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Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
The microcosm principle and concurrency in coalgebras
 I. HASUO, B. JACOBS, AND A. SOKOLOVA
, 2008
"... Coalgebras are categorical presentations of statebased systems. In investigating parallel composition of coalgebras (realizing concurrency), we observe that the same algebraic theory is interpreted in two different domains in a nested manner, namely: in the category of coalgebras, and in the final ..."
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Cited by 15 (10 self)
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Coalgebras are categorical presentations of statebased systems. In investigating parallel composition of coalgebras (realizing concurrency), we observe that the same algebraic theory is interpreted in two different domains in a nested manner, namely: in the category of coalgebras, and in the final coalgebra as an object in it. This phenomenon is what Baez and Dolan have called the microcosm principle, a prototypical example of which is “a monoid in a monoidal category.” In this paper we obtain a formalization of the microcosm principle in which such a nested model is expressed categorically as a suitable lax natural transformation. An application of this account is a general compositionality result which supports modular verification of complex systems.
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Cited by 14 (3 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
Bialgebraic methods in structural operational semantics
 ENTCS
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational specifications. An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various k ..."
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Cited by 5 (1 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational specifications. An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this talk, the current state of the art in the area of bialgebraic semantics is presented, and its prospects for the future are sketched. In particular, a combination of basic bialgebraic techniques with a categorical approach to modal logic is described, as an abstract approach to proving compositionality by decomposing modal logics over structural operational specifications. Keywords:
Final Report for EPSRC Grant GR/S46710/01 Topological Models for Computational Metalanguages Background and context
"... Denotational semantics seeks to provide compositional models of computation, programs and data at the right level of abstraction to be independent of languagespecific and implementation details, and domain theory provides the mathematical objects needed to construct such models. Although domain the ..."
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Denotational semantics seeks to provide compositional models of computation, programs and data at the right level of abstraction to be independent of languagespecific and implementation details, and domain theory provides the mathematical objects needed to construct such models. Although domain theory is a rich and highly developed mathematical theory, in its traditional form it fails to provide models for a number of significant computational phenomena, especially in combination. For example, although domain theory is able to model any two of: function types (as used in functional languages), probabilistic choice (as used in randomised algorithms) and computability (i.e., the requirement that programs are actually given by algorithms), it is not known how to model all three in combination. This research project undertook the study of a generalised domain theory based on widening the mathematical interpretation of the notion of “domain ” to include a broader collection of topological spaces than usually considered. (Traditional “domains ” can be viewed as topological spaces under their associated “Scott topology”.) The principal goal was to establish the main mathematical properties of the associated “topological domain theory”, and to demonstrate its ability to overcome limitations of traditional domain theory. That such a programme should be possible was suggested by the PI’s observation that “topological domains” arise naturally as a model for an abstract logicbased approach to domain theory known as “synthetic domain
GENERIC TRACE SEMANTICS VIA COINDUCTION ∗
, 2007
"... Vol. 3 (4:11) 2007, pp. 1–36 www.lmcsonline.org ..."
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Unifying Equivalences for Timed Transition Systems ∗
"... Timed transition systems are a widely studied model for realtime systems. The intention of the paper is to show how several categorical (open maps, pathbisimilarity and coalgebraic) approaches to an abstract characterization of bisimulation relate to each other and to the numerous suggested behavi ..."
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Timed transition systems are a widely studied model for realtime systems. The intention of the paper is to show how several categorical (open maps, pathbisimilarity and coalgebraic) approaches to an abstract characterization of bisimulation relate to each other and to the numerous suggested behavioral equivalences of linear time – branching time spectrum, in the setting of timed transition systems. 1