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54
A Framework for Comparing Models of Computation
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 1998
"... Abstract—We give a denotational framework (a “meta model”) within which certain properties of models of computation can be compared. It describes concurrent processes in general terms as sets of possible behaviors. A process is determinate if, given the constraints imposed by the inputs, there are e ..."
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Cited by 245 (54 self)
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Abstract—We give a denotational framework (a “meta model”) within which certain properties of models of computation can be compared. It describes concurrent processes in general terms as sets of possible behaviors. A process is determinate if, given the constraints imposed by the inputs, there are exactly one or exactly zero behaviors. Compositions of processes are processes with behaviors in the intersection of the behaviors of the component processes. The interaction between processes is through signals, which are collections of events. Each event is a valuetag pair, where the tags can come from a partially ordered or totally ordered set. Timed models are where the set of tags is totally ordered. Synchronous events share the same tag, and synchronous signals contain events with the same set of tags. Synchronous processes have only synchronous signals as behaviors. Strict causality (in timed tag systems) and continuity (in untimed tag systems) ensure determinacy under certain technical conditions. The framework is used to compare certain essential features of various models of computation, including Kahn process networks, dataflow, sequential processes, concurrent sequential processes with rendezvous, Petri nets, and discreteevent systems. I.
What's Ahead for Embedded Software?
 Software?”, Computer
, 2000
"... at "components" and "frameworks" might entail. Otherwise, we have little hope of getting a useful model because the prevailing component architectures in software engineering are not suitable for embedded systems. Most frameworks have four service categories: . Ontology. A framework defines wha ..."
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Cited by 80 (10 self)
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at "components" and "frameworks" might entail. Otherwise, we have little hope of getting a useful model because the prevailing component architectures in software engineering are not suitable for embedded systems. Most frameworks have four service categories: . Ontology. A framework defines what it means to be a component. Is a component a subroutine? A state transformation? A process? An object? An aggregate of components may or may not be a component. Certain semantic properties of components also flow from the definition. Is a component active or passivecan it autonomously initiate interactions with other components or does it simply react to stimulus? . Epistemology. A framework defines states of knowledge. What does the framework know about the components? What do components know about one another? Can components interrogate one another to obtain information (that is, is there reflection or introspection)? What do components know<F1
Convex drawings of Planar Graphs and the Order Dimension of 3Polytopes
 ORDER
, 2000
"... We define an analogue of Schnyder's tree decompositions for 3connected planar graphs. Based on this structure we obtain: Let G be a 3connected planar graph with f faces, then G has a convex drawing with its vertices embedded on the (f 1) (f 1) grid. Let G be a 3connected planar graph. The d ..."
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Cited by 34 (14 self)
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We define an analogue of Schnyder's tree decompositions for 3connected planar graphs. Based on this structure we obtain: Let G be a 3connected planar graph with f faces, then G has a convex drawing with its vertices embedded on the (f 1) (f 1) grid. Let G be a 3connected planar graph. The dimension of the incidence order of vertices, edges and bounded faces of G is at most 3. The second result is originally due to Brightwell and Trotter. Here we give a substantially simpler proof.
Deformations of Coxeter Hyperplane Arrangements
 J. Combin. Theory Ser. A
, 1997
"... We investigate several hyperplane arrangements that can be viewed as deformations of Coxeter arrangements. In particular, we prove a conjecture of Linial and Stanley that the number of regions of the arrangement x i \Gamma x j = 1; 1 i ! j n; is equal to the number of alternating trees. Remarkab ..."
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Cited by 31 (6 self)
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We investigate several hyperplane arrangements that can be viewed as deformations of Coxeter arrangements. In particular, we prove a conjecture of Linial and Stanley that the number of regions of the arrangement x i \Gamma x j = 1; 1 i ! j n; is equal to the number of alternating trees. Remarkably, these numbers have several additional combinatorial interpretations in terms of binary trees, partially ordered sets, and tournaments. More generally, we give formulae for the number of regions and the Poincar'e polynomial of certain finite subarrangements of the affine Coxeter arrangement of type A n\Gamma1 . These formulae enable us to prove a "Riemann hypothesis" on the location of zeros of the Poincar'e polynomial. We also consider some generic deformations of Coxeter arrangements of type A n\Gamma1 . 1 Introduction The Coxeter arrangement of type A n\Gamma1 is the arrangement of hyperplanes given by x i \Gamma x j = 0; 1 i ! j n: (1.1) This arrangement has n! regions. They corre...
Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets
 EVOLUTIONARY PROGRAMMING VII, PROCEEDINGS OF THE 7TH ANNUAL CONFERENCE ON EVOLUTIONARY PROGRAMMING
, 1998
"... The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a realvalued function or of finding paretooptimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to t ..."
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Cited by 29 (7 self)
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The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a realvalued function or of finding paretooptimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to the set of minimal elements in finite time with probability one, provided that the search space is finite, the timeinvariant variation operator is associated with a positive transition probability function and that the selection operator obeys the socalled `elite preservation strategy.'
Multiple Indicators, partially ordered sets, and linear extensions: Multicriterion ranking and prioritization
, 2004
"... ..."
Evolutionary Search under Partially Ordered Fitness Sets
 IN PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON INFORMATION SCIENCE INNOVATIONS IN ENGINEERING OF NATURAL AND ARTIFICIAL INTELLIGENT SYSTEMS (ISI 2001
, 2001
"... The search for minimal elements in partially ordered sets is a generalization of the task of finding Paretooptimal elements in multicriteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a populationbased evolutionary search is, as a matter o ..."
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Cited by 19 (3 self)
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The search for minimal elements in partially ordered sets is a generalization of the task of finding Paretooptimal elements in multicriteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a populationbased evolutionary search is, as a matter of principle, capable of finding several minimal elements in a single run and gains therefore a steadily increase of popularity. Here, we present an evolutionary algorithm which population converges with probability one to the set of minimal elements within a finite number of iterations.
Heterogenous Simulation  mixing discreteevent model with dataflow
, 1996
"... This paper relates to systemlevel design of signal processing systems, which are often heterogeneous in implementation technologies and design styles. The heterogeneous approach, by combining small, specialized models of computation, achieves generality and also lends itself to automatic synthesis ..."
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Cited by 17 (4 self)
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This paper relates to systemlevel design of signal processing systems, which are often heterogeneous in implementation technologies and design styles. The heterogeneous approach, by combining small, specialized models of computation, achieves generality and also lends itself to automatic synthesis and formal verification. Key to the heterogeneous approach is to define interaction semantics that resolve the ambiguities when different models of computation are brought together. For this purpose, we introduce a tagged signal model as a formal framework within which the models of computation can be precisely described and unambiguously differentiated, and their interactions can be understood. In this paper, we will focus on the interaction between dataflow models, which have partially ordered events, and discreteevent models, with their notion of time that usually defines a total order of events. A variety of interaction semantics, mainly in handling the different notions of time in the two models, are explored to illustrate the subtleties involved. An implementation based on the Ptolemy system from U.C. Berkeley is described and critiqued.
Entropy, independent sets and antichains: A new approach to Dedekind’s problem
 PROC. AMER. MATH. SOC
, 2002
"... For nregular, Nvertex bipartite graphs with bipartition A ∪ B, a precise bound is given for the sum over independent sets I of the quantity µ I∩A  λ I∩B . (In other language, this is bounding the partition function for certain instances of the hardcore model.) This result is then extended to ..."
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Cited by 16 (1 self)
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For nregular, Nvertex bipartite graphs with bipartition A ∪ B, a precise bound is given for the sum over independent sets I of the quantity µ I∩A  λ I∩B . (In other language, this is bounding the partition function for certain instances of the hardcore model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a wellknown bound for Dedekind’s Problem given by Kleitman and Markowsky in 1975.
Preference modelling
 State of the Art in Multiple Criteria Decision Analysis
, 2005
"... This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and ob ..."
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Cited by 12 (0 self)
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This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and nonclassical logics become necessary. We then present different types of preference structures reflecting the behavior of a decisionmaker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with "compact representation of preferences " introduced for special purposes. We end the paper with some concluding remarks.