implicational base describes a k meet semidistributive lattice can be done in polynomial time

dynamic maintenance of directed hypergraphs abstract in this paper we are concerned with the on line maintenance of directed hypergraphs a generalization of directed graphs previously introduced in the literature in particular we show how to maintain efficiently information about hyperpaths while new hyperarcs are inserted we present a data structure which allows us to check whether there exists a hyperpath between an arbitrarily given pair of nodes in constant time and to return such a hyperpath in a time which is linear in its size the total time required to maintain the data structure during the insertion of new hyperarcs is o mn where m is the total size of the description of the hyperarcs and n is the number of nodes this generalizes a previous result known for directed graphs and has applications in several areas of computer science such as rewriting systems database schemes logic programming and problem solving an extension of these results to hyperpaths between sets of nodes is also presented

output feedback control of uncertain nonlinear systems using a self structuring adaptive fuzzy observer this paper describes the design of an output feedback controller based on an adaptive fuzzy observer for uncertain single input single output nonlinear dynamical systems we have focused on the realization of a minimal dynamic order for the adaptive fuzzy observer for this purpose we adopt an adaptive fuzzy observer in which no strictly positive real spr condition is needed and we combine a self structuring scheme with an on line estimation of fuzzy parameters by using this proposed scheme we can reduce the dynamic order of the adaptive output feedback fuzzy control system the lyapunov synthesis approach is used to guarantee a global uniform ultimate boundedness property of the state estimation error and tracking error as well as all other signals in the closed loop system no a priori knowledge of an upper limits on the uncertainties including optimal parameters and modeling errors is required the theoretical results are illustrated through simulation examples

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

a theory of finite closure spaces based on implications abstract although many notions familiar from topology and matroid theory make sense for arbitrary closure spaces we claim that implicational bases are most worthwhile studying they are applied in the theory of relational data bases and in formal concept analysis further applications in combinatorics and algebra are foreseeable the main theorem describes the structure of minimum respectively optimal implicational bases of any finite closure space it has strong corollaries for specific closure spaces e g having a geometric respectively modular respectively lower distributive lattice of closed sets

complexity results for 1 safe nets we study the complexity of several standard problems for 1 safe petri nets and some of its subclasses we prove that reachability liveness and deadlock are all pspace complete for 1 safe nets we also prove that deadlock is np complete for free choice nets and for 1 safe free choice nets finally we prove that for arbitrary petri nets deadlock is equivalent to reachability and liveness

robust quasi lpv control based on neural state space models we derive a synthesis result for robust linear parameter varying lpv output feedback controllers for nonlinear systems modeled by neural state space models this result is achieved by writing the neural state space model on a linear fractional transformation lft form in a nonconservative way separating the system description into a linear part and a nonlinear part linear parameter varying control synthesis methods are then applied to design a nonlinear control law for this system since the model is assumed to have been identified from input output measurement data only it must be expected that there is some uncertainty on the identified nonlinearities the control law is therefore made robust to noise perturbations after formulating the controller synthesis as a set of linear matrix inequalities lmis with added constraints some implementation issues are addressed and a simulation example is presented

stable neural controller design for unknown nonlinear systems using backstepping we propose from an adaptive control perspective a neural controller for a class of unknown minimum phase feedback linearizable nonlinear system with known relative degree the control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural network structure the resulting controller however moves the complex mechanics involved in a typical backstepping design from off line to online with appropriate choice of the network size and neural basis functions the same controller can be trained online to control different nonlinear plants with the same relative degree with semi global stability as shown by the simple lyapunov analysis meanwhile the controller also preserves some of the performance properties of the standard backstepping controllers simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

send and split method for minimum concave cost network flows many problems from inventory production and capacity planning and from network design exhibit scale economies and can be formulated in terms of finding minimum additive concave cost nonnegative network flows we reduce the problem to an equivalent one in which the arc flow costs are nonnegative and give a dynamic programming method called the send and split method to solve it the main work of the method entails repeatedly solving set splitting and minimum cost chain problems in uncapacitated networks with n nodes a arcs and d 1 demand nodes i e nodes with nonzero exogenous demand the algorithm requires up to n2 13d s2d operations additions and comparisons where s n log2n 3a is the number of operations required to solve a minimum cost chain problem with nonnegative arc costs on the augmented graph formed by appending a node and an arc thereto from each node in the graph if also the network is k planar i e the graph is planar with all demand nodes lying on the boundary of k faces the method requires at most n2 kd3k sd2k operations the algorithm can be applied to capacitated networks because they can be reduced to equivalent uncapacitated ones these results unify significantly generalize e g to cyclic problems and sometimes improve upon e g for tandem facilities known polynomial time dynamic programming algorithms for wagner and whitin s wagner h m whitin t m 1958 dynamic version of the economic lot size model management sci 5 89 96 dynamic economic order quantity problem zangwill s zangwill w i 1969 a backlogging model and a multi echelon model of a dynamic economic lot size production system a network approach management sci 15 506 527 generalization to tandem facilities and veinott s veinott jr a f 1969 minimum concave cost solution of leontief substitution models of multi facility inventory systems oper res 17 262 291 increasing capacity warehousing problem the networks for the finite period versions of these problems are each 1 planar the method improves upon zangwill s zangwill w i 1968 minimum concave cost flows in certain networks management sci 14 429 450 related oand running time dynamic programming method for finding minimum additive concave cost non negative flows in circuitless single source networks we also implement the method to solve in polynomial time the d 1 demand node and k planar versions of the minimum cost forest and steiner problems in graphs the running time for the d 1 demand node steiner problem in graphs is comparable to that of dreyfus and wagner s dreyfus s e wagner r a 1971 the steiner problem in graphs networks1 195 207 method

bounded state reconstruction error for lpv systems with estimated parameters the note deals with the state reconstruction of a class of discrete time systems with time varying parameters while usually the parameters are assumed to be online available and exactly known the special and realistic situation when the parameters are known with a finite accuracy is considered the main objective of the note is to show that despite of the resulting mismatch between the true system and the model the state reconstruction error boundedness can be guaranteed and an explicit bound can be derived the proof is based upon the concept of input to state stability

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

solving multi item capacitated lot sizing problems using variable redefinition mixed integer programming models are typically not used to solve realistic sized production scheduling problems because they require exorbitant solution times we impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy the linear programming relaxation of the new models is very effective in generating bounds we show that these bounds are equal to those that could be generated using lagrangian relaxation or column generation the linear programming bounds increase in effectiveness as the problems become larger perhaps of greatest significance is that practitioners can obtain our results using only standard off the shelf codes such as lindo or mpsx 370 we report computational experience in several computing environments hardware and software on problems with up to 200 products and 10 time periods 2000 0 1 variables

on the effectiveness of high gain observer based residuals for a class of non linear control systems the design of a high gain observer based residual is considered for a class of non linear systems input output maps are derived for use in residual design to increase design flexibility an invest

concept lattices with negative information classical formal concept analysis fca extracts represents and manages knowledge from positive information i e its fundamental data model is a binary relation between a set of objects and attributes indicating the presence of a property in an object however some applications require to treat the absence of some property in an object as a negative information to be explicitly represented and managed too although mixed positive and negative information has been addressed in the past in fca such approaches maintain the standard framework which hides the specific semantics and avoids the further use of direct techniques and methods for mixed information in this work the foundations of fca are extended and in particular mixed concept lattices are studied in depth the main result of this work is a characterization theorem specifying in lattice theoretic terms which lattices are isomorphic to a mixed concept lattice

polyhedral characterization of discrete dynamic programming many interesting combinatorial problems can be optimized efficiently using recursive computations often termed discrete dynamic programming in this paper we develop a paradigm for a general class of such optimizations that yields a polyhedral description for each model in the class the elementary concept of dynamic programs as shortest path problems in acyclic graphs is generalized to one seeking a least cost solution in a directed hypergraph sufficient conditions are then provided for binary integrality of the associated hyperflow problem given a polynomially solvable dynamic program the result is a linear program in polynomially many variables and constraints having the solution vectors of the dynamic program as its extreme point optima that is the linear program provides a succinct characterization of the solutions to the underlying optimization problem expressed through an appropriate change of variables we also discuss projecting this formulation to recover constraints on the original variables and illustrate how some important dynamic programming solvable models fit easily into our paradigm a classic multiechelon lot sizing problem in production and a host of optimization problems on recursively defined classes of graphs are included

lattices closures systems and implication bases a survey of structural aspects and algorithms abstract concept lattices and closed set lattices are graphs with the lattice property they have been increasingly used this last decade in various domains of computer science such as data mining knowledge representation databases or information retrieval a fundamental result of lattice theory establishes that any lattice is the concept lattice of its binary table a consequence is the existence of a bijective link between lattices contexts via the table and a set of implicational rules via the canonical direct basis the possible transformations between these objects give rise to relevant tools for data analysis in this paper we present a survey of lattice theory from the algebraic definition of a lattice to that of a concept lattice through closure systems and implicational rules including the exploration of fundamental bijective links between lattices reduced contexts and bases of implicational rules and concluding with the presentation of the main generation algorithms of these objects

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

flows on hypergraphs we consider the capacitated minimum cost flow problem on directed hypergraphs we define spanning hypertrees so generalizing the spanning tree of a standard graph and show that like in the standard and in the generalized minimum cost flow problems a correspondence exists between bases and spanning hypertrees then we show that like for the network simplex algorithms for the standard and for the generalized minimum cost flow problems most of the computations performed at each pivot operation have direct hypergraph interpretations

approximate reasoning by similarity based sld resolution in gerla and sessa fuzzy logic and soft computing kluwer norwell 1999 pp 19 31 a methodology that allows to manage uncertain and imprecise information in the frame of the declarative paradigm of logic programming has been proposed with this aim a similarity relation r between function and predicate symbols in the language of a logic program is considered approximate inferences are then possible since similarity relation allows us to manage alternative instances of entities that can be considered equal with a given degree the declarative semantics of the proposed transformation technique of logic programs is analyzed the notion of fuzzy least herbrand model is also introduced in this paper the corresponding operational semantics is provided by introducing a modified version of sld resolution this top down refutation procedure overcomes failure situations in the unification process by using the similarity relation a generalized notion of most general unifier provides a numeric value which gives a measure of the exploited approximation in this way the sld resolution is enhanced since it is possible both to handle uncertain or imprecise information and to compute approximate answer substitutions with an associated approximation degree when failures of the exact inference process occur it can lead to the implementation of a more general prolog interpreter without detracting from the elegance of the language

linear connectivity problems in directed hypergraphs we introduce a notion of hyperconnection formally called l hyperpath between vertices in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs we show that some interesting questions in problem domains such as distributed secret sharing and routing in packet filtered networks are basically questions about the existence of l hyperpaths in directed hypergraphs we study the computational complexity of problems related to l hyperpaths and the l cyclomatic number of directed hypergraphs the minimum number of hyperedges that need to be deleted to make a directed hypergraph free of l hypercycles we prove that the l hyperpath existence problem the l cyclomatic number problem the minimum l cyclomatic set problem and the minimal l cyclomatic set problem are each complete for the complexity class np s 2 p p 2 p and dp respectively

global adaptive observers for nonlinear systems via filtered transformations the problem of determining global adaptive observers for a class of single output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation under additional geometric conditions the original state can be observed as well the results obtained are based on a nonlinear change of coordinates driven by auxiliary filters filtered transformations

an analysis of stochastic shortest path problems we consider a stochastic version of the classical shortest path problem whereby for each node of a graph we must choose a probability distribution over the set of successor nodes so as to reach a certain destination node with minimum expected cost the costs of transition between successive nodes can be positive as well as negative we prove natural generalizations of the standard results for the deterministic shortest path problem and we extend the corresponding theory for undiscounted finite state markovian decision problems by removing the usual restriction that costs are either all nonnegative or all nonpositive

an adaptive fuzzy hybrid state observer for bioprocesses in order to monitor and control bioprocesses online measurements of certain biological variables like biomass concentration are normally required unfortunately there is a lack of highly reliable and low cost instruments for online measuring these important variables these limitations have motivated the use of observers this paper describes a state observer for bioprocesses based on a hybrid fuzzy model the model combines the mass balances and a fuzzy inference system for approximating the uncertain dynamic of the kinetic reactions the convergence stability and robustness of the observer are analyzed the main features of this observer are illustrated by considering a lactic fermentation

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

hydras directed hypergraphs and horn formulas abstract we introduce a new graph parameter the hydra number arising from the minimization problem for horn formulas in propositional logic the hydra number of a graph g v e is the minimal number of hyperarcs of the form u v w required in a directed hypergraph h v f such that for every pair u v the set of vertices reachable in h from u v is the entire vertex set v if u v e and it is u v otherwise here reachability is defined by forward chaining a standard marking algorithm various bounds are given for the hydra number we show that the hydra number of a graph can be upper bounded by the number of edges plus the path cover number of the line graph of a spanning subgraph which is a sharp bound in several cases on the other hand we construct single headed graphs for which that bound is off by a constant factor furthermore we characterize trees with low hydra number and give a lower bound for the hydra number of trees based on the number of vertices that are leaves in the tree obtained from t by deleting its leaves this bound is sharp for some families of trees we give bounds for the hydra number of complete binary trees and also discuss a related minimization problem

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

perfect codes from cayley graphs over lipschitz integers the search for perfect error correcting codes has received intense interest since the seminal work by hamming decades ago golomb and welch studied perfect codes for the lee metric in multidimensional torus constellations in this work we focus our attention on a new class of four dimensional signal spaces which include tori as subcases our constellations are modeled by means of cayley graphs defined over quotient rings of lipschitz integers previously unexplored perfect codes of length one will be provided in a constructive way by solving a typical problem of vertices domination in graph theory the codewords of such perfect codes are constituted by the elements of a principal left ideal of the considered quotient ring the generalization of these techniques for higher dimensional spaces is also considered in this work by modeling their signal sets through cayley dickson algebras

a hypergraph multi exchange heuristic for the single source capacitated facility location problem abstract in this paper we introduce a large scale neighborhood search procedure for solving the single source capacitated facility location problem sscflp the neighborhood structures are induced by innovative split multi customer multi exchanges where clusters of customers assigned to one facility can be moved simultaneously to multiple destination facilities and vice versa to represent these exchanges we use two types of improvement hypergraphs the improvement hypergraphs are built dynamically and the moving customers associated with each hyperedge are selected by solving heuristically a suitably defined mixed integer program we develop a hypergraph search framework including forward and backward procedures to identify improving solutions efficiently our proposed algorithm can obtain improving moves more quickly and even find better solutions than a traditional multi exchange heuristic ahuja orlin pallottino scuttella 2004 in addition when compared with the kernel search algorithm guastaroba speranza 2014 which at present is the most effective for solving sscflp our algorithm is not only competitive but can find better solutions or even the best known solution to some very large scale benchmark instances from the literature

a taxonomy of fairness and temporal logic problems for petri nets in this paper we define a temporal logic for reasoning about petri nets we show the model checking problem for this logic to be ptime equivalent to the petri net reachability problem using this logic and two refinements we show the fair nontermination problem to be ptime equivalent to reachability for several definitions of fairness for other versions of fairness this problem is shown to be either ptime equivalent to the boundedness problem or highly undecidable in all 24 versions of fairness are examined

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

linear time analysis of properties of conflict free and general petri nets we introduce the notion of a t path within petri nets and propose to adopt the model of directed hypergraphs in order to determine properties of nets in particular we study the relationships between t paths and firable sequences of transitions let us consider a petri net p and the set of places with a positive marking in m 0 i e p 0 p m 0 p 0 if we regard the net as a directed graph the existence of a simple path from any place in p 0 to a transition t is of course a necessary condition for the potential firability of t this is sufficient only if the net is a state machine where t t 1 for all t t in this paper we show that the existence of a t path from any subset of p 0 to a transition t is a more restrictive condition and is again a necessary condition for the potential firability of t but in this case a if p is a conflict free petri net this is also a sufficient condition b if p is a general petri net t is potentially firable by increasing the number of tokens inp 0 for conflict free nets cfpn we consider the following problems a determining the set of firable transitions b determining the set of coverable places c determining the set of live transitions d deciding the boundedness of the net for all these problems we provide algorithms requiring linear space and time i e o p t a for a net p previous results for this class of networks are given by howell et al 1987 20 providing algorithms for solving problems in conflict free nets in o p x t time and space given a petri net and a marking m the well known coverability problem consists in finding a reachable marking m such that m m this problem is known to be expspace hard rackoff 1978 33 for general petri nets we provide a partial answer to this problem m is coverable by augmentation if it is coverable from an augmented markingm 0 of the initial marking m 0 m 0 m 0 and for all p p m 0 p 0 if m 0 p 0 we solve this problem in linear time the algorithms for computing t paths are incremental it is possible to modify the network adding new places transitions arcs tokens and update the set of potentially firable transitions and coverable places without recomputing them from scratch this feature is meaningful when used during the interactive design of a system

quasi perfect lee distance codes a construction of perfect quasiperfect lee distance codes in z sub k sup 2 is introduced for this class of codes a constant time encoding scheme is defined the minimum code distance is derived and the maximum covering radius is calculated efficient decoding schemes are investigated and developed in general a code of this class can be decoded in o t sub 1 where t sub 1 is the number of errors that can be corrected special cases however can be decoded in constant time

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

perfect codes for metrics induced by circulant graphs an algebraic methodology for defining new metrics over two dimensional signal spaces is presented in this work we have mainly considered quadrature amplitude modulation qam constellations which have previously been modeled by quotient rings of gaussian integers the metric over these constellations based on the distance concept in circulant graphs is one of the main contributions of this work a detailed analysis of some degree four circulant graphs has allowed us to detail the weight distribution for these signal spaces a new family of perfect codes over gaussian integers will be defined and characterized by providing a solution to the perfect t dominating set problem over the circulant graphs presented finally we will show how this new metric can be extended to other signal sets by considering hexagonal constellations and circulant graphs of degree six

extended luenberger observer for non linear multivariable systems for non linear multiple input multiple output systems xdot f x u y h x u nonlinear observers are designed using a transformation into the non linear observer canonical form and an extended linearization the differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory and dimensioned by eigenvalue assignment with reference to the extended kalman filter algorithm this non linear observer design is called the extended luenberger observer this observer design is possible for all sufficiently smooth and locally observable systems in comparison with single output systems the non linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs

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

non linear observer design by observer canonical forms this paper studies the non linear observer design problem by observer canonical forms we present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non linear state coordinate change under which a time variable system is transformed into an observer canonical form these conditions give the multiple versions of li and tao 1986 for the single output case then a comparison is made with the lie algebraic conditions obtained by krener and respondek 1985 and modified by the authors in a recent paper xia and gao 1987

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

max horn sat and the minimum cut problem in directed hypergraphs in this paper we consider the maximum horn satisfiability problem which is reduced to the problem of finding a minimum cardinality cut on a directed hypergraph for the latter problem we propose different ip formulations related to three different definitions of hyperpath weight we investigate the properties of their linear relaxations showing that they define a hierarchy the weakest relaxation is shown to be equivalent to the relaxation of a well known ip formulation of max horn sat and to a max flow problem on hypergraphs the tightest relaxation which is a disjunctive programming problem is shown to have integer optimum the intermediate relaxation consists in a set covering problem with a possible exponential number of constraints this latter relaxation provides an approximation of the convex hull of the integer solutions which as proven by the experimental results given is much tighter than the one known in the literature 1998 the mathematical programming society inc published by elsevier science b v

a directed hypergraph model for random time dependent shortest paths abstract we consider routing problems in dynamic networks where arc travel times are both random and time dependent the problem of finding the best route to a fixed destination is formulated in terms of shortest hyperpaths on a suitable time expanded directed hypergraph the latter problem can be solved in linear time with respect to the size of the hypergraph for several definitions of hyperpath length different criteria for ranking routes can be modeled by suitable definitions of hyperpath length we also show that the problem becomes intractable if a constraint on the route structure is imposed

graphs tessellations and perfect codes on flat tori quadrature amplitude modulation qam like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori such signal sets can be related to spherical block and trellis codes and may be viewed as geometrically uniform gu in the graph metric in a sense that extends the concept introduced by forney homogeneous signal sets of any order can then be labeled by a cyclic group induced by translations on the euclidean plane we construct classes of perfect codes on square graphs including lee spaces and on hexagonal and triangular graphs all on flat tori extension of this approach to higher dimensions is also considered

graph algorithms for functional dependency manipulation abstract a graph theoretic approach for the representation of functional dependenoes in relauonal databases is introduced and applied in the construction of algorithms for manipulating dependencies this approach allows a homogeneous treatment of several problems closure minimization etc which leads to simpler proofs and m some cases more efficient algorithms than in the current literature categories and subject descriptors f 2 2 analysis of algorithms and problem complexity nonnumencal algorithms and problems computations on d screte structures g 2 2 diserete mathematics graph theory graph algorithms h 2 1 database management logical design normal forms schema and subschema general terms algorithms design management theory additional key words and phrases closure computational complexity functional dependency fd graph minimal coverings relational database 1 introduction

the demand weighted vehicle routing problem abstract in this paper we present an exact method for the demand weighted vehicle routing problem this problem arises when the objective is to minimize the distance traveled by the vehicles weighted by the number of passengers on the routes the resulting model is a non convex mixed integer quadratic program and we show how to reformulate this problem as a linear integer program with auxiliary variables the reformulation provides very tight lower bounds on the optimal solution value and little enumeration is required however the reformulated model is very large and therefore it is solved with a branch price and cut algorithm using coin or software we provide computational results with actual data from a large urban university

an algorithm for the general petri net reachability problem an algorithm is presented for the general petri net reachability problem it is based on a generalization of the basic reachability tree construction which is made symmetric with respect to the ini

discovery of the d basis in binary tables based on hypergraph dualization discovery of strong association rules or implications is an important task in data management and it finds application in artificial intelligence data mining and the semantic web we introduce a novel approach for the discovery of a specific set of implications called the d basis that provides a representation for a reduced binary table based on the structure of its galois lattice at the core of the method are the d relation defined in a lattice theoretic framework and the hypergraph dualization algorithm that allows us to effectively produce the set of transversals for a given sperner hypergraph the latter algorithm first developed by specialists from rutgers center for operations research has already found numerous applications in solving optimization problems in data base theory artificial intelligence and game theory one application of the method is for analysis of gene expression data related to a particular phenotypic variable and some initial testing is done for data provided by the university of hawaii cancer center

directed hypergraphs just as ordinary hypergraphs are a generalization of graphs directed hypergraphs dh are a natural generalization of digraphs a dh consists of a set of vertices v and a set of hyperarcs h where a hyperarc is a pair s v s non empty subset of v and v v dhs have a variety of applications they have been used to represent functional dependency in databases horn formulae in propositional logic and or graphs context free grammars etc in the paper after providing a brief historical introduction on the notion of dh and some relevant applications various problems regarding dhs are surveyed and analyzed in particular we consider the complexity of the reachability problem together with its application in the related satisfiability problem for horn cnf formulae and the computation of transitive closure and transitive reduction of directed hypergraphs together with its application to the computation of minimum coverings for a set of functional dependencies finally a short introduction to the problem of computing shortest hyperpaths in directed hypergraphs is provided

modeling toroidal networks with the gaussian integers in this paper we consider a broad family of toroidal networks denoted as gaussian networks which include many previously proposed and used topologies we will define such networks by means of the gaussian integers the subset of the complex numbers with integer real and imaginary parts nodes in gaussian networks are labeled by gaussian integers which confer these topologies an algebraic structure based on quotient rings of the gaussian integers in this sense gaussian integers reveal themselves as the appropriate tool for analyzing and exploiting any type of toroidal network using this algebraic approach we can characterize the main distance related properties of gaussian networks providing closed expressions for their diameter and average distance in addition we solve some important applications like unicast and broadcast packet routing or the perfect placement of resources over these networks

minimal representation of directed hypergraphs in this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed various concepts of minimal representations of directed hypergraphs called minimal equivalent hypergraphs are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs in particular we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph number of hyperarcs number of adjacency lists required for the representation length of the overall description etc the relationships among the various concepts of minimality are discussed and their computational properties are analyzed in order to derive such results a graph representation of hypergraphs is introduced

adaptive fuzzy neural network control for a dsp based permanent magnet linear synchronous motor servo drive an adaptive fuzzy neural network afnn control system is proposed to control the position of the mover of a field oriented control permanent magnet linear synchronous motor pmlsm servo drive system to track periodic reference trajectories in this paper in the proposed afnn control system an fnn with accurate approximation capability is employed to approximate the unknown dynamics of the pmlsm and a robust compensator is proposed to confront the inevitable approximation errors due to finite number of membership functions and disturbances including the friction force the adaptive learning algorithm that can learn the parameters of the fnn on line is derived using lyapunov stability theorem moreover to relax the requirement for the value of lumped uncertainty in the robust compensator which comprises a minimum approximation error optimal parameter vectors higher order terms in taylor series and friction force an adaptive lumped uncertainty estimation law is investigated furthermore all the control algorithms are implemented in a tms320c32 dsp based control computer the simulated and experimental results due to periodic reference trajectories show that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

shortest path and minimum delay algorithms in networks with time dependent edge length in this paper the shortest path problem in networks in which the delay or weight of the edges changes with time according to arbitrary functions is considered algorithms for finding the shortest path and minimum delay under various waiting constraints are presented and the properties of the derived path are investigated it is shown that if departure time from the source node is unrestricted then a shortest path can be found that is simple and achieves a delay as short as the most unrestricted path in the case of restricted transit it is shown that there exist cases in which the minimum delay is finite but the path that achieves it is infinite

finding hypernetworks in directed hypergraphs abstract the term hypernetwork more precisely s hypernetwork and s d hypernetwork has been recently adopted to denote some logical structures contained in a directed hypergraph a hypernetwork identifies the core of a hypergraph model obtained by filtering off redundant components therefore finding hypernetworks has a notable relevance both from a theoretical and from a computational point of view in this paper we provide a simple and fast algorithm for finding s hypernetworks which substantially improves on a method previously proposed in the literature we also point out two linearly solvable particular cases finding an s d hypernetwork is known to be a hard problem and only one polynomially solvable class has been found so far here we point out that this particular case is solvable in linear time

generating alternative mixed integer programming models using variable redefinition dropping the complicating constraints in a mixed integer linear program often yields a special structure subproblem that can be reformulated using a different set of decision variables once the new variables have been identified the entire problem can be reformulated in terms of the new variables we develop a theory of variable redefinition based on relating the two sets of decision variables by a linear transformation and describe methods for reformulating the special structure problem the reformulated models have a more accurate linear relaxation than the problems from which they were derived an important property within the context of linear programming based branch and bound modeling approaches

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

state observer based adaptive fuzzy output feedback control for a class of uncertain nonlinear systems this paper aims to develop state observer based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances an adaptive fuzzy observer is proposed to estimate the system state variables it is shown that the observation errors obtained from the observer are uniformly ultimately bounded applying the estimated system state for design of an output feedback controller the uniformly ultimate boundedness of the tracking errors for the resulting closed loop system can be guaranteed a typical robot arm system is employed in our simulation studies and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

problems concerning fairness and temporal logic for conflict free petri nets abstract in this paper we examine the complexity of the fair nontermination problem for conflict free petri nets under several definitions of fairness for each definition of fairness we are able to show the problem to be complete for either np ptime or nlogspace we then address the question of whether these results extend to the more general model checking problem with respect to the temporal logic for petri nets introduced by suzuki since many of the model checking problems concerning finite state systems can be reduced to a version of the fair nontermination problem it would seem plausible that the model checking problem for conflict free petri nets would be decidable however it turns out that unless the logic is severely restricted model checking is undecidable for conflict free petri nets in particular the problem is undecidable even when formulas are of the form g invariantly where contains no temporal logic operators on the other hand we show that model checking for conflict free petri nets is np complete for l f x the logic restricted to the operators f eventually x next time and with negations allowed only on the predicates

optimality of stationary halting policies and finite termination of successive approximations the existence of an optimal stopping policy that is stationary and halting in a discrete time parameter finite state finite action branching markov decision chain is here characterized by the finite termination of successive approximations we call a policy stopping if the expected population size at time n converges to zero as n approaches infinity and halting if the expected population at time n is zero for some n we show that when the rewards are real valued the nth iterate of successive approximations is a fixed point of the optimal return operator for some n when initiated with the value of a stationary halting policy if and only if there exists a halting stationary optimal stopping policy similar results are shown for a gauss seidel improvement of successive approximations

quasi perfect codes from cayley graphs over integer rings the problem of searching for perfect codes has attracted great attention since the paper by golomb and welch in which the existence of these codes over lee metric spaces was considered since perfect codes are not very common the problem of searching for quasi perfect codes is also of great interest in this aspect also quasi perfect lee codes have been considered for 2 d and 3 d lee metric spaces in this paper constructive methods for obtaining quasi perfect codes over metric spaces modeled by means of gaussian and eisenstein jacobi integers are given the obtained codes form ideals of the integer ring thus preserving the property of being geometrically uniform codes moreover they are able to correct more error patterns than the perfect codes which may properly be used in asymmetric channels therefore the results in this paper complement the constructions of perfect codes previously done for the same integer rings finally decoding algorithms for the quasi perfect codes obtained in this paper are provided and the relationship of the codes and the lee metric ones is investigated

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

growth optimality for branching markov decision chains this paper considers a multiplicative process called branching markov decision chains in which the output at the end of the nth period equals the product of n nonnegative matrices chosen at the beginning of periods 1 n respectively times a positive fixed terminal reward vector it is assumed that the above transition matrices are drawn out of a finite set of matrices given in product form i e the rows of the matrices can be selected independently out of finite sets of nonnegative row vectors for each coordinate s we define the geometric and algebraic growth rates respectively of the sth coordinate of the stream of output these growth rates are defined so that the magnitude of the corresponding sequence is of the order nnk where is the geometric growth rate and k is the algebraic growth rate the main result of this paper is the constructive establishment of the existence of a transition matrix whose repeated use will guarantee for each coordinate the achievement of the best geometri

adaptive observers for single output nonlinear systems an adaptive version of the nonlinear observer obtained by a j krener et al 1983 is presented this version involves the cancellation of nonlinear terms by output injection as an intermediate step necessary and sufficient conditions are given for transforming a nonlinear system by state space change of coordinates into the special adaptive observer form that was used by y bastin et al 1988 to design adaptive observers

how to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems this paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer high gain hg observer sliding mode like observer etc for a class of single input single output siso uncertain or ill defined affine nonlinear systems indeed the corrective term of the proposed observer involves a well defined design function which is shown to be satisfied by the commonly used hg based observers namely for the usual hg observers and the sliding mode observers together with their implementable versions the design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error this particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real spr condition

gainfree leontief substitution flow problems leontief substitution systems have been studied by economists and operations researchers for many years we show how such linear systems are naturally viewed asleontief substitution flow problems on directed hypergraphs and that important solution properties follow from structural characteristics of the hypergraphs we give a strongly polynomial non simplex algorithm for leontief substitution flow problems that satisfy againfree property leading to acyclic extreme solutions integrality conditions follow easily from this algorithm another structural property support disjoint reachability leads to necessary and sufficient conditions for extreme solutions to be binary in a survey of applications we show how the leontief flow paradigm links polyhedral combinatorics expert systems mixed integer model formulation and some problems in graph optimization

auction algorithms for shortest hyperpath problems the auction reduction algorithm is a strongly polynomial version of the auction method for the shortest path problem in this paper we extend the auction reduction algorithm to different types of shortest hyperpath problems in directed hypergraphs the results of preliminary computational experiences show that the auction reduction method is comparable to other known methods for specific classes of hypergraphs

the image containment problem and some classes of polynomial instances the image containment problem icp is a minimum cost design problem concerning the containment of particular polyhedra called zonotopes that are images of boxes through linear transformations the icp is np hard here we study a family of nontrivial icp instances called worst case demand wcd instances we prove that such instances can be recognized and solved in polynomial time via linear programming then we characterize the classes of instances that are wcd independently on the choice of the cost vector structurally worst case demand classes swcd and we show that recognizing whether a class of instances is swcd is a conp complete problem finally we describe two families of swcd classes that are interesting from an applicative point of view the classes defined by the incidence matrices of particular directed graphs and those defined by pre leontief matrices

hydras complexity on general graphs and a subclass of trees abstract hydra formulas were introduced in 1 a hydra formula is a horn formula consisting of definite horn clauses of size 3 specified by a set of bodies of size 2 and containing clauses formed by these bodies and all possible heads a hydra formula can be specified by the undirected graph formed by the bodies occurring in the formula the minimal formula size for hydras is then called the hydra number of the underlying graph in this paper we aim to answer some open questions regarding complexity of determining the hydra number of a graph which were left open in 1 in particular we show that the problem of checking whether a graph g v e is single headed i e whether the hydra number of g is equal to the number of edges is np complete we also consider hydra number of trees and we describe a family of trees for which the hydra number can be determined in polynomial time

the joy of implications aka pure horn formulas pure horn clauses have also been called among others functional dependencies strong association rules or simply implications we survey the mathematical theory of implications with an emphasis on the progress made in the last 30 years