A significant part of today's Internet traffic is generated by peer-to-peer ( P2P) applications, used originally for file sharing, and more recently for real-time multimedia communications and live media streaming.

Distributed hash tables ( DHTs) or “structured overlay networks” have gained momentum in the last few years as the breaking technology to implement scalable, robust and efficient Internet applications. DHTs provide a lookup service similar to a hash table: (key, value) pairs are stored in the DHT, and any participating node can efficiently retrieve the value associated with a given key. The responsibility for maintaining the mapping from names to values is distributed among the nodes, in such a way that a change in the set of participants causes a minimal amount of disruption. This allows DHTs to scale to extremely large numbers of nodes and to handle continual node arrivals, departures, and failures.

Chord is one of the simplest protocols addressing key lookup in a distributed hash table: the only operation that Chord supports is that given a key it route onto a node which is supposed to host the entry (key,value). Chord adapts efficiently as nodes join and leave the system. Theoretical analysis and simulations showed that the Chord protocol scales up logarithmically with the number of nodes. In Chord, every node can join and leave the system without any peer negotiation, even though this feature can be implemented at the application layer. Chord uses consistent hashing in order to map keys and nodes' addresses, hosting the distributed table, to the same logical address space. All the peers use a unique hash function, which is the only way to map physical addresses and keys to a single logical address space. Peers can join the Chord just by sending a message to any node belonging to the Chord overlay. No reputation mechanism is required to accept, reject, or reward peers that are more reliable or more virtuous than others. Merging two Chord rings together is a costly operation because of the induced message complexity and the substantial time the distributed finger tables need to stabilize. Both of the rings need to know their relative hash functions and have to decide which ring will absorb the other, the latter point being critical because of the politics and security reliance. We propose to connect smaller Chord networks in an unstructured way via special nodes playing the role of neural synapses.

Schematically, the main features of Babelchord are:

Routing over SW/HW-Barriers.Namely, the ability to route queries through different, unrelated, DHTs (possibly separated by firewalls) by “crossing floors”. A peer “on the border” of a firewall can bridge two overlays (having two different hash functions) that were not meant to communicate with each other unless one wants to merge one floor into the other (operation with a complexity linear in the number of nodes). The possibility to implement strong or weak security requirements makes Babelchord suitable for employment in Internet applications where software or social barriers are an important issue to deal with.

Social-based.Every peer has data structures recording peers and floors which are more “attractive” than others. A “hot” node is a node which is stable (alive) and which is responsible for managing a large number of (keys-values) in all hosted DHTs. A “hot” floor is a floor responsible for a high number of successful lookups. Following a personal “good deal” strategy, a peer can decide to invite a hot node on a given floor it belongs to, or to join a hot floor, or even create from scratch a new floor (and then invite some hot nodes), or accept/decline an invitation to join a hot floor. This social-behavior makes the Babelchord network topology to change dynamically. As observed in other P2Pprotocols, like Bittorrent, peers with similar characteristics are more willing to group together on a private floor and thus will eventually improve their overall communications quality. Finally, the “good deal” strategy is geared up to be further enhanced with a reputation-system for nodes and floors.

Neural-inspired.Since every floor has a proper hash function, a Babelchord network can be thought of as a sort of meta overlay networkor meta-DHT, where inter-floor connections take place via crossroad nodes, a sort of neural synapses, without sharing a global knowledge of the hash functions and without a time consuming floor merging. The more synapses you have, the higher the possibility of having successful routing is.

Because of the aforementioned original features, the following are examples of applications for which Babelchord can provide good groundwork (in addition, of course, to all genuine Chord-based applications, like cooperative mirroring, time-shared storage, distributed indexes and large-scale combinatorial search).

Anti Internet censorship applications.Internet censorship is the control or the suppression of the publishing or accessing information on the Internet. Many applications and networks have been recently developed in order to bypass the censorship: among the many we recall Psiphon ( http:// psiphon. ca), Tor ( http:// www. torproject. org), and many others. Babelchord can support such applications by taking advantage of intra-floor routing in order to bypass software barriers.

Fully Distributed social-networks applications.Social-networks are emerging as one of the Web 2.0 applications. Famous social networks, such as Facebook or LinkedIn are based on a client-server architecture; very often those sites are down for maintenance. Babelchord could represent a scalable and reliable alternative to decentralize key search and data storage.

Large-scale brain model and simulations.(Via a distributed, neural-based, network.) As well explained by R.D. DeGroot (Project founded by KNAW, Netherlands), supercomputers exist now with raw computational powers exceeding that of a human brain. Technological and production advances will soon place such computing power within the hands of cognitive and medical neuroscience research groups. For the first time it will be possible to execute brain-scale simulations of cognitive and pharmacological processes over millions and then billions of neurons - even at the biological model level. Babelchord could help modeling as a meta-overlay network for the human brain.

We investigate Synapse , a scalable protocol for information retrieval over the inter-connection of heterogeneous overlay networks. Applications of top of Synapse see those intra-overlay networks as a unique inter-overlay network.

Scalability in Synapse is achieved via co-located nodes, i. e. nodes that are part of multiple overlay networks at the same time. Co-located nodes, playing the role of neural synapsesand connected to several overlay networks, give a larger search area and provide alternative routing.

Synapse can either work with “open” overlays adapting their protocol to synapse interconnection requirements, or with “closed” overlays that will not accept any change to their protocol. Built-in primitives to deal with social networking give an incentive for nodes cooperation. Results from simulation and experiments show that Synapse is scalable, with a communication and state overhead scaling similarly as the networks interconnected. thanks to alternate routing paths, Synapse also gives a practical solution to network partitions. We precisely capture the behavior of traditional metrics of overlay networks within Synapse and present results from simulations as well as some actual experiments of a client prototype on the Grid'5000 platform. The prototype developed implements the Synapse protocol in the particular case of the inter-connection of many Chord overlay networks.

The inter-connection of overlay networks has been recently identified as a promising model to cope with today's Internet issues such as scalability, resource discovery, failure recovery or routing efficiency, in particular in the context of information retrieval. Some recent researches have focused on the design of mechanisms for building bridges between heterogeneous overlay networks for the purpose of improving cooperation between networks that have different routing mechanisms, logical topologies and maintenance policies. However, more comprehensive approaches of such inter-connections for information retrieval and both quantitative and experimental studies of its key metrics, such as satisfaction rate or routing length, are still missing.

Many disparate overlay networks may not only simultaneously co-exist in the Internet but also compete for the same resources on shared nodes and underlying network links. One of the problems of the overlay networking area is how heterogeneous overlay networks may interactand cooperatewith each other. Overlay networks are heterogeneous and basically unable to cooperate each other in an effortless way, without merging, an operation which is very costly since it not scalable and not suitable in many cases for security reasons. However, in many situations, distinct overlay networks could take advantage of cooperating for many purposes: collective performance enhancement, larger shared information, better resistance to loss of connectivity (network partitions), improved routing performance in terms of delay, throughput and packets loss, by, for instance, cooperative forwarding of flows.

As a basic example, let us consider two distant databases. One node of the first database stores one ( k e y, v a l u e)pair which is searched by a node of the second one. Without network cooperation those two nodes will never communicate together. As another example, we have an overlay network where a number of nodes got isolated by an overlay network failure, leading to a partition: if some or all of those nodes can be reached via an alternative overlay network, than the partition “could” be recovered via an alternative routing.

In the context of large scale information retrieval, several overlays may want to offer an aggregation of their information/data to their potential common users without losing control of it. Imagine two companies wishing to share or aggregate information contained in their distributed databases, obviously while keeping their proprietary routing and their exclusive right to update it. Finally, in terms of fault-tolerance, cooperation can increase the availability of the system, if one overlay becomes unavailable the global network will only undergo partial failure as other distinct resources will be usable.

We consider the tradeoff of having one vs.many overlays as a conflict without a cause: having a single global overlay has many obvious advantages and is the de factomost natural solution, but it appears unrealistic in the actual setting. In some optimistic case, different overlays are suitable for collaboration by opening their proprietary protocols in order to build an open standard; in many other pessimistic cases, this opening is simply unrealistic for many different reasons (backward compatibility, security, commercial, practical, etc.). As such, studying protocols to interconnect collaborative (or competitive) overlay networks is an interesting research vein.

The main contribution of thisresearch vein is to introduce, simulate and experiment with Synapse, a scalable protocol for information retrieval over the inter-connection of heterogeneous overlay networks. The protocol is based on co-located nodes, also called synapses, serving as low-cost natural candidates for inter-overlay bridges. In the simplest case (where overlays to be interconnected are ready to adapt their protocols to the requirements of interconnection), every message received by a co-located node can be forwarded to other overlays the node belongs to. In other words, upon receipt of a search query, in addition to its forwarding to the next hop in the current overlay (according to their routing policy), the node can possibly start a new search, according to some given strategy, in some or all other overlay networks it belongs to. This obviously implies to providing a Time-To-Live value and detection of already processed queries, to avoid infinite loop in the network, as in unstructured peer-to-peer systems.

We also study interconnection policies as the explicit possibility to rely on socialbased strategies to build these bridges between distinct overlays; nodes can invite or can be invited.

In case of concurrent overlay networks, inter-overlay routing becomes harder, as intra-overlays are provided as some black boxes: a controloverlay-network made of co-located nodes maps one hashed key from one overlay into the original key that, in turn, will be hashed and routed in other overlays in which the co-located node belongs to. This extra structure is unavoidable to route queries along closed overlays and to prevent routing loops.

Our experiments and simulations show that a small number of well-connected synapses is sufficient in order to achieve almost exhaustive searches in a “synapsed” network of structured overlay networks. We believe that Synapse can give an answer to circumventing network partitions; the key points being that: ( i)several logical links for one node leads to as many alternative physical routes through these overlay, and ( i i)a synapse can retrieve keys from overlays that it doesn't even know simply by forwarding their query to another synapse that, in turn, is better connected. Those features are achieved in Synapse at the cost of some additional data structures and in an orthogonal way to ordinary techniques of caching and replication. Moreover, being a synapse can allow for the retrieval of extra information from many other overlays even if we are not connected with.

We have begun a formal specification associated to a PiNetimplementation, of a DHT(Distributed Hash Table) oriented network. The specification is done via a relation on network states (small step semantics). A network state is the set of all individuals network nodes states. A node state consists of a, possibly sorted, set of neighbors, i. e. the nodes known by a specific node, a local memory and a queue of messages received by the node to be executed. The semantics describe the behavior of incoming messages in each nodes. The specificity of the formalized DHTare:

( i)as in Chord, the path found between any two nodes of the network has a length which is in , where nis the number of nodes of the network; ( i i)the graph induced by the neighbors is symmetric, i. e. if a node acan communicate with a node b, then bcan communicate with a. This fact is generally ensured by the transport layer ( TCP, UDP...) and thus the associated improvement (path lengths are divided by two) comes at a low price; ( i i i)the dynamic nature of such network, i. e. the fact that nodes can join and leave the network, requires to readjust the neighbors of some nodes. This readjustment is called stabilization. In contrast to Chord, where stabilization is done via a periodic background process which is hard to tune, our stabilization is done during the routing of messages and thus 1) does not make any administrative charge when the network is sleeping 2) uses only few words in already existing packets and so has a very limited impact to the average network latency.

Following a formal general specification of such networks, we have developed a java simulator, coupled to a real implementation intended to catch the exact precise behavior of several topologies used in P2P systems.

The Distributed Lexicographic Placement (DLP)-Table is a P2Papproach for the service discovery within large scale grids. It relies on a prefix tree structured overlay network. It provides load balancing, efficient mapping of nodes of the tree onto processors of the network and fault-tolerance mechanisms, formally proved to be self-stabilizing, i. e. converging to a correct topology in a finite time starting from an arbitrary topology and memory state. It has been initially developed within the INRIA GRAAL project team.

In collaboration with Eddy Caron, Frédéric Desprez and Franck Petit of GRAAL, we have written a chapter to appear in the future book entitled “Handbook of Research on P2P and Grid Systems for Service-Oriented Computing: Models, Methodologies and Applications” and published by IGI Global  . This chapter gives a more popularizingview of the system and its features.

A journal paper about the stabilizing part of this architecture has been accepted for publication in Parallel Processing Letters  .

We studied an explicitly typed lambda calculus “à la Church” based on the union and intersection types discipline; this system is the counterpart of the standard type assignment calculus “à la Curry.” Our typed calculus enjoys Subject Reduction and confluence, and typed terms are strongly normalizing when the universal type is omitted. Moreover, both type checking and type reconstruction are decidable. In contrast to other typed calculi, a system with union types will fail to be “coherent” in the sense of Tannen, Coquand, Gunter, and Scedrov: different proofs of the same typing judgement will not necessarily have the same meaning. In response, we introduce a decidable notion of equality on type-assignment derivations inspired by the equational theory of bicartesian-closed categories .

We address the problem of designing a -calculus à laChurch corresponding to Curry-style type assignment to an untyped -calculus with intersection and union types. In particular, we define a typed language such that its relationship with the intersection-union type assignment system fulfills the following desiderata: (i) typed and type assignment derivations are isomorphic, i. e., the application of an erasing functionon all typed terms and contexts (in a typed derivation judgment) produces a derivable type assignment derivation with the same structure, and every type assignment derivation is obtained from a typed one with the same structure by applying the same erasure; (ii) type checking and type reconstruction are decidable; (iii) reduction on typed terms has the same fundamental nice properties of reduction on terms receiving a type in the type-assignment system, namely confluence, preservation of typing under reduction, and strong normalization of terms typable without the universal type .

The main goal of this research vein is the design and prototype implementation of logical frameworks in which it would be possible to smoothly encode various probabilistic logics, and other logics considered in general to be exotic, such as Modal, Program, Linear or Relevance logics. It may also involve the formalization and possible creation of a certified SAT checker for one or more probabilistic logics within the proof assistant Coq.

The theoretical background behind this involves:

At this point, formalization of one of the probabilistic logics, namely LPP₂, in the proof assistant Coq, is well under way. In this probabilistic logic, one can make statements of the form "the probability of A is at least s", where Ais a classical formula, and sis a rational number from the interval [0, 1], but with formulas themselves still remaining either true or false. The syntax, the semantics, and a complete axiomatization with appropriate inference rules have been encoded in Coq, and the soundness of the system (the validity of axioms with respect to the semantics and the preservation of validity by the inference rules) has been proven formally. The formal proof of completeness and an analysis of possible formalization of a SAT checker for this logic are in progress, and we expect sufficient progress for appropriate publication in the first half of 2010.