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31
Algebraic Approaches to Nondeterminism  an Overview
 ACM Computing Surveys
, 1997
"... this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University ..."
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this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University
with the same algebraic geometry
 Proceedings of the International Conference on Mathematical Logic, Algebra and Set Theory, dedicated to 100 anniversary of P.S.Novikov, Proceedings MIAN
, 2002
"... Abstract. Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of g ..."
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Cited by 18 (3 self)
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Abstract. Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in Θ and of geometric relations between them. The main problem considered in the paper is when different H1 and H2 have the same geometry.
Towards a formal foundation for domain specific modeling languages
 Proceedings of the Sixth ACM International Conference on Embedded Software (EMSOFT’06
, 2006
"... Embedded system design is inherently domain specific and typically model driven. As a result, design methodologies like OMG’s model driven architecture (MDA) and model integrated computing (MIC) evolved to support domain specific modeling languages (DSMLs). The success of the DSML approach has encou ..."
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Cited by 14 (10 self)
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Embedded system design is inherently domain specific and typically model driven. As a result, design methodologies like OMG’s model driven architecture (MDA) and model integrated computing (MIC) evolved to support domain specific modeling languages (DSMLs). The success of the DSML approach has encouraged work on the heterogeneous composition of DSMLs, model transformations between DSMLs, approximations of formal properties within DSMLs, and reuse of DSML semantics. However, in the effort to produce a mature design approach that can handle both the structural and behavioral semantics of embedded system design, many foundational issues concerning DSMLs have been overlooked. In this paper we present a formal foundation for DSMLs and for their construction within metamodeling frameworks. This foundation allows us to algorithmically decide if two DSMLs or metamodels are equivalent, if model transformations preserve properties, and if metamodeling frameworks have metametamodels. These results are key to building correct embedded systems with DSMLs.
Characterizing classes defined without equality
 Studia Logica
, 1997
"... �������� � In this paper we mainly deal with firstorder languages without equality and introduce a weak form of equality predicate, the socalled Leibniz equality. This equality is characterized algebraically by means of a natural concept of congruence; in any structure, it turns out to be the maxi ..."
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Cited by 7 (1 self)
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�������� � In this paper we mainly deal with firstorder languages without equality and introduce a weak form of equality predicate, the socalled Leibniz equality. This equality is characterized algebraically by means of a natural concept of congruence; in any structure, it turns out to be the maximum congruence of the structure. We show that firstorder logic without equality has two distinct complete semantics (full semantics and reduced semantics) related by a reduction operator. The last and main part of the paper contains a series of Birkhoffstyle theorems characterizing certain classes of structures defined without equality, not only full classes but also reduced ones. 1. Preliminaries 1.1. Basic Notation and Terminology. Let the triple L = 〈F, R, ρ 〉 be a first order language; F and R denote pairwise disjoint sets of function and relation symbols of L respectively (R must be nonempty), and ρ is the arity function from F ∪ R into the set of natural numbers. We use capital Gothic letters A, B, C,..., with appropriate subscripts, to represent structures over L, also called Lstructures. In order to be consistent with the notation, we denote by A the universe of A, and by FA and RA the interpretations on A of the collections of function and relation symbols of L respectively, i.e., FA = {f A: f ∈ F} and RA = {r A: r ∈ R}. The corresponding boldface letter A is used to denote the underlying algebra 〈A, FA 〉 of A, and we normally write f A instead of f A. Lowercase boldface letters a,b,... are used to indicate members of the cartesian product of some family of sets. So, if A is an Lstructure, a = 〈a1,..., an 〉 belongs to A n, f ∈ F and r ∈ R, and h is any mapping with domain A, then f A a, a ∈ r A and ha are shorthand for f A a1... an, 〈a1,..., an 〉 ∈ r A and 〈ha1,..., han〉, respectively. By an Lalgebra we mean the underlying algebra of any Lstructure; of course, if the set of function symbols is empty, an Lalgebra simply means an arbitrary
Algebraic relational approach for geospatial feature correlation
 In: Proceedings of International Conference on Imaging Science, Systems, and Technology (CISST’2002, June 2427, 2002), Las Vegas
, 2002
"... In Geometry in Action: Cartography and geographic Information Systems David Eppstein [6] lists several important problems of computational geometry for cartography and GIS. This paper considers two of them: (1) matching/correlating similar features from different geospatial databases (the conflation ..."
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Cited by 6 (2 self)
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In Geometry in Action: Cartography and geographic Information Systems David Eppstein [6] lists several important problems of computational geometry for cartography and GIS. This paper considers two of them: (1) matching/correlating similar features from different geospatial databases (the conflation problem), and (2) handling approximate and inconsistent data. These problems are of great practical importance for end users defense and intelligence analysts, geologists, geographers, ecologists and others. An adequate mathematical formulation and solution of these problems is still an open question due their complexity. This paper analyzes relations between these problems and topics in computational topology and geometry. This analysis concludes that a fundamentally new mathematical approach is needed. The paper develops such new approach based on the general concept of an abstract algebraic system. Such a system can uniformly express all major algebraic constructs such as groups, fields, algebras and models. We also show the benefit of developing a fundamentally new approach algebraic invariants for geospatial data analysis and correlation using this concept.
Matching Image Feature Structures Using Shoulder Analysis Method, In: Algorithms and technologies for multispectral, hyperspectral and ultraspectral imagery IX. Vol
 5425, International SPIE military and aerospace symposium, AEROSENSE
"... The problems of imagery registration, conflation, fusion and search require sophisticated and robust methods. An algebraic approach is a promising new option for developing such methods. It is based on algebraic analysis of features represented as polylines. The problem of choosing points when attem ..."
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Cited by 4 (3 self)
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The problems of imagery registration, conflation, fusion and search require sophisticated and robust methods. An algebraic approach is a promising new option for developing such methods. It is based on algebraic analysis of features represented as polylines. The problem of choosing points when attempting to prepare a linear feature for comparison with other linear features is a significant challenge when orientation and scale is unknown. Previously we developed an invariant method known as Binary Structural Division (BSD). It is shown to be effective in comparing feature structure for specific cases. In cases where a bias of structure variability exists however, this method performs less well. A new method of Shoulder Analysis (SA) has been found which enhances point selection, and improves the BSD method. This paper describes the use of shoulder values, which compares the actual distance traveled along a feature to the linear distance from the start to finish of the segment. We show that shoulder values can be utilized within the BSD method, and lead to improved point selection in many cases. This improvement allows images of unknown scale and orientation to be correlated more effectively.
A Coalgebraic Modelling of HeadDriven Phrase Structure Grammar
 Proposal to NASA Langley Research Center, Madic Team #2
, 2000
"... This paper provides a coalgebraic modelling of HeadDriven Phrase Structure Grammar. HPSG is a licensing theory in the sense that grammaticality is defined in terms of abstract grammar principles, wellformedness conditions on linguistic analyses rather then by a set of rules that would explicite ..."
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Cited by 3 (0 self)
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This paper provides a coalgebraic modelling of HeadDriven Phrase Structure Grammar. HPSG is a licensing theory in the sense that grammaticality is defined in terms of abstract grammar principles, wellformedness conditions on linguistic analyses rather then by a set of rules that would explicitely generate an analysis. Since coalgebras are very well suited for modelling licensing theories, we provide a conceptually particularly adequate formalisation for HPSG by showing that HPSG can indeed be modeled with coalgebras. We also show that the category of grammar models contains a final coalgebra. This final coalgebra we propose as the model of an HPSG grammar, because it models the analyses of the structurally different readings of all and only those utterances licensed by the grammar while eliminating spurious ambiguities. 1
Streams, Stream Transformers and Domain Representations
 Prospects for Hardware Foundations, Lecture Notes in Computer Science
, 1998
"... We present a general theory for the computation of stream transformers of the form F: (R B) (T A), where time T and R, and data A and B, are discrete or continuous. We show how methods for representing topological algebras by algebraic domains can be applied to transformations of continuous ..."
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Cited by 3 (3 self)
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We present a general theory for the computation of stream transformers of the form F: (R B) (T A), where time T and R, and data A and B, are discrete or continuous. We show how methods for representing topological algebras by algebraic domains can be applied to transformations of continuous streams. A stream transformer is continuous in the compactopen topology on continuous streams if and only if it has a continuous lifting to a standard algebraic domain representation of such streams. We also examine the important problem of representing discontinuous streams, such as signals T A, where time T is continuous and data A is discrete.
REPRESENTABLE IDEMPOTENT COMMUTATIVE RESIDUATED LATTICES
"... Abstract. It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The ngenerated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebra ..."
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Cited by 2 (1 self)
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Abstract. It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The ngenerated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of positive relevance logic containing the mingle and GödelDummett axioms has a solvable deducibility problem. 1.
Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions
"... Abstract. We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with g ..."
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Abstract. We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with general realizability models rather than with a particular model of computation. Consequently, all the results are applicable in various established schools of computability, such as type 1 and type 2 effectivity, domain representations, equilogical spaces, and others. 1