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We study the complexity relationship between three models of unbounded memory automata: nu-automata ($\nu$-A), Layered Memory Automata (LaMA)and History-Register Automata (HRA). These are all extensions of finite state automata with unbounded memory over infinite alphabets. We prove that the membership problem is NP-complete for all of them, while they fall into different classes for what concerns non-emptiness. The problem of non-emptiness is known to be Ackermann-complete for HRA, we prove that it is PSPACE-complete for $\nu$-A.

We study the complexity relationship between three models of unbounded memory automata: nu-automata (ν-A), Layered Memory Automata (LaMA)and History-Register Automata (HRA). These are all extensions of finite state automata with unbounded memory over infinite alphabets. We prove that the membership problem is NP-complete for all of them, while they fall into different classes for what concerns non-emptiness. The problem of non-emptiness is known to be Ackermann-complete for HRA, we prove that it is PSPACE-complete for ν-A.

Several notions of synchronizability of a message-passing system have been introduced in the literature. Roughly, a system is called synchronizable if every execution can be rescheduled so that it meets certain criteria, e.g., a channel bound. We provide a framework, based on MSO logic and (special) tree-width, that unifies existing definitions, explains their good properties, and allows one to easily derive other, more general definitions and decidability results for synchronizability., LIPIcs, Vol. 203, 32nd International Conference on Concurrency Theory (CONCUR 2021), pages 14:1-14:18

Ensuring that communication-centric systems interact according to an intended protocol is an important but difficult problem, particularly for systems with some reactive or timed components. To rise to this challenge, we study the integration of session-based concurrency and Synchronous Reactive Programming (SRP). We propose a process calculus for multiparty sessions enriched with features from SRP. In this calculus, protocol participants may broadcast messages, suspend themselves while waiting for a message, and also react to events. Our main contribution is a session type system for this calculus, which enforces session correctness in terms of communication safety and protocol fidelity, and ensures two time-related properties that we call output persistence and input timeliness. Our type system departs significantly from existing ones, specifically as it captures the notion of logical instant typical of SRP.; Assurer que les systèmes centrés sur la communication interagissent en accord avec un protocole donné est un problème important et difficile à résoudre, en particulier lorsque certains composants de ces systèmes sont réactifs ou temporisés. Pour relever ce défi, nous étudions l’intégration de primitives de la programmation réactive synchrone (PRS) dans les calculs de sessions. Nous proposons un calcul de sessions multi-parties enrichi avec des fonctionnalités typiques de la PRS. Dans ce calcul, les participants d’une session peuvent diffuser des messages, se suspendre dans l’attente de messages, et également réagir à des événements. Notre contribution principale est un système de types pour ce calcul, qui garantit deux propriétés classiques des calculs de sessions : l’absence d’erreurs de communication et la conformité au protocole. De plus, ce système de types assure deux propriétés liées au temps, que nous appelons “persistance des outputs” et “gestion sans latence des inputs”. Notre système de types se démarque de façon significative des systèmes de types de session existants, en particulier en ce qu’il rend compte de la notion d’instant logique qui est caractéristique de la PRS.

We study k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two results (both for mailbox and peer-to-peer automata): first, the reachability problem is decidable for k-synchronizable systems; second, the membership problem (whether a given system is k-synchronizable) is decidable as well. Our proofs fix several important issues in previous attempts to prove these two results for mailbox automata.

In this paper, we work on the notion of k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two results (both for mailbox and peer-to-peer automata): first, the reachability problem is decidable for k-synchronizable systems; second, the membership problem (whether a given system is k-synchronizable) is decidable as well. Our proofs fix several important issues in previous attempts to prove these two results for mailbox automata.

In this paper we show how Spiking Neural Networks can be formalised using Timed Automata Networks. Neurons are modelled as timed automata waiting for inputs on a number of different channels (synapses), for a given amount of time (the accumulation period). When this period is over, the current potential value is computed taking into account the current sum of weighted inputs, and the previous decayed potential value. If the current potential overcomes a given threshold , the automaton emits a broadcast signal over its output channel, otherwise it restarts another accumulation period. After each emission, the automaton is constrained to remain inactive for a fixed refractory period after which the potential is reset. Spiking Neural Networks can be formalised as sets of automata, one for each neuron, running in parallel and sharing channels according to the structure of the network. The inputs needed to feed networks are defined through timed automata as well: we provide a language (and its encoding into timed automata) to model patterns of spikes and pauses and a way of generating unpredictable sequences.

In this paper we present a novel approach to model Spiking Neural Networks. These networks, referred as third generation ones, add a new dimension to the second generation: the temporal axis. We propose a formalisation of Spiking Neural Networks based on Timed Automata Networks. Neurons are modelled as timed automata waiting for inputs on a number of different channels (synapses), for a given amount of time (the accumulation period). When this period is over, the current potential value is computed taking into account the current inputs and the previous decayed potential value. If the current potential overcomes a given threshold, the automaton emits a broad- cast signal over its output channel, otherwise it restarts another accumulation period. After each emission, the automaton is constrained to remain inactive for a fixed refractory period. Spiking neural networks are formalised as sets of automata, one for each neuron, running in parallel and sharing channels ac- cording to the structure of the network. The model is then validated against some properties defined via proper temporal logic formulae.

ANDy , Activity Networks with Delays, is a discrete time framework aimed at the qualitative modelling of time-dependent activities. The modular and concise syntax makes ANDy suitable for an easy and natural modelling of time-dependent biological systems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entities levels may change as a result of an activity or may decay gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and it well adapts to the modelling of toxic behaviours. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems. A small case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.

ANDy , Activity Networks with Delays, is a discrete time framework aimed at the qualitative modelling of time-dependent activities. The modular and concise syntax makes ANDy suitable for an easy and natural modelling of time-dependent biological systems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entities levels may change as a result of an activity or may decay gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and it well adapts to the modelling of toxic behaviours. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems. A small case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.

This paper presents a model of session-based concurrency with mechanisms for runtime adaptation. Thus, our model allows to specify communication-centric systems whose session behavior can be dynamically updated at runtime. We propose an event-based approach: adaptation requests, issued by the system itself or by its environment, are assimilated to events which may trigger runtime adaptation routines. Based on type-directed checks, these routines naturally enable the reconfiguration of processes with active sessions. We develop a type system that ensures communication safety and consistency properties: while the former guarantees absence of runtime communication errors, the latter ensures that update actions do not disrupt already established sessions.

This paper presents a model of session-based concurrency with constructs for runtime adaptation. Our model allows for the dynamic update of the behavior of communication-centric systems. We propose an event-based approach: adaptation requests, issued by the system or its environment, are assimilated to events which may trigger runtime adaptation routines. Based on type-directed checks, these routines naturally enable the reconfiguration of processes with active sessions. An associated type system ensures communication safety and consistency properties: while the former guarantees absence of runtime communication errors, the latter ensures that update actions do not disrupt established sessions.

International audience; A high-level Petri net framework is introduced for the toxic risk assessment in biological and bio-synthetic systems. Unlike empirical techniques mostly used in toxicology or toxicogenomics, we propose a systemic approach consisting of a series of behavioral rules (reactions) that depend on abstract discrete "expression" levels of involved agents (species). We introduce a finite state high-level Petri net model allowing exhaustive verification (model-checking) of properties related to equilibrium alteration or appearing of hazardous behaviors. The approach is applied to the study of the impact of the aspartame assimilation into the blood glucose regulation process.

International audience; In this paper we shall survey and discuss in detail the work on the relative expressiveness of recursion and replication in various process calculi. Namely, CCS, the pi-calculus, the Ambient calculus, Concurrent Constraint Programming and calculi for Cryptographic Protocols. We shall give evidence that the ability of expressing recursive behaviour via replication often depends on the scoping mechanisms of the given calculus which compensate for the restriction of replication.

We propose a formalisation of spiking neural networks based on timed automata networks. Neurons are modelled as timed automata waiting for inputs on a number of different channels (synapses), for a given amount of time (the accumulation period). When this period is over, the current potential value is computed taking into account the current inputs and the previous decayed potential value. If the current potential overcomes a given threshold, the automaton emits a broadcast signal over its output channel, otherwise it restarts another accumulation period. After each emission, the automaton is constrained to remain inactive for a fixed refractory period. Spiking neural networks are formalised as sets of automata, one for each neuron, running in parallel and sharing channels according to the structure of the network. The model is then validated against some crucial properties defined via proper temporal logic formulae.