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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
Trace Semantics for Coalgebras
, 2003
"... Traditionally, traces are the sequences of labels associated with paths in transition systems X # P(A X). ..."
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Cited by 21 (7 self)
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Traditionally, traces are the sequences of labels associated with paths in transition systems X # P(A X).
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 13 (9 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.
Generic trace theory
 International Workshop on Coalgebraic Methods in Computer Science (CMCS 2006), volume 164 of Elect. Notes in Theor. Comp. Sci
, 2006
"... Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms ..."
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Cited by 10 (5 self)
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Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms of “trace semantics” are instances of a single categorical construction, namely coinduction in a Kleisli category. This claim is based on our main technical result that an initial algebra in
Combining a Monad and a Comonad
"... We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2category, givi ..."
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Cited by 2 (0 self)
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We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2category, giving accounts of the EilenbergMoore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2categorical denitions necessary to support this analysis. This work is supported by EPSRC grants GR/J84205: Frameworks for programming language semantics and logic and GR/M56333: The structure of programming languages : syntax and semantics, and British Council grant 747 FCS R34807: Data and program renement using algebraic structure. y The author acknowledges the support of STA through COE budget for Global Information Processing Project. 1 1 Introduction In recent years, th...
Towards Bialgebraic Semantics for CSP
, 2010
"... This paper extends bialgebraic semantics [1, 2] to take into account notions of behaviour that lead to process equivalences coarser than bisimulation. For that purpose, the requirement of finality for the characterisation of behaviours is relaxed to quasifinality, which informally consists in releg ..."
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Cited by 1 (1 self)
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This paper extends bialgebraic semantics [1, 2] to take into account notions of behaviour that lead to process equivalences coarser than bisimulation. For that purpose, the requirement of finality for the characterisation of behaviours is relaxed to quasifinality, which informally consists in relegating to the underlying category the conditions that finality must satisfy in the main category of coalgebras. This setting is then applied to the failure semantics of CSP.
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
A Coalgebraic Perspective on Minimization and Determinization ⋆
"... Abstract. Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we ..."
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Abstract. Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we show that for coalgebras in categories equipped with factorization structures, there exists an abstract procedure for equivalence checking. Then, we consider coalgebras in categories without suitable factorization structures: under certain conditions, it is possible to apply the above procedure after transforming coalgebras with reflections. This transformation can be thought of as some kind of determinization. We will apply our theory to the following examples: conditional transition systems and (nondeterministic) automata. 1
Towards Bialgebraic Semantics for the Linear Time – Branching Time Spectrum
, 2012
"... Process algebra, e.g. CSP, offers different semantical observations (e.g. traces, failures, divergences) on a single syntactical system description. These observations are either computed algebraically from the process syntax, or “extracted ” from a single operational model. Bialgebras capture both ..."
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Process algebra, e.g. CSP, offers different semantical observations (e.g. traces, failures, divergences) on a single syntactical system description. These observations are either computed algebraically from the process syntax, or “extracted ” from a single operational model. Bialgebras capture both approaches in one framework and characterize their equivalence; however, due to use of finality, lack the capability to simultaneously cater for various semantics. We suggest to relax finality to quasifinality. This allows for several semantics, which also can be coarser than bisimulation. As a case study, we show that our approach works out in the case of the CSP failures model.