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From Bialgebraic Semantics to Congruence Formats
, 2005
"... A general and abstract framework to defining congruence formats for various process equivalences coalgebraic approach to process equivalence, based on a notion of test suite. The resulting technique is illustrated on the example of completed trace equivalence. Rather than providing formal proofs, th ..."
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Cited by 10 (4 self)
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A general and abstract framework to defining congruence formats for various process equivalences coalgebraic approach to process equivalence, based on a notion of test suite. The resulting technique is illustrated on the example of completed trace equivalence. Rather than providing formal proofs, the paper is guiding the reader through the process of deriving a congruence format in the test suite approach.
SOS formats and metatheory: 20 years after
, 2007
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical ..."
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Cited by 10 (5 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical
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 8 (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
A Hierarchy of SOS Rule Formats
, 2005
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using socalled Transition System Specifications (TS ..."
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Cited by 6 (1 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using socalled Transition System Specifications (TSS’s) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated metatheorems. Properties that are guaranteed by such rule formats range from welldefinedness of the operational semantics and compositionality of behavioral equivalences to security and probabilityrelated issues. In this paper, we provide an initial hierarchy of SOS rules formats and metatheorems formulated around them.
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:
GSOS for probabilistic transition systems (Extended Abstract)
, 2002
"... We introduce probabilistic GSOS, an operator specification format for (reactive) probabilistic transition systems which arises as an adaptation of the known GSOS format for labelled (nondeterministic) transition systems. Like the standard one, the format is well behaved in the sense that on all mode ..."
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Cited by 1 (1 self)
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We introduce probabilistic GSOS, an operator specification format for (reactive) probabilistic transition systems which arises as an adaptation of the known GSOS format for labelled (nondeterministic) transition systems. Like the standard one, the format is well behaved in the sense that on all models bisimilarity is a congruence and the uptocontext proof principle is valid. Moreover, every specification has a final model which can be shown to offer unique solutions for guarded recursive equations. The format covers operator specifications from the literature, so that the wellbehavedness results given for those arise as instances of our general one.
A Proof System for Compositional Verification of Probabilistic Concurrent Processes
"... Abstract. We present a formal proof system for compositional verification of probabilistic concurrent processes. Processes are specified using an SOSstyle process algebra with probabilistic operators. Properties are expressed using a probabilistic modal µcalculus. And the proof system is formulate ..."
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Abstract. We present a formal proof system for compositional verification of probabilistic concurrent processes. Processes are specified using an SOSstyle process algebra with probabilistic operators. Properties are expressed using a probabilistic modal µcalculus. And the proof system is formulated as a sequent calculus in which sequents are given a quantitative interpretation. A key feature is that the probabilistic scenario is handled by introducing the notion of Markov proof, according to which proof trees contain probabilistic branches and are required to satisfy a condition formulated byinterpretingthemas Markov Decision Processes. We present simple but illustrative examples demonstrating the applicability of the approach to the compositional verification of infinite state processes. Our main result is the soundness of the proof system, which is proved by applying the coupling method from probability theory to the game semantics of the probabilistic modal µcalculus. 1
A Proof System for Reasoning about Probabilistic Concurrent Processes
"... The need of formally specify and verify the behavior of increasingly complex systems is posing many new challenges, one of them being the difficulty of proving and reasoning over properties of systems that exhibit some kind of probabilistic behavior. Following [1], we consider probabilistic concurre ..."
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The need of formally specify and verify the behavior of increasingly complex systems is posing many new challenges, one of them being the difficulty of proving and reasoning over properties of systems that exhibit some kind of probabilistic behavior. Following [1], we consider probabilistic concurrent processes formalized as probabilistic transition systems given as a pair 〈P, { a}a∈L〉, where L is some set of labels, D(P) is the set of probability distributions on the set of states P, and a − → ⊆ P × D(P) is the alabeled transition relation. This definition generalizes that of standard labeled transition system. The modal µcalculus has proven to be a very expressive and yet tractable logic for expressing properties of labeled transition systems. In [2, 3] an extension of this logic to the context of probabilistic transition systems, called quantitative modal µcalculus or just qMµ, is studied and its semantics (assigning real values in [0, 1] to pairs of states and formulae) is given denotationally by means of fixed points. However understanding µcalculus (and qMµ) formulae denotationally can be very hard. In [4] the authors propose a different semantics based on Two Player Stochastic games for qMµ very similar to the, nowadays standard, Two Player game
Compositionality of Probabilistic HennessyMilner Logic through Structural Operational Semantics
"... Abstract. We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced t ..."
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Abstract. We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced to the question of whether its subterms satisfy a derived formula obtained via the operational semantics. 1