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A calculus of mobile processes, I
, 1992
"... We present the acalculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The ..."
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Cited by 1184 (31 self)
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We present the acalculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen, who added mobility to CCS while preserving its algebraic properties. The rrcalculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links. After an illustrated description of how the ncalculus generalises conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the ncalculus of higherorder functions (the Icalculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence indexed by distinctionsi.e., assumptions of inequality among names. These theories are based upon a semantics in terms of a labeled transition system and a notion of strong bisimulation, both of which are expounded in detail in a companion paper. We also report briefly on workinprogress based upon the corresponding notion of weak bisimulation, in which internal actions cannot be observed.
Computation in Networks of Passively Mobile FiniteState Sensors
 Distributed Computing
, 2004
"... We explore the computational power of networks of small resourcelimited mobile agents. We define two new models of computation based on pairwise interactions of finitestate agents in populations of finite but unbounded size. With a fairness condition on interactions, we define the concept of stabl ..."
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Cited by 116 (14 self)
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We explore the computational power of networks of small resourcelimited mobile agents. We define two new models of computation based on pairwise interactions of finitestate agents in populations of finite but unbounded size. With a fairness condition on interactions, we define the concept of stable computation of a function or predicate, and give protocols that stably compute functions in a class including Boolean combinations of thresholdk, parity, majority, and simple arithmetic. We prove that all stably computable predicates are in NL. With uniform random sampling of pairs to interact, we define the model of conjugating automata and show that any counter machine with O(1) counters of capacity O(n) can be simulated with high probability by a protocol in a population of size n. We prove that all predicates computable with high probability in this model are in P #RL.
Bigraphs and Mobile Processes (revised)
, 2004
"... A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and comm ..."
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Cited by 66 (7 self)
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A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In Part I we illustrate...
Pure bigraphs: structure and dynamics
, 2005
"... Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a c ..."
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Cited by 62 (5 self)
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Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a constituent of bigraphs, this paper is a devoted to pure bigraphs, which in turn underlie various more refined forms. Elsewhere it is shown that behavioural analysis for Petri nets, πcalculus and mobile ambients can all be recovered in the uniform framework of bigraphs. The paper first develops the dynamic theory of an abstract structure, a wide reactive system (Wrs), of which a Brs is an instance. In this context, labelled transitions are defined in such a way that the induced bisimilarity is a congruence. This work is then specialised to Brss, whose graphical structure allows many refinements of the theory. The latter part of the paper emphasizes bigraphical theory that is relevant to the treatment of dynamics via labelled transitions. As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in detail. The paper also mentions briefly the use of bigraphs to model pervasive computing and
ADHESIVE AND QUASIADHESIVE CATEGORIES
 THEORETICAL INFORMATICS AND APPLICATIONS
, 1999
"... We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be ex ..."
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Cited by 55 (3 self)
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We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Doublepushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
Axioms For Bigraphical Structure
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2005
"... This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #calculus, mobile ambients and Petri nets, in a way th ..."
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Cited by 41 (8 self)
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This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #calculus, mobile ambients and Petri nets, in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a wellbehaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as the paper demonstrates; this is because bigraphs treat locality and connectivity orthogonally
Stably Computable Properties of Network Graphs
 DISTRIBUTED COMPUTING IN SENSOR SYSTEMS: FIRST IEEE INTERNATIONAL CONFERENCE, DCOSS 2005, MARINA DEL REY, CA, USA, JUNE/JULY, 2005, PROCEEDINGS, VOLUME 3560 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... We consider a scenario in which anonymous, finitestate sensing devices are deployed in an adhoc communication network of arbitrary size and unknown topology, and explore what properties of the network graph can be stably computed by the devices. We show that they can detect whether the network ..."
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Cited by 37 (10 self)
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We consider a scenario in which anonymous, finitestate sensing devices are deployed in an adhoc communication network of arbitrary size and unknown topology, and explore what properties of the network graph can be stably computed by the devices. We show that they can detect whether the network has degree bounded by a constant d, and, if so, organize a computation that achieves asymptotically optimal linear memory use. We define a model of stabilizing inputs to such devices and show that a large class of predicates of the multiset of final input values are stably computable in any weaklyconnected network. We also show
Transition systems, link graphs and Petri nets
, 2004
"... A framework is defined within which reactive systems can be studied formally. The framework is based upon scategories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavi ..."
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Cited by 29 (5 self)
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A framework is defined within which reactive systems can be studied formally. The framework is based upon scategories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavioural preorders and equivalences, such as the failures preorder (treated elsewhere) and bisimilarity, which are guaranteed to be congruential. The theory rests upon the notion of relative pushout previously introduced by the authors. The framework
Deriving bisimulation congruences: 2categories vs. precategories
 In FOSSACS ’03, volume 2620 of LNCS
, 2003
"... Grelative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis tow ..."
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Cited by 24 (7 self)
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Grelative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis towards a comprehensive solution. As an example, we construct GRPOs in a category of ‘bunches and wirings. ’ We then examine the approach based on Milner’s precategories and Leifer’s functorial reactive systems, and show that it can be recast in a much simpler way into the 2categorical theory of GRPOs.
Urn Automata
, 2003
"... Urn automata are a new class of automata consisting of an input tape, a finitestate controller, and an urn containing tokens with a finite set of colors, where the finitestate controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the comput ..."
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Cited by 16 (9 self)
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Urn automata are a new class of automata consisting of an input tape, a finitestate controller, and an urn containing tokens with a finite set of colors, where the finitestate controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the computational power of urn automata, showing that an urn automaton with O(f(n)) tokens can, with high probability, simulate a probabilistic Turing machine using O(log f(n)) space and vice versa, as well as giving several technical results showing that the computational power of urn automata is not a#ected by variations in parameters such as the size of the state space, the number of tokens sampled per step, and so forth. Motivated by problems in distributed computing, we consider a special class of urn automata called pairing automata that model systems of finitestate machines that interact through random pairwise encounters.