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Nominal Unification
 Theoretical Computer Science
, 2003
"... We present a generalisation of firstorder unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #equivalent, i.e. equal up to renaming bound names. For the a ..."
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We present a generalisation of firstorder unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #equivalent, i.e. equal up to renaming bound names. For the applications we have in mind, we must consider the simple, textual form of substitution in which names occurring in terms may be captured within the scope of binders upon substitution. We are able to take a `nominal' approach to binding in which bound entities are explicitly named (rather than using nameless, de Bruijnstyle representations) and yet get a version of this form of substitution that respects #equivalence and possesses good algorithmic properties. We achieve this by adapting an existing idea and introducing a key new idea. The existing idea is terms involving explicit substitutions of names for names, except that here we only use explicit permutations (bijective substitutions). The key new idea is that the unification algorithm should solve not only equational problems, but also problems about the freshness of names for terms. There is a simple generalisation of the classical firstorder unification algorithm to this setting which retains the latter's pleasant properties: unification problems involving #equivalence and freshness are decidable; and solvable problems possess most general solutions.
Model checking for nominal calculi
 IN FOSSACS, VOLUME 3441 OF LNCS
, 2005
"... Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we f ..."
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Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we focus on HistoryDependent automata, a syntaxfree automatonbased model of mobility. HistoryDependent automata have provided the formal basis to design and implement some existing verification toolkits. We then introduce a novel syntaxfree setting to model the symbolic semantics of a nominal calculus. Our approach relies on the notions of reactive systems and observed borrowed contexts introduced by Leifer and Milner, and further developed by Sassone, Lack and Sobocinski. We argue that the symbolic semantics model based on borrowed contexts can be conveniently applied to web service discovery and binding.
Spatial Information Distribution in Constraintbased
"... Abstract. We introduce spatial and epistemic process calculi for reasoning about spatial information and knowledge distributed among the agents of a system. We introduce domaintheoretical structures to represent spatial and epistemic information. We provide operational and denotational techniques f ..."
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Cited by 2 (2 self)
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Abstract. We introduce spatial and epistemic process calculi for reasoning about spatial information and knowledge distributed among the agents of a system. We introduce domaintheoretical structures to represent spatial and epistemic information. We provide operational and denotational techniques for reasoning about the potentially infinite behaviour of spatial and epistemic processes. We also give compact representations of infinite objects that can be used by processes to simulate announcements of common knowledge and global information. Introduction. Distributed systems have changed substantially in the recent past with the advent of phenomena like social networks and cloud computing. In the previous incarnation of distributed computing [16] the emphasis was on consistency, faulttolerance, resource management and related topics; these were all characterized by interaction between processes. Research proceeded along two lines: the algorithmic side which
Namespace logic: A logic for a reflective higherorder calculus
"... Abstract. In [19] it was observed that a theory like the πcalculus, dependent on a theory of names, can be closed, through a mechanism of quoting, so that (quoted) processes provide the necessary notion of names. Here we expand on this theme by examining a construction for a HennessyMilner logic c ..."
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Abstract. In [19] it was observed that a theory like the πcalculus, dependent on a theory of names, can be closed, through a mechanism of quoting, so that (quoted) processes provide the necessary notion of names. Here we expand on this theme by examining a construction for a HennessyMilner logic corresponding to an asynchronous messagepassing calculus built on a notion of quoting. Like standard HennessyMilner logics, the logic exhibits formulae corresponding to sets of processes, but a new class of formulae, corresponding to sets of names, also emerges. This feature provides for a number of interesting possible applications from security to data manipulation. Specifically, we illustrate formulae for controlling process response on ranges of names reminiscent of a (static) constraint on port access in a firewall configuration. Likewise, we exhibit formulae in a namesasdata paradigm corresponding to validation for fragment of XML Schema. 1
This work is licensed under the Creative Commons AttributionNoncommercialNo Derivative Works License. Towards an Embedding of Graph Transformation in Intuitionistic Linear Logic
"... Linear logics have been shown to be able to embed both rewritingbased approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of doublepushout graph transformations into quantified linear logic, leading to a CurryHoward style isomorphism bet ..."
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Linear logics have been shown to be able to embed both rewritingbased approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of doublepushout graph transformations into quantified linear logic, leading to a CurryHoward style isomorphism between graphs / transformations and formulas / proof terms. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs / transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties. 1
Policybased Coordination in PAGODA:
"... PAGODA (Policy And GOal Based Distributed Autonomy) is a modular architecture for specifying and prototyping autonomous systems. A PAGODA node (agent) interacts with its environment by sensing and affecting, driven by goals to achieve and constrained by policies. A PAGODA system is a collection of P ..."
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PAGODA (Policy And GOal Based Distributed Autonomy) is a modular architecture for specifying and prototyping autonomous systems. A PAGODA node (agent) interacts with its environment by sensing and affecting, driven by goals to achieve and constrained by policies. A PAGODA system is a collection of PAGODA nodes cooperating to achieve some mutual goal. This paper describes a specification of PAGODA using the Russian Dolls model of policybased coordination. In PAGODA there are two forms of coordination: local and global. Local coordination is used to compose the components of a PAGODA node. The local coordinator is concerned with ensuring component level synchronization constraints, cross component message ordering constraints, routing of notifications, and interaction with the external world. The global coordinator is concerned with dissemination of information, negotiation of responsibilities, and synchronization of activities. Requirements for a PAGODA node coordinator are given and an example set of policies is specified. Principles for showing that the policies satisfy the requirements are discussed as a first step toward a logic of policybased coordination. Development of a distributed coordinator is the subject of ongoing work. Some challenges and possible solutions are discussed.
PERMISSIONBASED SEPARATION LOGIC FOR MESSAGEPASSING CONCURRENCY
, 2010
"... Vol. 7 (3:07) 2011, pp. 1–47 www.lmcsonline.org ..."
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September 14, 2010 0:12 WSPC/INSTRUCTION FILE jktir Knots as processes: a new kind of invariant
"... We exhibit an encoding of knots into processes in the picalculus such that knots are ambient isotopic if and only their encodings are weakly bisimilar. ..."
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We exhibit an encoding of knots into processes in the picalculus such that knots are ambient isotopic if and only their encodings are weakly bisimilar.
This work is licensed under the Creative Commons Attribution License. Choreographies with Secure Boxes and Compromised Principals
"... We equip choreographylevel session descriptions with a simple abstraction of a security infrastructure. Message components may be enclosed within (possibly nested) ”boxes ” annotated with the intended source and destination of those components. The boxes are to be implemented with cryptography. S ..."
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We equip choreographylevel session descriptions with a simple abstraction of a security infrastructure. Message components may be enclosed within (possibly nested) ”boxes ” annotated with the intended source and destination of those components. The boxes are to be implemented with cryptography. Strand spaces provide a semantics for these choreographies, in which some roles may be played by compromised principals. A skeleton is a partially ordered structure containing local behaviors (strands) executed by regular (noncompromised) principals. A skeleton is realized if it contains enough regular strands so that it could actually occur, in combination with any possible activity of compromised principals. It is delivery guaranteed (DG) realized if, in addition, every message transmitted to a regular participant is also delivered. We define a novel transition system on skeletons, in which the steps add regular strands. These steps solve tests, i.e. parts of the skeleton that could not occur without additional regular behavior. We prove three main results about the transition system. First, each minimal DG realized skeleton is reachable, using the transition system, from any skeleton it embeds. Second, if no step is possible from a skeleton A, then A is DG realized. Finally, if a DG realized A ′ is accessible from A, then A′ is minimal. Thus, the transition system provides a systematic way to construct the possible behaviors of the choreography, in the presence of compromised principals. 1