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22
A Graphical Representation for Biological Processes in the Stochastic picalculus
 Transactions in Computational Systems Biology
, 2006
"... Abstract. This paper presents a graphical representation for the stochastic πcalculus, which is formalised by defining a corresponding graphical calculus. The graphical calculus is shown to be reduction equivalent to stochastic π, ensuring that the two calculi have the same expressive power. The gr ..."
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Cited by 37 (15 self)
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Abstract. This paper presents a graphical representation for the stochastic πcalculus, which is formalised by defining a corresponding graphical calculus. The graphical calculus is shown to be reduction equivalent to stochastic π, ensuring that the two calculi have the same expressive power. The graphical representation is used to model a couple of example biological systems, namely a bistable gene network and a mapk signalling cascade. One of the benefits of the representation is its ability to highlight the existence of cycles, which are a key feature of biological systems. Another benefit is its ability to animate interactions between system components, in order to visualise system dynamics. The graphical representation can also be used as a front end to a simulator for the stochastic πcalculus, to help make modelling and simulation of biological systems more accessible to non computer scientists. 1
Automata with group actions
 In LICS
, 2011
"... Abstract—Our motivating question is a MyhillNerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alp ..."
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Cited by 25 (7 self)
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Abstract—Our motivating question is a MyhillNerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts; nominal sets are the special case of our framework where letters can be only compared for equality. We use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality, we obtain automata equivalent in expressive power to finite memory automata, as defined by Francez and Kaminski. I.
Towards Nominal Computation
, 2012
"... Nominal sets are a different kind of set theory, with a more relaxed notion of finiteness. They offer an elegant formalism for describing λterms modulo αconversion, or automata on data words. This paper is an attempt at defining computation in nominal sets. We present a rudimentary programming lan ..."
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Cited by 16 (4 self)
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Nominal sets are a different kind of set theory, with a more relaxed notion of finiteness. They offer an elegant formalism for describing λterms modulo αconversion, or automata on data words. This paper is an attempt at defining computation in nominal sets. We present a rudimentary programming language, called Nλ. The key idea is that it includes a native type for finite sets in the nominal sense. To illustrate the power of our language, we write short programs that process automata on data words.
A graphical representation for the stochastic picalculus
 In Proceedings of Bioconcur’05
, 2005
"... Abstract. This paper presents a graphical representation for the stochastic picalculus, which builds on previous formal and informal notations. The graphical representation is used to model a Mapk signalling cascade and an evolved gene network. One of the main benefits of the representation is its ..."
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Cited by 11 (2 self)
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Abstract. This paper presents a graphical representation for the stochastic picalculus, which builds on previous formal and informal notations. The graphical representation is used to model a Mapk signalling cascade and an evolved gene network. One of the main benefits of the representation is its ability to clearly highlight the existence of cycles, which are a key aspect of many biological systems. Another advantage is its ability to animate interactions between biological system components, in order to clarify the overall system function. The paper also shows how the graphical representation can be used as a front end to a stochastic simulator for the picalculus, in order to allow the direct simulation of graphical models. This complements the existing textual interface of the simulator, with a view to making modelling and simulation of biological systems more accessible to non computer scientists. 1
Automata theory in nominal sets
, 2012
"... Abstract. We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we ..."
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Cited by 9 (4 self)
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Abstract. We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize nominal sets due to Gabbay and Pitts.
Model checking usage policies
, 2008
"... We propose a model for specifying, analysing and enforcing safe usage of resources. Our usage policies allow for parametricity over resources, and they can be enforced through finite state automata. The patterns of resource access and creation are described through a basic calculus of usages. In spi ..."
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Cited by 8 (4 self)
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We propose a model for specifying, analysing and enforcing safe usage of resources. Our usage policies allow for parametricity over resources, and they can be enforced through finite state automata. The patterns of resource access and creation are described through a basic calculus of usages. In spite of the augmented flexibility given by resource creation and by policy parametrization, we devise an efficient (polynomialtime) modelchecking technique for deciding when a usage is resourcesafe, i.e. when it complies with all the relevant usage policies.
Events, Causality and Symmetry
, 2008
"... The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences ..."
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Cited by 6 (2 self)
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The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.
Analysis of deadlocks in object groups
 In FMOODS/FORTE
, 2011
"... Abstract. Object groups are collections of objects that perform collective work. We study a calculus with object groups and develop a descriptions of method’s behaviours. 1 ..."
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Cited by 6 (3 self)
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Abstract. Object groups are collections of objects that perform collective work. We study a calculus with object groups and develop a descriptions of method’s behaviours. 1
Model Checking Quantified Computation Tree Logic
 Proceedings of the 17th International Conference on Concurrency Theory (CONCUR’06
, 2006
"... Abstract. Propositional temporal logic is not suitable for expressing properties on the evolution of dynamically allocated entities over time. In particular, it is not possible to trace such entities through computation steps, since this requires the ability to freely mix quantification and temporal ..."
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Cited by 3 (0 self)
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Abstract. Propositional temporal logic is not suitable for expressing properties on the evolution of dynamically allocated entities over time. In particular, it is not possible to trace such entities through computation steps, since this requires the ability to freely mix quantification and temporal operators. In this paper we study Quantified Computation Tree Logic (QCTL), which extends the wellknown propositional computation tree logic, PCTL, with first and (monadic) second order quantification. The semantics of QCTL is expressed on algebra automata, which are automata enriched with abstract algebras at each state, and with reallocations at each transition that express an injective renaming of the algebra elements from one state to the next. The reallocations enable minimization of the automata modulo bisimilarity, essentially through symmetry reduction. Our main result is to show that each combination of a QCTL formula and a finite algebra automaton can be transformed to an equivalent PCTL formula over an ordinary Kripke structure, while maintaining the symmetry reduction. The transformation is structurepreserving on the formulae. This gives rise to a method to lift any model checking technique for PCTL to QCTL. 1
Investigations into Algebra and Topology over Nominal Sets
, 2011
"... The last decade has seen a surge of interest in nominal sets and their applications to formal methods for programming languages. This thesis studies two subjects: algebra and duality in the nominal setting. In the first part, we study universal algebra over nominal sets. At the heart of our approach ..."
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Cited by 2 (0 self)
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The last decade has seen a surge of interest in nominal sets and their applications to formal methods for programming languages. This thesis studies two subjects: algebra and duality in the nominal setting. In the first part, we study universal algebra over nominal sets. At the heart of our approach lies the existence of an adjunction of descent type between nominal sets and a category of manysorted sets. Hence nominal sets are a full reflective subcategory of a manysorted variety. This is presented in Chapter 2. Chapter 3 introduces functors over manysorted varieties that can be presented by operations and equations. These are precisely the functors that preserve sifted colimits. They play a central role in Chapter 4, which shows how one can systematically transfer results of universal algebra from a manysorted variety to nominal sets. However, the equational logic obtained is more expressive than the nominal equational logic of Clouston and Pitts, respectively, the nominal algebra of Gabbay and Mathijssen. A uniform fragment of our logic with the same expressivity