Other Computer Sciences Commons^™

Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari

Engineering Faculty Articles and Research

Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good …

Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz

Engineering Faculty Articles and Research

We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces—the duals of Boolean algebras—and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for the study …

Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil

Engineering Faculty Articles and Research

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.

Temporal Data Classification Using Linear Classifiers, Peter Revesz, Thomas Triplet

School of Computing: Conference and Workshop Papers

Data classification is usually based on measurements recorded at the same time. This paper considers temporal data classification where the input is a temporal database that describes measurements over a period of time in history while the predicted class is expected to occur in the future. We describe a new temporal classification method that improves the accuracy of standard classification methods. The benefits of the method are tested on weather forecasting using the meteorological database from the Texas Commission on Environmental Quality.

Equational Coalgebraic Logic, Alexander Kurz, Raul Leal

Engineering Faculty Articles and Research

Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss’s logic. The three logics are …

Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan

Engineering Faculty Articles and Research

Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate …

Back-Up Server For Computer Science Department, Victoria Gaylord

Mahurin Honors College Capstone Experience/Thesis Projects

Because Western Kentucky University does not maintain a back-up system for its departments, the Computer Science Department has implemented its own. Using Bacula software on a Unix server, files from faculty desktop computers and servers are backed up to a tape drive on a daily basis. The server is protected from outside threats with a carefully configured firewall script. This paper explains how both the firewall and the back-up software were implemented and how successful that implementation has been.

Some Peer-To-Peer, Democratically And Voluntarily Produced Thoughts About 'The Wealth Of Networks: How Social Production Transforms Markets And Freedom,' By Yochai Benkler, Ann Bartow

Law Faculty Scholarship

In this review essay, Bartow concludes that The Wealth of Networks: How Social Production Transforms Markets and Freedom by Yochai Benkler is a book well worth reading, but that Benkler still has a bit more work to do before his Grand Unifying Theory of Life, The Internet, and Everything is satisfactorily complete. It isn't enough to concede that the Internet won't benefit everyone. He needs to more thoroughly consider the ways in which the lives of poor people actually worsen when previously accessible information, goods and services are rendered less convenient or completely unattainable by their migration online. Additionally, the …

Pi-Calculus In Logical Form, Marcello M. Bonsangue, Alexander Kurz

Engineering Faculty Articles and Research

Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiation, and showing that they are dual to standard constructs in functor categories. We show that initial algebras of functors defined in terms of these constructs give rise to a logic that is sound, complete, and characterises bisimilarity. The approach is modular, and we apply it to derive a logical formulation of pi-calculus. The resulting logic is a …

Coalgebras And Their Logics, Alexander Kurz

Engineering Faculty Articles and Research

"Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics."

Weak Factorizations, Fractions And Homotopies, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

We show that the homotopy category can be assigned to any category equipped with a weak factorization system. A classical example of this construction is the stable category of modules. We discuss a connection with the open map approach to bisimulations proposed by Joyal, Nielsen and Winskel.

Preface, Thomas Hildebrandt, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.

Algebraic Semantics For Coalgebraic Logics, Clemens Kupke, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T-coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for coalgebras of an endofunctor T, we construct an endofunctor L such that L-algebras provide a sound and complete (algebraic) semantics of the logic. We show that if L is dual to T, then soundness and completeness of the algebraic semantics immediately yield the …

Coalgebras And Modal Expansions Of Logics, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

In this paper we construct a setting in which the question of when a logic supports a classical modal expansion can be made precise. Given a fully selfextensional logic S, we find sufficient conditions under which the Vietoris endofunctor V on S-referential algebras can be defined and we propose to define the modal expansions of S as the logic that arises from the V-coalgebras. As an example, we also show how the Vietoris endofunctor on referential algebras extends the Vietoris endofunctor on Stone spaces. From another point of view, we examine when a category of ‘spaces’ (X,A), ie sets X …

Spatiotemporal Databases: Models For Attracting Students To Research, Ágnes Bércesné Novák, Peter Revesz, Zsolt Tuza

School of Computing: Conference and Workshop Papers

In higher education professors often make much effort to introduce their students to research. Unfortunately, the present standard database systems curriculum is composed of well-settled subjects that do not lead to research. The challenge is to bring the research frontier closer to students at beginner level. In this paper we describe how it can be done in the area of spatiotemporal databases. We propose a new database systems curriculum and illustrate its benefits by mentioning several highly succsesful student projects in some recent experimental introductory database systems courses that followed the new curriculum.

Stone Coalgebras, Clemens Kupke, Alexander Kurz, Yde Venema

Engineering Faculty Articles and Research

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor. Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. …

Cxquery: A Novel Xml Query Language, Peter Revesz, Yi Chen

School of Computing: Conference and Workshop Papers

XML is becoming the data exchange standard on the Internet. Previously proposed XML query languages, such as XQuery, Quilt, YALT, Lorel, and XML-QL, lack schema definition of the query result; therefore, they are limited for defining views, integrating data, updating, and further querying, all of which are often needed in e-Business applications. We propose a novel XML query language called CXQuery, which defines the schema of the query results explicitly and can easily define views, and integrate, update, and query XML data. In addition, CXQuery can express spatial and spatio-temporal queries using a constraint-based querying approach.

Preface, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.

Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.

Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.

Modal Rules Are Co-Implications, Alexander Kurz

Engineering Faculty Articles and Research

In [13], it was shown that modal logic for coalgebras dualises—concerning definability— equational logic for algebras. This paper establishes that, similarly, modal rules dualise implications:It is shown that a class of coalgebras is definable by modal rules iff it is closed under H (images) and Σ (disjoint unions). As a corollary the expressive power of rules of infinitary modal logic on Kripke frames is characterised.

Notes On Coalgebras, Cofibrations And Concurrency, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

We consider categories of coalgebras as (co)-fibred over a base category of parameters and analyse categorical constructions in the total category of deterministic and non-deterministic coalgebras.

(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz

Engineering Faculty Articles and Research

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.

Safe Stratified Datalog With Integer Order Programs, Peter Revesz

School of Computing: Conference and Workshop Papers

Guaranteeing termination of programs on all valid inputs is important for database applications. Termination cannot be guaranteed in Stratified Datalog with integer (gap)-order programs on generalized databases because they express any Turing-computable function. This paper introduces a restriction of those programs that can express only computable queries. The restricted language has a high expressive power and a non-elementary data complexity.

Constraint Objects, Divesh Srivastava, Raghu Ramakrishnan, Peter Revesz

School of Computing: Conference and Workshop Papers

We describe the Constraint Object Data Model (CODM), which enhances an object-based data model with existential constraints to naturally represent partially specified information. We present the Constraint Object Query Language (COQL), a declarative, rule-based query language that can be used to infer relationships about and monotonically refine information represented in the CODM. COQL has a model-theoretic and an equivalent fixed-point semantics, based on the notions of constraint entailment and "proofs in all possible worlds." We also provide a novel polynomial-time algorithm for quantifier elimination for set-order constraints, a restricted class of set constraints that uses membership of subset-equal.

Centre For Computer Aided Management: An Overview, V B Kaujalagi

IIMB Management Review

No abstract provided.

An Exact Analysis For Efficient Computation Of Random-Pattern Testability In Combinational Circuits, Sharad C. Seth, Bhargab B. Bhattacharya, Vishwani Agrawal

School of Computing: Conference and Workshop Papers

Experimental evidence shows that low testability in a typical circuit is much more likely due to poor observability than poor controllability. Thus, from theoretical and practical standpoints, it is important to develop an accurate model for observability computation. One such model, in terms of supergates, is proposed in the first part of this paper thus complimenting our earlier work. It is now possible to obtain exact random-pattern testability for each line in a circuit.

The second part of the paper analyzes the supegate structure of a circuit from a graph theoretic viewpoint. Finding a supergate is related to determining the …