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Automata and coinduction (an exercise in coalgebra
 LNCS
, 1998
"... The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which ..."
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Cited by 78 (18 self)
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The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.
Semistructured Data and XML
, 1998
"... This paper argues that the research on semistructured data is receiving a new set of challenges with the advent of XML (Extensible Markup Language [Bos97, Con98]). This is a new standard approved by the World Wide Web Consortium that many believe will become the de facto data exchange format for th ..."
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Cited by 63 (1 self)
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This paper argues that the research on semistructured data is receiving a new set of challenges with the advent of XML (Extensible Markup Language [Bos97, Con98]). This is a new standard approved by the World Wide Web Consortium that many believe will become the de facto data exchange format for the Web. XML supports the electronic exchange of machinereadable data (while HTML is designed primarily for humanreadable documents). XML data shares many features of semistructured data: its structure can be irregular, is not always known ahead of time, and may change frequently and without notice. On the other hand it is easy to convert data from any source into XML which will make it attractive for organizations to "publish" their information sources in XML, and thus make them available to other XML applications on the Web. For XML applications to reach their full potential however, we need to build the right tools to process data in this new format. Existing Web tools (browsers, search engines) are oriented toward document operations . For XML we need database operations , like data extraction, data integration, data translation, data storage. The research done so far on semistructured data may offer some solutions to the database problems posed by XML. For example the recently proposed query language for XML, called XMLQL [DFF
HYPERSOLVER: A Graphical Tool for Commonsense Set Theory
, 1996
"... This paper investigates an alternative set theory (due to Peter Aczel) called Hyperset Theory. Aczel uses a graphical representation for sets and thereby allows the representation of nonwellfounded sets. A program, called HYPERSOLVER, which can solve systems of equations defined in terms of sets ..."
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Cited by 1 (1 self)
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This paper investigates an alternative set theory (due to Peter Aczel) called Hyperset Theory. Aczel uses a graphical representation for sets and thereby allows the representation of nonwellfounded sets. A program, called HYPERSOLVER, which can solve systems of equations defined in terms of sets in the universe of this new theory is presented. This may be a useful tool for commonsense reasoning. 1 INTRODUCTION Set theory has long occupied a unique place in mathematics since it allows various other branches of mathematics to be formally defined within it. The theory has ignited many debates on its nature and a number of different axiomatizations were developed to formalize its underlying `philosophical' principles. Collecting entities into an abstraction for further thought (i.e., set construction) is an important process in mathematics, and this brings in assorted problems [5]. The theory had many groundshaking crises (like the discovery of the Russell's Paradox [6]) throughout it...
A Faster Parallel Implementation of the KanellakisSmolka Algorithm for Bisimilarity Checking
 In Proceedings of the International Computer Symposium
, 1998
"... Bisimulation equivalence is one of the most important equivalence relations that capture the notion of `behavioral equivalence' of concurrent systems. In this paper we present a randomized parallel implementation of the KanellakisSmolka algorithm that tests the bisimilarity of two finite CC ..."
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Bisimulation equivalence is one of the most important equivalence relations that capture the notion of `behavioral equivalence' of concurrent systems. In this paper we present a randomized parallel implementation of the KanellakisSmolka algorithm that tests the bisimilarity of two finite CCS specifications in O(n) time with O(n 2 ) processors, when the semantic models are given as (S1 ; A; T1 ; s1 ) and (S2 ; A; T2 ; s2 ), respectively (jS1 j + jS2 j = n; jT1 j + jT2 j = m), and jAj = 1. We claim that our implementation is faster than that of Lee and Rajasekaran [12] by a factor of O(lg n) 1 . 1 Introduction Over the past decades much attention have been paid to the study of theories of concurrency such as CCS [9], CSP [5], calculus, and ACP. And a fair portion of these research efforts were devoted to the study of the notion of `equivalence' of systems. Since bisimulation equivalence relation was proposed as a notion of behavioral equivalence in [8], this equivalence re...
A functional hitchhiker’s guide to hereditarily finite sets, Ackermann encodings and pairing functions
 Computing Research Repository
"... The paper is organized as a selfcontained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available at ..."
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The paper is organized as a selfcontained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available at
Under consideration for publication in Math. Struct. in Comp. Science WellFounded Coalgebras, Revisited
, 2013
"... Theoretical models of recursion schemes have been well studied under the names wellfounded coalgebras, recursive coalgebras, corecursive algebras, and Elgot algebras. Much of this work focuses on conditions ensuring unique or canonical solutions, e.g. when the coalgebra is wellfounded. If the coal ..."
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Theoretical models of recursion schemes have been well studied under the names wellfounded coalgebras, recursive coalgebras, corecursive algebras, and Elgot algebras. Much of this work focuses on conditions ensuring unique or canonical solutions, e.g. when the coalgebra is wellfounded. If the coalgebra is not wellfounded, then there can be multiple solutions. The standard semantics of recursive programs gives a particular solution, namely the least solution in a flat Scott domain, which may not be the desired one. We have recently proposed programming language constructs to allow the specification of alternative solutions and methods to compute them. We have implemented these new constructs as an extension of OCaml. In this paper, we prove some theoretical results characterizing wellfounded coalgebras that slightly extend results of Adámek, Lücke, and Milius (2007), along with several examples for which this extension is useful. We also give several examples that are not wellfounded but still have a desired solution. In each case, the function would diverge under the standard semantics of recursion, but can be specified and computed with the programming language constructs we have proposed. 1.
AntiRealist Classical Logic and Realist Mathematics
, 2009
"... Abstract. I sketch an application of a semantically antirealist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically antirealist defence of a kind of mathematical realism. In the paper, I begin the development of the view and compare it to ortho ..."
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Abstract. I sketch an application of a semantically antirealist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically antirealist defence of a kind of mathematical realism. In the paper, I begin the development of the view and compare it to orthodox positions in the philosophy of mathematics.