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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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Cited by 17 (6 self)
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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
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:
Structural Operational Semantics and Modal Logic, Revisited
"... A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal l ..."
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Cited by 3 (1 self)
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A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal logic as a study of coalgebras in slice categories of adjunctions. Secondly, a more concrete understanding of the assumptions of the theorem is provided, where proving compositionality amounts to finding a syntactic distributive law between two collections of predicate liftings. Keywords: structural operational semantics, modal logic, coalgebra 1
Pointwise Extensions of GSOSDefined Operations
"... Distributive laws of syntax over behaviour (cf. [1, 3]) are, among other things, a wellstructured way of defining algebraic operations on final coalgebras. For a simple example, consider the set B ω of infinite streams of elements of B; this carries a final coalgebra w = 〈hd,tl〉: B ω → B × B ω for ..."
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Cited by 2 (2 self)
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Distributive laws of syntax over behaviour (cf. [1, 3]) are, among other things, a wellstructured way of defining algebraic operations on final coalgebras. For a simple example, consider the set B ω of infinite streams of elements of B; this carries a final coalgebra w = 〈hd,tl〉: B ω → B × B ω for the endofunctor F = B × − on Set. If B comes with a binary operation +, one can define an addition operation ⊕ on streams coinductively: hd(σ ⊕ τ) = hd(σ) + hd(τ) tl(σ ⊕ τ) = tl(σ) ⊕ tl(τ). It is easy to see that these equations define a distributive law, i.e., a natural transformation λ: ΣF ⇒ FΣ, where ΣX = X 2 is the signature endofunctor corresponding to a single binary operation. The operation ⊕: B ω × B ω → B ω is now defined as the unique morphism to the final coalgebra as in: ΣB ω B ω
Ministry of University and Research project SisteR (PRIN 20088HXMYN).
, 2011
"... Abstract Name passing calculi are nowadays one of the preferred formalisms for the specification of concurrent and distributed systems with a dynamically evolving topology. Despite their widespread adoption as a theoretical tool, though, they still face some unresolved semantic issues, since the sta ..."
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Abstract Name passing calculi are nowadays one of the preferred formalisms for the specification of concurrent and distributed systems with a dynamically evolving topology. Despite their widespread adoption as a theoretical tool, though, they still face some unresolved semantic issues, since the standard operational, denotational and logical methods often proved inadequate to reason about these formalisms. A domain which has been successfully employed for languages with asymmetric communication, like the πcalculus, are presheaf categories based on (injective) relabellings, such as Set I.Calculiwithsymmetric binding, in the spirit of the fusion calculus, give rise to novel research challenges. In this work we examine the explicit fusion This work was carried out during the first author’s tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. The third author has been supported by the Comunidad de Madrid program ProMeSaS (S0505/TIC/0407) and by the Netherlands Organization for Scientific
Unified Categorical Models for Three Typical Resource Allocation Problems ⋆
"... This paper concerns formalization of resource allocation using category theory, rather than a new algorithm to solve these problems. The unified and efficient categorical models for three specific resource allocation problemsincluding dinning philosophers problem, drinking philosophers problem and ..."
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This paper concerns formalization of resource allocation using category theory, rather than a new algorithm to solve these problems. The unified and efficient categorical models for three specific resource allocation problemsincluding dinning philosophers problem, drinking philosophers problem and committee coordination problem is originally presented based on ChandyMisra’s acyclic precedence graph strategy and our previous experience in defining the categorical semantics for distributed dinning philosophers problem. Four categories (including Dinners Category, Drinkers Category, Committees Category and Functors Category) defined in our paper not only facilitate to formalize usual concepts (such as task, resource, precedence) of resource allocation problems, but also give good directions to reason the relationships between these three typical problems. Finally, we formally proof some properties of symmetry, safety (nondeadlock), liveness (nonstarvation) and concurrency, which all satisfied in our models.