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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 323 (67 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 f ..."
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Cited by 106 (11 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
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 49 (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...
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. ..."
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Cited by 44 (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.
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 40 (9 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.'
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 30 (5 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.
Hyperplane arrangements, interval orders and trees
 Proc. Natl. Acad. Sci
, 1996
"... 1 Hyperplane arrangements The main object of this paper is to survey some recently discovered connections between hyperplane arrangements, interval orders, and trees. We will only indicate the highlights of this development; further details and proofs will appear elsewhere. First we review some bas ..."
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Cited by 30 (0 self)
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1 Hyperplane arrangements The main object of this paper is to survey some recently discovered connections between hyperplane arrangements, interval orders, and trees. We will only indicate the highlights of this development; further details and proofs will appear elsewhere. First we review some basic facts about hyperplane arrangements. A hyperplane arrangement is a finite collection A of affine hyperplanes in a (finitedimensional) affine space A. We will consider here only the case A = Rn (regarded as an affine space). The theory of hyperplane arrangements has been extensively developed and has deep connections with many other areas of mathematics, such as algebraic geometry, algebraic topology, and the theory of hypergeometric functions; see for example [16][17]. We will be primarily concerned with the number r(A) of regions of A, i.e., the number of connected components of the space Rn − H∈AH. Closely related to this number is the number b(A) of bounded regions of A. A fundamental object associated with the arrangement A is its intersection poset LA (actually a meet semilattice), defined as follows. The elements of LA are the nonempty intersections of subsets of the hyperplanes in A, including the empty intersection A. The elements of LA are ordered by reverse inclusion, so in particular LA has a unique minimal element 0 ̂ = A. LA will have a unique maximal element (and thus be a lattice) if and only if the intersection of all the hyperplanes in A is nonempty. For the basic facts about posets and lattices we are using here, see [27, Ch. 3]. The characteristic
Multiple Indicators, partially ordered sets, and linear extensions: Multicriterion ranking and prioritization
, 2004
"... ..."
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 27 (2 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.
Pattern avoidance and the Bruhat order
 JOURNAL OF COMBINATORIAL THEORY, SERIES A 114 (2007) 888–905
, 2007
"... The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, the ..."
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Cited by 24 (6 self)
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The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, the permutations whose principal order ideals have a form related to boolean posets are also completely described. It is determined when the set of permutations avoiding a particular set of patterns is an order ideal, and the rank generating functions of these ideals are computed. Finally, the Bruhat order in types B and D is studied, and the elements with boolean principal order ideals are characterized and enumerated by length.