Partial Order

In this paper we study the definition of generalized powerset of terms in the context of partially ordered monads. We provide a definition of the powerset of terms over acSLAT and study some possible directions for the definition of a partially ordered term monad. Keywords: partially ordered monad, generalised terms.

Aux membres de mon jury, qui m'ont fait l'honneur de bien vouloir examiner mon travail. En premier lieu aux rapporteurs, pour l'attention bienveillante portée à mon mémoire. A Claude Marché, pour son soutien constant et actif dans la préparation de cette habilitation. A Eric Goubault, chef du laboratoire MEASI, qui a guidé mes premiers pas sur le sujet, et toujours encouragée depuis. Comment en quelques mots évoquer plus de 10 ans à bénéficier de son énergie et de sa curiosité scientifique? Plus généralement à mes collègues du CEA et de Digiteo; ce travail leur doit tout. Tout spécialement Karim Tekkal et Franck Védrine, grâce à qui l'aventure Fluctuat, avec ses hauts et ses bas, est restée un plaisir. A Khalil Ghorbal, mon premier étudiant en thèse, forcément unique.

We present a method which accepts Interval Temporal Logic (ITL) formulas as specification and automatically generates state machines. The specification in ITL can also be used as a con- straint for a state machine which is an abstraction for an existing sequential circuit, which can be useful for redesign or engineering change. The generated state machines can be further pro-

We study underdamped Josephson junction series arrays that are globally coupled through a resistive shunting load and driven by an rf bias current. They can be an experimental realization of many phenomena currently studied in globally coupled logistic maps. We study their spatiotemporal dynamics and we find coherent, ordered, partially ordered, turbulent, and quasiperiodic phases. The ordered phase corresponds to giant Shapiro steps in the IV characteristics. In the turbulent phase there is a saturation of the broad-band noise for a large number of junctions. This corresponds to a breakdown of the law of large numbers as seen in globally coupled maps. Coexisting with this phenomenon, we find an emergence of pseudosteps in the IV characteristics. This e8ect can be experimentally distinguished from the true Shapiro steps, which do not have broad-band noise emission. We study the stability of the breakdown of the law of large numbers against thermal Buctuations. We find that it is stable below a critical temperature T,q. A measurement of the broad-band noise as a function of temperature T will show three diferent regimes: below T ~the broad-band noise decreases when increasing T, and there is turbulence and the breakdown of the law of large numbers. Between T q and a second critical temperature T,2 the broad-band noise is constant and the dynamics is dominated by the chaos of the individual junctions. Finally above T z all the broad-band noise is due to thermal Huctuations, since it increases linearly with T.

In this paper we compare overall as well as downside risk measures with respect to the criteria of first and second order stochastic dominance. While the downside risk measures, with the exception of tail conditional expectation, are consistent with first order stochastic dominance, overall risk measures are not, even if we restrict ourselves to two-parameter distributions. Most common risk measures preserve consistent preference orderings between prospects under the second order stochastic dominance rule, although for some of the downside risk measures such consistency holds deep enough in the tail only. In fact, the partial order induced by many risk measures is equivalent to sosd. Tail conditional expectation is not consistent with respect to second order stochastic dominance.

machine-independent) complexity theory is basically a theory which establishes limits on what may be said about the complexity of specific recursive functions. (For example, the speed-up theorem shows that it is not always possible to discover close upper and lower bounds for the complexity of a function.) As such, its basic proof method is diagonalization. Sacks, Spector, etc. [2], [3] have developed extensive diagonalization machinery for theorems about degrees of unsolvability. Thus far, we have not applied any except the simplest of the methods devised by the recursion theorists to complexity theory. In this paper, we present two results which arise very naturally out of complexity theory and whose proofs seem to require use of priority constructions.

The application of partial order theory and Hasse diagram technique in environmental science is getting increasing attention. One of the latest developments in the field of Hasse diagram technique is the use of random linear extensions to estimate ranking probabilities. In the original algorithm for estimating the ranking probability it is assumed that the order between two incomparable pair of objects can be chosen randomly. However, if the total set of linear extensions is considered there is a specific probability that one object will be larger than another, which can be far from 50%. In this study it is investigated if an approximation of the mutual ranking probability can improve the algorithm. Applying an approximation of the mutual ranking probability the estimation of the ranking probabilities are significantly improved. Using a test set of 39 partial orders with randomly chosen values the relative mean root square difference (MRSD) decrease in average from 7.9% to 2.2% and a maximum relative improvement of 90% can be found. In the most successful case the relative MRSD goes as low as 0.77%.

The application of partial order theory and Hasse diagram technique in environmental science is getting increasing attention. One of the latest developments in the field of Hasse diagram technique is the use of random linear extensions to estimate ranking probabilities. In the original algorithm for estimating the ranking probability it is assumed that the order between two incomparable pair of objects can be chosen randomly. However, if the total set of linear extensions is considered there is a specific probability that one object will be larger than another, which can be far from 50%. In this study it is investigated if an approximation of the mutual ranking probability can improve the algorithm. Applying an approximation of the mutual ranking probability the estimation of the ranking probabilities are significantly improved. Using a test set of 39 partial orders with randomly chosen values the relative mean root square difference (MRSD) decrease in average from 7.9% to 2.2% and a maximum relative improvement of 90% can be found. In the most successful case the relative MRSD goes as low as 0.77%.

Partial order theory (POT) is an attractive and operationally simple method that allows ordering of compounds, based on selected structural and/or electronic descriptors (modeled order), or based on their end points, e.g., solubility (experimental order). If the modeled order resembles the experimental order, compounds that are not experimentally investigated can be assigned a position in the model that eventually might lead to a prediction of an end-point value. However, in the application of POT in quantitative structure-activity relationship modeling, only the compounds directly comparable to the noninvestigated compounds are applied. To explore the possibilities of improving the methodology, the theory is extended by application of the so-called linear extensions of the model order. The study show that partial ordering combined with linear extensions appears as a promising tool providing probability distribution curves in the range of possible end-point values for compounds not being experimentally investigated.

This paper continues the series of publications about applications of partial ordering. The focus of this publication is the derivation of approximate analytical expressions for the averaged rank and the ranking probabilities. To derive such combinatorial formulas a local partial order is suggested as an approximation. The performance of the approximation is rather high; we therefore conclude that three very simple descriptors of the local partial order seem to be sufficient to get a rough impression of the linear order, induced by the averaged ranks and the ranking probabilities of empirical partially ordered sets. Linear order derived from the partial order, ranking probabilities, and other characteristics are considered as parts of a so-called "General Ranking Model" (GRM). Following the local partial order, the averaged rank of an object x can be estimated applying the following simple formula: Rk av ) (S+1)*(N+1)/(N+1-U). S is the number of successors of the object x, N is the total number of objects (of the quotient set), and U is the number of objects incomparable with x. More complex formulas for the ranking probabilities are given in the text. A list of abbreviations and symbols can be found in Tables and.

In this project, we apply the method of partial ordering on the ranking of 74 contaminated sites located in the county of West Zealand (Denmark). The method is based on the concept that the parameters are kept separated through the ranking analysis, and thus no weighing of the different parameter values is necessary. The ranking is displayed in a graphical form by the Hasse diagram technique to ease the interpretation. A critical comparison is made of the ranking of contaminated sites by the partial ordering method and an index function used by the county of West Zealand. Comparing the ranking by the partial ordering method to the index function shows that the choice of score points and index function highly influences the ranking result, as only four sites are equally ranked. The importance of the parameters used to identify the environmental hazard of the contaminated sites is analyzed in order to evaluate the influence of each parameter on the ranking. From among a total of six d...

Partial order theory and Hasse diagrams appears to be a promising tool for decision-making in environmental issues. Alternatives or objects are said to be partial ordered when it is impossible to find a mutual relationship (< or >) for all criteria. This is often the case in complicated real life situations. However, sometimes it is attractive to apply a total order, i.e. linear rank, and not just the partial order. Based on ranking probabilities and linear extensions it is possible to derive a total order. A linear extension is a projection of the partial order into a total order that comply with all the relations in the partial order. When all linear extensions are known the ranking probabilities can be found as the probability for an object to occupy a specific rank. However, the total number of linear extensions is proportional with the faculty of the number of objects in the partial order. Therefore it is practically impossible to identify all possible linear extensions for partial orders with more than around 20 objects. This study reviews and evaluates a method which estimates the ranking probability based on sampling of a minor random fraction of the linear extensions. Using standard statistics the necessary number of random linear extensions is described as a function of the ranking probability estimate and the restrictions on the confidence interval around the ranking probability. The analysis reveals a smaller systematic uncertainty, which occurs due to the random selection of ranking between two incomparable objects. The discrepancy appears to be dependent on the structure of the partial order. The method using random linear extensions thus appears as a valuable tool for analysing larger partially ordered sets, which are practically impossible to handle using the total set of linear extensions.

The combined monitoring-based and modelling-based priority setting scheme (COMMPS) used to establish a priority setting list within the EU Water Framework Directive plays a major role in the European environmental policy on chemical substances. The COMMPS procedure can be classified as a so-called scoring method. The applied functional relationship and weight factors are established based on expert judgement, which unfortunately appears to be vulnerable to subjective inputs. In this study an alternative priority setting methods based on partial order theory (POT) and random linear extensions (RLE) is suggested and compared to the COMMPS procedure. The POT/RLE is characterised as being based on fewer assumptions concerning functional relationships and does not apply weighting factors. Using the POT/RLE methodology a different ranking result occur than when using the COMMPS procedure. Eight of the top 20 substances from the COMMPS procedure are not ranked within the top 20 when using POT/RLE. From the viewpoint of environmental protection, especially the substances that have been given low priority in the COMMPS procedure, but a high rank in POT/RLE, are of interest in a regulatory context. These substances are naphthalene, trichloromethane, isoproturon, metolachlor, endosulfan, acenaphthene, alachlor and dichloromethane. An analysis of the ability of the descriptors to separate the single substance discloses that the most significant descriptor is the concentrations detected in the environment. Further, the frequency of detection is not applied as a descriptor in the COMMPS procedure. However, if this descriptor was to be applied the analysis revealed that it would have been the third most significant descriptor.

The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. More precisely it has counits with no corresponding units, and a partially defined duality. There exist open games with the same types as unit maps, given by agents with the strategic goal of predicting a future value. Such agents appear in earlier work on selection functions. We explore the algebraic properties of these agents via the symmetric monoidal bicategory whose 2-cells are morphisms between open games, and show how the resulting structure approximates a compact closed category with a family of lax commutative bialgebras.

X-ray-absorption measurements of liquid and solid krypton at room temperature in the pressure range 0.1-30 GPa have been performed using the dispersive setup and diamond-anvil cells as a pressure device. The evolution of the near-edge structures as a function of pressure, including the first intense resonance, has been interpreted using multiple-scattering calculations. It is shown that the near-edge structures are reproduced taking into account two-body and three-body terms associated with the first-neighbor atoms. Extended x-rayabsorption fine-structure ͑EXAFS͒ spectra have been analyzed in the framework a multiple-scattering dataanalysis approach taking proper account of the atomic background including the ͓1s4 p͔, ͓1s3d͔, and ͓1s3 p͔ double-electron excitation channels. Isobaric Monte Carlo ͑MC͒ computer simulations based on empirical pair potentials, as proposed by Barker ͑K2͒ and Aziz ͑HFD-B͒, have been performed to make a quantitative comparison of theoretical and experimental local structural details of condensed krypton at high pressures. From the analysis of EXAFS data we were able to obtain simultaneous information on average distance, width, and asymmetry of the first-neighbor distribution, as a function of pressure. These parameters yield a unique insight on the potential function because they are affected by both minimum position and curvature of the effective pair potential. The trend of the first-neighbor distribution as a function of pressure is in quantitative agreement with the HFD-B potential at moderate pressures, deviations are found at higher pressures where EXAFS spectra are very sensitive to the hard-core repulsive part of the potential. The weak EXAFS signal of liquid krypton at room temperature and 0.75 GPa has been found in accord with the results of the MC simulations within the noise of the measurement. ͓S0163-1829͑96͒06937-8͔

The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized (ψ, φ)-weak contractions in partially ordered cone metric spaces. Also, some illustrative examples are presented. 2010 MSC: 54H25, 47H10.

This paper simultaneously makes new contributions to political science, probability and statistics, and linear algebra. We describe a new method, "Sinkhorn ratings," for pairwise-comparison based ranking of chessplayers, web pages, or football teams; it also may be used to rank the candidates in an election in which each vote is a partial ordering of the candidates. We also describe the first "strongly polynomial time" algorithm for finding the Perron-Frobenius eigenvector of a matrix with non-negative entries, and the second strongly polynomial time algorithm (and the first practical one) for Sinkhorn balancing a matrix with non-negative entries. The former also may be regarded as the first strongly polynomial algorithm for finding the stationary distribution of an N -state Markov chain with known transition matrix. Along the way we also present a new formulation of the Perron-Frobenius eigenvector and Markov stationary distribution problems as concave-∪ minimization problems, and present a powerful new technique for proving monotonicity statements e.g. about Markov chains.

CHRISTOS A. ATHANASIADIS, J ÖRG RAMBAU, AND FRANCISCO SANTOS ABSTRACT. Given an affine surjection of polytopes : P → Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes : C(n d ) → C(n d) for all 1 d < d < n .

we will call them simply semialgebras for short. We collect some material, which mostly can be found in [4]. Using the Propositions 1.3, 1.5 and 1.7, one observes immediately that every invariant wedge is a semialgebra and that every semialgebra is a Lie wedge. (For a rough orientation the following statement may be helpful: There are “many ” Lie wedges that are not semialgebras, but there are only “few” semialgebras that are not invariant.) There is a classification of invariant wedges due to Olshanskiĭ, Vinberg, Paneitz, Kumaresan, Ranjan, Hilgert and Hofmann that can be found in [4]. Furthermore, much in known about Lie algebras that contain pointed invariant wedges with inner points. Spindler has given an explicit construction of all these Lie algebras in [6]. Thus, the invariant wedges may serve as a supply of well understood semialgebras. However, not every semialgebra is invariant. There is another class of wellknown semialgebras, namely those that are special in the sense of

The problem of expressing and solving satisfiability problems (SAT) with qualitative preferences is central in many areas of Computer Science and Artificial Intelligence. In previous papers, it has been shown that qualitative preferences on literals allow for capturing qualitative/quantitative preferences on literals/formulas; and that an optimal model for a satisfiability problems with qualitative preferences on literals can be computed via a simple modification of the Davis-Logemann-Loveland procedure (DLL): Given a SAT formula, an optimal solution is computed by simply imposing that DLL branches according to the partial order on the preferences. Unfortunately, it is well known that introducing an ordering on the branching heuristic of DLL may cause an exponential degradation in its performances. The experimental analysis reported in these papers hightlights that such degradation can indeed show up in the presence of a significant number of preferences. In this paper we propose an alternative solution which does not require any modification of the DLL heuristic: Once a solution is computed, a constraint is added to the input formula imposing that the new solution (if any) has to be better than the last computed. We implemented this idea, and the resulting system can lead to significant improvements wrt the original proposal when dealing with MIN- ONE/MAX-SAT problems corresponding to qualitative preferences on structured instances.

We consider the problem of partial order production: arrange the elements of an unknown totally ordered T into a target partially ordered set S, by comparing a minimum number of pairs in T . Special cases of this problem include sorting by comparisons, selection, multiple selection, and heap construction. We give an algorithm performing IT LB + o(IT LB) + O(n) comparisons in the worst case. Here, n denotes the size of the ground sets, and IT LB denotes a natural information-theoretic lower bound on the number of comparisons needed to produce the target poset. The overall complexity of our algorithm is polynomial. This answers a question of Yao (SICOMP, 1989). Our strategy is to extend the poset S to a weak order W whose corresponding information-theoretic lower bound is provably not much larger than that for S. Taking W instead of S as a target poset, we then solve the problem by applying a multiple selection algorithm that performs not much more than IT LB comparisons. We base our analysis on the entropy of the target poset S, a quantity that can be efficiently computed and provides a good estimate of IT LB since the latter is, up to a linear error term, n times the entropy of S.

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P , and solving the problem amounts to discovering an unknown linear extension of P , using pairwise comparisons. The information-theoretic lower bound on the number of comparisons needed in the worst case is log e(P ), the binary logarithm of the number of linear extensions of P . In a breakthrough paper, Jeff Kahn and Jeong Han Kim (J. Comput. System Sci. 51 (3), [390][391][392][393][394][395][396][397][398][399] 1995) showed that there exists a polynomial-time algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our approach relies on graph entropy. However, our algorithms differ in essential ways from theirs. Rather than resorting to convex programming for computing the entropy, we approximate the entropy, or make sure it is computed only once, in a restricted class of graphs, permitting the use of a simpler algorithm. Specifically, we present:

The relationship between posets that are cycle-free and graphs that have more than one end is considered. We show that any locally finite bipartite graph corresponding to a cycle-free partial order has more than one end, by showing a correspondence between the ends of the graph and those of the Hasse graph of its Dedekind-MacNeille completion. If, in addition, the cycle-free partial order is k-CS-transitive for some k ≥ 3 we show that the associated graph is end-transitive. Using this approach we go on to prove that, for infinite locally finite 3-CS-transitive posets with maximal chains of height 2, the properties of being crown-free and being cycle-free are equivalent. In contrast to this we show that the non-locally finite bipartite graphs arising from skeletal cycle-free partial orders each have only one end. We include a corrected proof of a result from an earlier paper on the axiomatizability of the class of cycle-free partial orders.

We construct the Fock space representation of quantum affine algebras using combinatorics of Young walls. We also show that the crystal basis of the Fock space representation can be realized as the abstract crystal consisting of proper Young walls. We then generalize Lascoux-Leclerc-Thibon algorithm to obtain an effective algorithm for constructing the global bases of basic representations.

Assuming data domains are partially ordered, we apply Paredaens' and Bancilhon's Theorem to examine the expressiveness of the extended relational algebra (the PORA), which allows the ordering predicate to be used in formulae of the selection operator (σ). The PORA expresses exactly the set of all possible relations which are invariant under order-preserving automorphism of databases. Our main result shows that there is a one-toone correspondence between three hierarchies of: (1) computable queries, (2) query languages and (3) partially ordered domains.

The article presents a common fixed point result in Menger space in four selfmappings by using the control function [13] in the context of compatible mappings of type (P) and additionally provides some implications and applications as corollaries. This research generalizes the findings of Chaudhary et al. [9], and Pathak et al., [24] as well as expanding on some similar findings in the literature.

For many years, the intuitions underlying partial-order planning were largely taken for granted. Only in the past few years has there been renewed interest in the fundamental principles underlying this paradigm. In this paper, we present a rigorous comparative analysis of partial-order and total-order planning by focusing on two specific planners that can be directly compared. We show that there are some subtle assumptions that underly the wide-spread intuitions regarding the supposed efficiency of partial-order planning. For instance, the superiority ofpartial-order planning can depend critically upon the search strategy and the structure of the search space. Understanding the underlying assumptions is crucial for constructing efficient planners.

In this paper we compare the utility of different commitment strategies in planning. Under a "least commitment strategy", plans are represented as partial orders and operators are ordered only when interactions are detected. We investigate claims of the inherent advantages of planning with partial orders, as compared to planning with total orders. By focusing our analysis on the issue of operator ordering commitment, we are able to carry out a rigorous comparative analysis of two planners. We show that partial-order planning can be more efficient than total-order planning, but we also show that this is not necessarily so.

In this work, we study the possibility of inserting an increasing continuous lattice-valued function between two comparable semicontinuous functions on a preordered topological space. Depending on the monotonicity conditions imposed on the semicontinuous functions, new characterizations of di! erent classes of preordered topological spaces are obtained. Among them are char- acterizations of normally preordered and extremally preorder-disconnected spaces. Conditions for

Ce document se concentre sur l’optimisation des opérations de maintenance chez
Tassili Airlines, avec pour objectif principal de minimiser le temps d’immobilisation des
avions. Pour atteindre cet objectif, nous avons utilisé un outil de Recherche Opérationnelle : l’Ordonnancement des opérations de maintenance, en respectant les contraintes de précédence et de ressources (techniciens).
Notre objectif est également de produire un planning pour l’affectation des techniciens
aux tâches en fonction de leurs compétences. Le problème est un problème d’ordonnancement de projet avec contraintes de ressources multi-compétences (MS-RCPSP). Nous avons modélisé ce problème sous forme de Programme Linéaire en Nombres Entiers Mixtes (PLMNE) et l’avons résolu à l’aide de méthodes exactes. Lorsque les méthodes exactes ne sont pas applicables en raison de la complexité du problème étudié, nous avons utilisé des heuristiques pour obtenir des bonnes solutions quand si possible. Les algorithmes ont été implémentés dans une application développée en Python, permettant ainsi une gestion optimale des opérations de maintenance de la compagnie

We present a case study of artificial intelligence techniques applied to the control of production printing equipment. Like many other real-world applications, this complex domain requires high-speed autonomous decision-making and robust continual operation. To our knowledge, this work represents the first successful industrial application of embedded domain-independent temporal planning. Our system handles execution failures and multi-objective preferences. At its heart is an on-line algorithm that combines techniques from state-space planning and partial-order scheduling. We suggest that this general architecture may prove useful in other applications as more intelligent systems operate in continual, on-line settings. Our system has been used to drive several commercial prototypes and has enabled a new product architecture for our industrial partner. When compared with state-of-the-art off-line planners, our system is hundreds of times faster and often finds better plans. Our expe...

In contrast to most academic work on AI planning, many potential applications have an on-line character. For example, the true objective may not be to find the fastest plan, but to have solving plus plan execution end as soon as possible. Or additional goals may arrive while previous plans are still being executed. While specific planning systems have been built to address realworld problems in such settings, the fundamental algorithmic issues have often been obscured by the myriad complexities inherent in any deployed system. ...

We present an extension of a mathematical framework proposed by the authors to deal with the composition of heterogeneous reactive systems. Our extended framework encompasses diverse models of computation and communication such as synchronous, asynchronous, causality-based partial orders, and earliest execution times. We introduce an algebra of tag structures and morphisms between tag sets to define heterogeneous parallel composition formally and we use a result on pullbacks from category theory to handle properly the case of systems derived by composing many heterogeneous components. The extended framework allows us to establish theorems, from which design techniques for correct-by-construction deployment of abstract specifications can be derived. We illustrate this by providing a complete formal support for correct-by-construction distributed deployment of a synchronous design specification over an Ltta medium.

Concept of bi-soft topological spaces is introduced. Several notions of a soft topological space are generalized to study bi-soft topological spaces. Separation axioms play a vital role in study of topological spaces. These concepts have been studied in context of bi-soft topological spaces. There is a very close relationship between topology and rough set theory. An application of bi-soft topology is given in rough set theory.

We define a model for heuristic tree search which assumes that the quality of the heuristic used for ordering the successors of a node improves as depth increases. We show that a usual value ordering heuristic for solving constraint satisfaction problems fits to this model. Our model defines a partial order on the leaf nodes of the search tree, according to their probability to be a solution. We check which search strategies among interleaved depth-first search (IDFS), limited discrepancy search (LDS) and depth-bounded discrepancy search (DDS) visit the leaf nodes while respecting the partial order. Our study leads to conclude that, among these strategies, only Pure IDFS and a slight modification of improved LDS respect it.

While message sequence charts (MSCs) are widely used in industry to document the interworking of processes or objects, they are expressively quite weak, being based on the modest semantic notion of a partial ordering of events as defined, e.g., in the ITU standard. A highly expressive and rigorously defined MSC language is a must for serious, semantically meaningful tool support for use-cases and scenarios. It is also a prerequisite to addressing what we regard as one of the central problems in behavioral specification of systems: relating scenario-based inter-object specification to state-machine intra-object specification. This paper proposes an extension of MSCs, which we call live sequence charts (or LSCs), since our main extension deals with specifying "liveness", i.e., things that must occur. In fact, LSCs allow the distinction between possible and necessary behavior both globally, on the level of an entire chart and locally, when specifying events, conditions and progress over time within a chart. This also makes it possible to specify forbidden scenarios, and strengthens structuring constructs like as subcharts, branching and iteration. P. Ciancarini et al. (eds.), Formal Methods for Open Object-Based Distributed Systems

In this paper, we define the concept of non-commutative right multiplication Γ-semigroup as a generalization of non-commutative right multiplication semigroups using right Γ-ideals. We prove some results related to regular Γ-semigroups, simple Γ-semigroups, semisimple Γ-semigroups and cancellative Γsemigroups.

In the digital era, users encounter an endless stream of recommendations. The development of recommendation systems in AI has attracted extensive attention, yielding a substantial body of literature. However, we have not encountered any logical systems for reasoning about recommendation systems, despite the immense amount of reasoning involved in making recommendations. In this paper, we propose a new recommendation logic (RL) to study the reasoning behind recommendations, emphasizing their basis in users' revealed preferences. We explore the expressivity of RL by introducing a new notion of bisimulation and translating RL into a 3-variable fragment of a two-sorted first-order logic. We show that RL has the tree model property and that its model-checking problem can be solved in polynomial time, for which we propose an algorithm and prove its correctness. We believe that our work has the potential to advance personalized recommendations.

We define HyPOL, a local hyper logic for partial order models, expressing properties of sets of runs. These properties depict shapes of causal dependencies in sets of partially ordered executions, with similarity relations defined as isomorphisms of past observations. Unsurprisingly, since comparison of projections are included, satisfiability of this logic is undecidable. We then address model checking of HyPOL and show that, already for safe Petri nets, the problem is undecidable. Fortunately, sensible restrictions of observations and nets allow us to bring back model checking of HyPOL to a decidable problem, namely model checking of MSO on graphs of bounded treewidth.

In recent years, classical discrete event fault diagnosis techniques have been extended to Petri Net system models under partial order semantics [4]-[6]. We propose here to take further advantage of the partial order representation of concurrent processes; we explore the relational structure of occurrence nets to derive a covering relation. It indicates that occurrence of some event a inevitable leads to occurrence of some event b, before a, after a, or concurrently. Covering defines a decomposition of occurrence nets into facets; we introduce the facet-based concept of q-diagnosability -for qualitative diagnosability as opposed to quantitative criteria like in [6], [15] -, which is specific to partial order semantics. All objects considered can be computed from a finite unfolding prefix of bounded length.

We consider asynchronous diagnosis in (safe) Petri net models of distributed systems, using the partial order semantics of occurrence net unfoldings. Unlike the classical case, observability and diagnosability will appear in two different forms each: a strong form associated to interleaving semantics, and a weak form characteristic of nonsequential processes, and requiring an asynchronous progress assumption on those processes. We give algebraic characterizations for both types, and give verification methods. Sufficient conditions for strong diagnosability are derived from linear semiflows. The study of weak diagnosability leads us to the analysis of a relation in occurrence nets, first presented in : given the occurrence of some event a that reveals b, the occurrence of b is inevitable; here b may be concurrent to, or even in the future of a. We show that the reveals-relation can be effectively computed on a suitable bounded prefix of the unfolding, and show its use in asynchronous diagnosis. Based on this relation, a decomposition of the Petri net unfolding into facets is defined, yielding an abstraction technique that preserves and reflects maximal partially ordered runs.

This article presents a novel approach for modeling Water Distribution Networks (WDNs) based on physical principles, graph theory, and the pseudo-transient continuation method. The main feature of this approach is that it permits the representation of WDNs as fully interconnected networks of damped nonlinear oscillators, with each oscillator formulated as a Liénard system given in terms of the flow rates. This representation facilitates the design of control and observation algorithms, particularly in scenarios where the WDNs lack pressure sensors. To show the possible usages of this approach, a state observer for estimating the user's water demands is designed and numerically tested.

The underlying aim of this paper is first to state the Cyclic version of K-quasi-contractive mappings introduced by Fallahi and Aghanians [On quasi-contractions in metric spaces with a graph, Hacet. J. Math. Stat. 45 (4) (2016), 1033-1047]. Secondly, it seeks to show to show the existence of fixed point and best proximity points for such contractive mappings in a metric space with a graph, which can entail a large number of former fixed point and best proximity point results. One fundamental issue that can be distinguished between this work and previous studies is that it can also involve all of results stated by taking comparable and η-close elements.

In this paper, we define and consider, the category FPos-S of all S-fuzzy posets and action-preserving monotone maps between them. S-fuzzy poset congruences which play an important role in studying the categorical properties of S-fuzzy posets are introduced. More precisely, the correspondence between the S-fuzzy poset congruences and the fuzzy action and order preserving maps is discussed. We characterize S-fuzzy poset congruences on the Sfuzzy posets in terms of the fuzzy pseudo orders. Some categorical properties of the category FPos-S of all S-fuzzy posets is considered. In particular, we characterize products, coproducts, equalizers, coequalizers, pullbacks and pushouts in this category. Also, we consider all forgetful functors between the category FPos-S and the categories FPos of fuzzy posets, Pos-S of S-posets, Pos of posets, ActS of S-acts and Set of sets and study the existence of their left and right adjoints. Finally, epimorphisms, monomorphisms and order embeddings in FPos and FPos-S are studied.

A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.

A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.

1 Current unit test frameworks present broken unit tests in an arbitrary order, but developers want to focus on the most specific ones first. We have therefore inferred a partial order of unit tests corresponding to a coverage hierarchy of their sets of covered method signatures: When several unit tests in this coverage hierarchy break, we can guide the developer to the test calling the smallest number of methods. Our experiments with four case studies indicate that this partial order is semantically meaningful, since faults that cause a unit test to break generally cause less specific unit tests to break as well.

A single software fault may cause several tests to break, if they cover the same methods. The coverage sets of tests may not just overlap, but include one another. This information could be of great use to developers who would like to focus on the most specific test that concerns a given fault. Unfortunately, existing unit testing tools neither gather nor exploit this information. We have developed a simple approach that analyses a set of test suites, and infers the partial order corresponding to inclusion hierarchy of the coverage sets. When several tests in an inclusion chain break, we can guide the developer to the most specific test in the chain. Our first experiments with three case studies suggest that most unit tests for typical applications are, in fact, comparable to other tests, and can therefore be partially ordered. Furthermore, we show that this partial order is semantically meaningful, since faults that cause a test to break will, in nearly all cases cause less specifi...