### On Compositionality, Efficiency, and Applicability of Abstraction in Probabilistic Systems

"... Abstract. A branching bisimulation for probabilistic systems that is preserved under parallel composition has been defined recently for the alternating model. We show that besides being compositional, it is decidable in polynomial time and it preserves the properties expressible in probabilistic Com ..."

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Abstract. A branching bisimulation for probabilistic systems that is preserved under parallel composition has been defined recently for the alternating model. We show that besides being compositional, it is decidable in polynomial time and it preserves the properties expressible in probabilistic Computation Tree Logic (pCTL). In the ground-complete axiomatization, only a single axiom is added to the axioms for strong bisimulation. We show that the Concurrent Alternating Bit protocol can be verified using the process algebra and a set of recursive rules. 1

### A Formalization of Linkage Analysis

, 2000

"... ólfsd óttir et al.:A F o rm alization ofLink age A n alysis ..."

### Collège doctoral Axiomatisations and Types

, 2005

"... The focus of this thesis are the theoretical foundations for reasoning about algorithms and pro-tocols for modern distributed systems. Two important features of models for these systems are probability and typed mobility: probabilities can be used to quantify unreliable or unpredictable behaviour an ..."

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The focus of this thesis are the theoretical foundations for reasoning about algorithms and pro-tocols for modern distributed systems. Two important features of models for these systems are probability and typed mobility: probabilities can be used to quantify unreliable or unpredictable behaviour and types can be used to guarantee secure behaviour in systems with a mobile struc-ture. In this thesis we develop algebraic and type-based techniques for behavioural reasoning on probabilistic and mobile processes. In the first part of the thesis we study the algebraic theory of a process calculus which combines both nondeterministic and probabilistic behaviour in the style of Segala and Lynch’s probabilistic automata. We consider various strong and weak behavioural equivalences, and we provide complete axiomatisations for finite-state processes, restricted to guarded recursion in the case of the weak equivalences. In the second part of the thesis we investigate the algebraic theory of the π-calculus under the effect of capability types, which are one of the most useful forms of types in mobile process calculi. Capability types allow one to distinguish between the capability to read from a channel, to write

### Axioms for Probability and Nondeterminism

"... This paper studies a simple calculus for finite-state processes featuring both nondeterministic and probabilistic choice. We present a domain model and an operational semantics for our calculus. The denotational model uses the probabilistic powerdomain of Jones and Plotkin, combined with a geometric ..."

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This paper studies a simple calculus for finite-state processes featuring both nondeterministic and probabilistic choice. We present a domain model and an operational semantics for our calculus. The denotational model uses the probabilistic powerdomain of Jones and Plotkin, combined with a geometrically convex variant of the Plotkin powerdomain. The operational model defines transition rules under which a process makes transitions to probability distributions over states. We prove a full abstraction result that shows two processes have the same denotation if and only if they are probabilistically bisimilar. We also show that the expected laws for probability and nondeterminism are sound and complete with respect to the denotational model.

### Abstract QAPL 2007 Probabilistic Barbed Congruence

"... This paper defines a probabilistic barbed congruence which turns out to coincide with observational equivalence in a probabilistic extension of CCS. Based on this coincidence result, we provide a sound and complete axiomatisation for the barbed congruence in a finite fragment of probabilistic CCS. ..."

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This paper defines a probabilistic barbed congruence which turns out to coincide with observational equivalence in a probabilistic extension of CCS. Based on this coincidence result, we provide a sound and complete axiomatisation for the barbed congruence in a finite fragment of probabilistic CCS.

### QAPL 2007 Probabilistic Barbed Congruence

"... Abstract This paper defines a probabilistic barbed congruence which turns out to coincide with observational equivalence in a probabilistic extension of CCS. Based on this coincidence result, we provide a sound and complete axiomatisation for the barbed congruence in a finite fragment of probabilist ..."

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Abstract This paper defines a probabilistic barbed congruence which turns out to coincide with observational equivalence in a probabilistic extension of CCS. Based on this coincidence result, we provide a sound and complete axiomatisation for the barbed congruence in a finite fragment of probabilistic CCS.

### Labelled Markov Processes as Generalised Stochastic Relations

"... Labelled Markov processes (LMPs) are labelled transition systems in which each transition has an associated probability. In this paper we present a universal LMP as the spectrum of a commutative C ∗-algebra consisting of formal linear combinations of labelled trees. This yields a simple trace-tree s ..."

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Labelled Markov processes (LMPs) are labelled transition systems in which each transition has an associated probability. In this paper we present a universal LMP as the spectrum of a commutative C ∗-algebra consisting of formal linear combinations of labelled trees. This yields a simple trace-tree semantics for LMPs that is fully abstract with respect to probabilistic bisimilarity. We also consider LMPs with distinguished entry and exit points as stateful stochastic relations. This allows us to define a category LMP, with measurable spaces as objects and LMPs as morphisms. Our main result in this context is to provide a predicate-transformer duality for

### EXPRESS 2003 Preliminary Version Axioms for Probability and Nondeterminism

"... This paper presents a domain model for a process algebra featuring both probabilistic and nondeterministic choice. The former is modelled using the probabilistic powerdomain of Jones and Plotkin, while the latter is modelled by a geometrically convex variant of the Plotkin powerdomain. The main resu ..."

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This paper presents a domain model for a process algebra featuring both probabilistic and nondeterministic choice. The former is modelled using the probabilistic powerdomain of Jones and Plotkin, while the latter is modelled by a geometrically convex variant of the Plotkin powerdomain. The main result is to show that the expected laws for probability and nondeterminism are sound and complete with respect to the model. We also present an operational semantics for the process algebra, and we show that the domain model is fully abstract with respect to probabilistic bisimilarity. 1