arXiv subjects

Marino Miculan

Publications and source records attributed to Marino Miculan.

At least 19 recordsLinked to original sources

arXiv2025

On The Axioms Of $\mathcal{M},\mathcal{N}$-Adhesive Categories

Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if regular monos are adhesive, then the existence of a regular join for any pair of regular subobjects entails quasiadhesivity. It is also known (quasi)adhesive categories can be embedded in a Grothendieck topos via a functor preserving pullbacks and pushouts along (regular) monomorphisms. In this paper we extend these results to $\mathcal{M}, \mathcal{N}$-adhesive categories, a concept recently introduced to generalize the notion of (quasi)adhesivity. We introduce the notion of $\mathcal{N}$-adhesive morphism, which allows us to express $\mathcal{M}, \mathcal{N}$-adhesivity as a condition on the subobjects' posets. Moreover, $\mathcal{N}$-adhesive morphisms allows us to show how an $\mathcal{M},\mathcal{N}$-adhesive category can be embedded into a Grothendieck topos, preserving pullbacks and $\mathcal{M}, \mathcal{N}$-pushouts.

cs.LO↗

arXiv2022

A new criterion for $\mathcal{M}, \mathcal{N}$-adhesivity, with an application to hierarchical graphs

Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes far from immediate. In this paper we present a new criterion giving a sufficient condition for $\mathcal{M}, \mathcal{N}$-adhesivity, a generalisation of the original notion of adhesivity. We apply it to several existing categories, and in particular to hierarchical graphs, a formalism that is notoriously difficult to fit in the mould of algebraic approaches to rewriting and for which various alternative definitions float around.

cs.LO↗

arXiv2021

Fuzzy Algebraic Theories

In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics for this calculus and show that there is a notion of free model for any theory in this system, allowing us (with some restrictions) to recover models as Eilenberg-Moore algebras for some monad. We will also prove a completeness result: a formula is derivable from a given theory if and only if it is satisfied by all models of the theory. Finally, leveraging results by Milius and Urbat, we give HSP-like characterizations of subcategories of algebras which are categories of models of particular kinds of theories.

cs.LO↗

arXiv2021

Automated Symbolic Verification of Telegram's MTProto 2.0

MTProto 2.0 is a suite of cryptographic protocols for instant messaging at the core of the popular Telegram messenger application. In this paper we analyse MTProto 2.0 using the symbolic verifier ProVerif. We provide fully automated proofs of the soundness of MTProto 2.0's authentication, normal chat, end-to-end encrypted chat, and rekeying mechanisms with respect to several security properties, including authentication, integrity, secrecy and perfect forward secrecy; at the same time, we discover that the rekeying protocol is vulnerable to an unknown key-share (UKS) attack. We proceed in an incremental way: each protocol is examined in isolation, relying only on the guarantees provided by the previous ones and the robustness of the basic cryptographic primitives. Our research proves the formal correctness of MTProto 2.0 w.r.t. most relevant security properties, and it can serve as a reference for implementation and analysis of clients and servers.

cs.CR↗

arXiv2020

Closure hyperdoctrines, with paths

(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an abstract theoretical framework for the systematic investigation of the logical aspects of closure spaces. To this end, we introduce the notion of closure (hyper)doctrines, i.e. doctrines endowed with inflationary operators (and subject to suitable conditions). The generality and effectiveness of this concept is witnessed by many examples arising naturally from topological spaces, fuzzy sets, algebraic structures, coalgebras, and covering at once also known cases such as Kripke frames and probabilistic frames (i.e., Markov chains). Then, we show how spatial logical constructs concerning surroundedness and reachability can be interpreted by endowing hyperdoctrines with a general notion of paths. By leveraging general categorical constructions, we provide axiomatisations and sound and complete semantics for various fragments of logics for closure operators. Therefore, closure hyperdoctrines are useful both for refining and improving the theory of existing spatial logics, but especially for the definition of new spatial logics for new applications.

cs.LO↗

arXiv2020

Software Transactional Memory with Interactions

Software Transactional memory (STM) is an emerging abstraction for concurrent programming alternative to lock-based synchronizations. Most STM models admit only isolated transactions, which are not adequate in multithreaded programming where transactions need to interact via shared data before committing. To overcome this limitation, in this paper we present Open Transactional Memory (OTM), a programming abstraction supporting safe, data-driven interactions between composable memory transactions. This is achieved by relaxing isolation between transactions, still ensuring atomicity. This model allows for loosely-coupled interactions since transaction merging is driven only by accesses to shared data, with no need to specify participants beforehand.

cs.PL↗

arXiv2020

A CSP implementation of the directed bigraph embedding problem

Directed bigraphs are a meta-model which generalises Milner's bigraphs by taking into account the request flow between controls and names. A key problem about these bigraphs is that of bigraph embedding, i.e., finding the embeddings of a bigraph inside a larger one.We present an algorithm for computing embeddings of directed bigraphs, via a reduction to a constraint satisfaction problem. We prove soundness and completeness of this algorithm, and provide an implementation in jLibBig, a general Java library for manipulating bigraphical reactive systems, together with some experimental results.

cs.LO↗

arXiv2019

Towards a Formal Model for Composable Container Systems

In modern cloud-based architectures, containers play a central role: they provide powerful isolation mechanisms such that developers can focus on the logic and dependencies of applications while system administrators can focus on deployment and management issue. In this work, we propose a formal model for container-based systems, using the framework of Bigraphical Reactive Systems (BRSs). We first introduce local directed bigraphs, a graph-based formalism which allows us to deal with localized resources. Then, we define a signature for modelling containers and provide some examples of bigraphs modelling containers. These graphs can be analysed and manipulated using techniques from graph theory: properties about containers can be formalized as properties of the corresponding bigraphic representations. Moreover, it turns out that the composition of containers as performed by e.g. docker-compose, corresponds precisely to the composition of the corresponding bigraphs inside an ``environment bigraph'' which in turn is obtained directly from the YAML file used to define the composition of containers.

cs.LO↗

arXiv2019

A CSP implementation of the bigraph embedding problem

A crucial problem for many results and tools about bigraphs and bigraphical reactive systems is bigraph embedding. An embedding is more informative than a bigraph matching, since it keeps track of the correspondence between the various components of the redex (guest) within the agent (host). In this paper, we present an algorithm for computing embeddings based on a reduction to a constraint satisfaction problem. This algorithm, that we prove to be sound and complete, has been successfully implemented in LibBig, a library for manipulating bigraphical reactive systems. This library can be used for implementing a wide range of tools, and it can be adapted to various extensions of bigraphs.

cs.LO↗

arXiv2017

Loose Graph Simulations

We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly also problems which are "mixed" instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give the representation of a problem which extends both SGI and RLPM. Finally, we identify a subclass of the LGS problem that is polynomial.

cs.LO↗

arXiv2017

Reductions for Transition Systems at Work: Deriving a Logical Characterization of Quantitative Bisimulation

Weighted labelled transition systems (WLTSs) are an established meta-model aiming to provide general results and tools for a wide range of systems such as non-deterministic, stochastic, and probabilistic systems. In order to encompass processes combining several quantitative aspects, extensions of the WLTS framework have been further proposed, state-to-function transition systems (FuTSs) and uniform labelled transition systems (ULTraSs) being two prominent examples. In this paper we show that this hierarchy of meta-models collapses when studied under the lens of bisimulation-coherent encodings. Taking advantage of these reductions, we derive a fully abstract Hennessy-Milner-style logic for FuTSs, i.e., which characterizes quantitative bisimilarity, from a fully-abstract logic for WLTSs.

cs.LO↗

arXiv2016

Deciding Hedged Bisimilarity

The spi-calculus is a formal model for the design and analysis of cryptographic protocols: many security properties, such as authentication and strong confidentiality, can be reduced to the verification of behavioural equivalences between spi processes. In this paper we provide an algorithm for deciding hedged bisimilarity on finite processes, which is equivalent to barbed equivalence (and coarser than framed bisimilarity). This algorithm works with any term equivalence satisfying a simple set of conditions, thus encompassing many different encryption schemata.

cs.CR↗

arXiv2016

Disjunctive Probabilistic Modal Logic is Enough for Bisimilarity on Reactive Probabilistic Systems

Larsen and Skou characterized probabilistic bisimilarity over reactive probabilistic systems with a logic including true, negation, conjunction, and a diamond modality decorated with a probabilistic lower bound. Later on, Desharnais, Edalat, and Panangaden showed that negation is not necessary to characterize the same equivalence. In this paper, we prove that the logical characterization holds also when conjunction is replaced by disjunction, with negation still being not necessary. To this end, we introduce reactive probabilistic trees, a fully abstract model for reactive probabilistic systems that allows us to demonstrate expressiveness of the disjunctive probabilistic modal logic, as well as of the previously mentioned logics, by means of a compactness argument.

cs.LO↗

arXiv2016

A Specification of Open Transactional Memory for Haskell

Transactional memory (TM) has emerged as a promising abstraction for concurrent programming alternative to lock-based synchronizations. However, most TM models admit only isolated transactions, which are not adequate in multi-threaded programming where transactions have to interact via shared data before committing. In this paper, we present Open Transactional Memory (OTM), a programming abstraction supporting safe, data-driven interactions between composable memory transactions. This is achieved by relaxing isolation between transactions, still ensuring atomicity: threads of different transactions can interact by accessing shared variables, but then their transactions have to commit together-actually, these transactions are transparently merged. This model allows for loosely-coupled interactions since transaction merging is driven only by accesses to shared data, with no need to specify participants beforehand. In this paper we provide a specification of the OTM in the setting of Concurrent Haskell, showing that it is a conservative extension of current STM abstraction. In particular, we provide a formal semantics, which allows us to prove that OTM satisfies the \emph{opacity} criterion.

cs.PL↗

arXiv2015

Behavioural equivalences for coalgebras with unobservable moves

We introduce a general categorical framework for the definition of weak behavioural equivalences, building on and extending recent results in the field. This framework is based on parametrized saturation categories, i.e. categories whose hom-sets are endowed with complete orders and a suitable iteration operators; this structure allows us to provide the abstract definitions of various (weak) behavioural equivalence. We show that the Kleisli categories of many common monads are categories of this kind. This allows us to readily instantiate the abstract definitions to a wide range of existing systems (weighted LTS, Segala systems, calculi with names, etc.), recovering the corresponding notions of weak behavioural equivalences. Moreover, we can provide neatly new weak behavioural equivalences for more complex behaviours, like those definable on topological spaces, measurable spaces, etc.

cs.LO↗

arXiv2015

Structural operational semantics for non-deterministic processes with quantitative aspects

General frameworks have been recently proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format and a corresponding notion of bisimulation for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function GSOS (WF-GSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness and completeness of the WF-GSOS specification format, and that bisimilarities induced by these specifications are always congruences.

cs.LO↗

arXiv2015

Open Transactions on Shared Memory

Transactional memory has arisen as a good way for solving many of the issues of lock-based programming. However, most implementations admit isolated transactions only, which are not adequate when we have to coordinate communicating processes. To this end, in this paper we present OCTM, an Haskell-like language with open transactions over shared transactional memory: processes can join transactions at runtime just by accessing to shared variables. Thus a transaction can co-operate with the environment through shared variables, but if it is rolled-back, also all its effects on the environment are retracted. For proving the expressive power of TCCS we give an implementation of TCCS, a CCS-like calculus with open transactions.

cs.PL↗

arXiv2015

Distributed execution of bigraphical reactive systems

The bigraph embedding problem is crucial for many results and tools about bigraphs and bigraphical reactive systems (BRS). Current algorithms for computing bigraphical embeddings are centralized, i.e. designed to run locally with a complete view of the guest and host bigraphs. In order to deal with large bigraphs, and to parallelize reactions, we present a decentralized algorithm, which distributes both state and computation over several concurrent processes. This allows for distributed, parallel simulations where non-interfering reactions can be carried out concurrently; nevertheless, even in the worst case the complexity of this distributed algorithm is no worse than that of a centralized algorithm.

cs.DC↗