# Seminars

## Minimal Generating Sets for Semiflows

Speaker: Gerard Memmi LTCI, Telecom-Paris, Institut polytechnique de Paris

Tuesday, 23 Mai 2023, 14:00, Room 1Z56 and Zoom

We discuss important characteristics of finite generating sets for F+, the set of all semiflows with non-negative coordinates of a Petri Net. We endeavor to regroup a number of algebraic results dispersed throughout the Petri Nets literature and also to better position the re- sults while considering semirings such as N or Q+ then fields such as Q. As accurately as possible, we provide a range of new algebraic results on minimal semiflows, minimal supports, and finite minimal generating sets for a given family of semiflows. Minimality of semiflows and of sup- port are critical to develop effective analysis of invariants and behavioral properties of Petri Nets. Main results are concisely presented in a table and our contribution is highlighted. We conclude with the analysis of an example drawn from the telecommunication industry underlining the efficiency brought by using minimal semiflows of minimal supports.

## Co-verification for robotics: from simulation to verification

Speaker: Pedro Ribeiro Research Fellow, University of York

Tuesday, 6 June 2023, 14:00, 1Z71

Robots are expected to play important roles in furthering prosperity, however providing formal guarantees on their (safe) behaviour is not yet fully within grasp given the multifaceted nature of such cyber-physical systems. Simulation, favoured by practitioners, provides an avenue for experimenting with different scenarios before committing to expensive tests and proofs. In this talk, I will discuss how models may be brought together for (co-)verification of system properties, with simulation complementing verification. This will be cast using the model-driven RoboStar framework, that clearly identifies models of the software, hardware, and scenario, and has heterogeneous formal semantics amenable to verification using state-of-the-art model-checkers and theorem provers, such as Isabelle/UTP.

Pedro Ribeiro will be visiting the LMF the entire day - interactions welcome.

## Agenda

## Séminaires antérieurs

## Keynote: Verification of Stateful Security Protocols in Isabelle/HOL

Speaker: Achim Brucker, Chair of Computer Security, University Exeter, GB

Tuesday May 16 2023, 14:00, Room 1Z61

Communication networks like the Internet form a large distributed system where a huge number of components run in parallel, such as security protocols and distributed web applications. For what concerns security, it is obviously infeasible to verify them all at once as one monolithic entity; rather, one has to verify individual components in isolation.

While many typical components like the security protocol TLS have been studied intensively, there exists much less research on analyzing and ensuring the security of the composition of security protocols. This is a problem since the composition of systems that are secure in isolation can easily be insecure.

The verification of security protocols is one of the success stories of formal methods. There is a wide spectrum of methods available, ranging from fully automated methods to interactive theorem proving with proof assistants like Isabelle/HOL. Read more...

## On the edit distance between transducers

Speaker: C. Aiswarya, CMI

Wednesday, 19 April 2023, 16:00, 1Z56 ENS Nord and Zoom

**Abstract:** Given a metric over words, define the distance between two transducers with identical domain as the supremum of the distances of their respective outputs over all inputs. This is a useful generalisation for comparing transducers that goes beyond the equivalence problem. Two transducers are said to be close (resp. k-close) if their distance is bounded (resp. at most k). We will discuss the decidability of the problem that asks whether two given transducers are close (resp. k-close), for common edit distances.

This is a joint work with Amaldev Manuel and Saina Sunny.

Aiswarya will be at LMF from 2 April to 2 June 2023 as a Visiting Professor of ENS Paris-Saclay.

## String constraints with subword ordering: complexity of satisfiability

Speaker: C. Aiswarya, CMI

Monday, 17 April 2023, 15:00, Salle 1Z14 and Zoom

**Abstract:** We consider a variant of string constraints given by membership constraints in context-free languages and subword relation between variables. The satisfiability problem for this variant turns out to be undecidable. We consider a fragment in which the subword-order constraints do not impose any cyclic dependency between variables. We show that this fragment is \nexptime-complete. As an application of our result, we settle the complexity of control state reachability in acyclic lossy channel pushdown systems, which was shown to be decidable in Atig-Bouajjani-Touilli-08. We show that this problem is \nexptime-complete.

This is a joint work with Prakash Saivasan and Soumodev Mal, which appeared in LICS 22.

Aiswarya will be at LMF from 2 April to 2 June 2023 as a Visiting Professor of ENS Paris-Saclay.

## The Future of Model-based Testing

Speaker: Jan Peleska, Universität Bremen, Saarbrücken, Germany

Friday 17 March 2023, 14:00, Room 1Z56

**Abstract:**
Since the 1970s, model-based testing (MBT) has been comprehensively investigated in the research communities, and its industrial application has been fostered for at least two decades. Though convincing success stories about MBT have been published, we have to admit that its acceptance in industry is still not as good as it should be. This is reflected, for example, by the facts that commercial MBT tools are not selling as well as had been originally envisaged by the “campaigners of MBT” (such as myself) and that MBT has not been integrated into the verification plans of the key players in the embedded systems world.
Read more...

## Strategy Complexity of Zero-Sum Games on Graphs

Speaker: Pierre Vandenhove

Tuesday, 14 Mars 2023, 14:00, 1Z77

**Abstract:** In this seminar, I will present the results obtained as part of my PhD thesis cosupervised by Patricia Bouyer at LMF and Mickael Randour at Université de Mons (Belgium). This seminar precedes my thesis defense which will take place in Mons in April. I include here a short abstract; more details are available at my website.

We study zero-sum turn-based games on graphs. Such games can be used to model the interaction between a computer system and its environment, assumed to be antagonistic. The synthesis problem consists in automatically building a controller for the system that guarantees a given objective no matter what happens in the environment, that is, a winning strategy in the derived game.

## A Gentle Introduction to Matching Logic and its Applications

Speaker: Dorel Lucanu

Wednesday, 29 March 2023, 14:00, Salle 1Z56, hybrid

**Abstract:** Matching Logic (ML) allows
to uniformly specify and reason about programming languages and properties
of their programs. It was developed as a logical foundation of the
K framework.

ML is expressive enough to specify all properties within various logical systems such as FOL, separation logic, lambda-calculus, (dependent) type systems, and modal mu-calculus. In particular, it supports operational semantics (term rewriting) and axiomatic semantics (Hoare triples). ML has a sound fixed Hilbert-style proof system that supports formal reasoning for all specifications. In this talk we give a gentle introduction to (Applicative) Matching Logic [3], we show how the initial algebraic semantics can be encoded as ML theories [4], and how ML is used to formaly define programming languages semantics and program properties.

## The Frobenius Anatomy of Distributed Quantum Protocols

Speaker: Alexis Toumi, email: alexis@toumi.email

Tuesday, 10 January 2023, 14:00, Salle 1Z31

**Abstract:** Distributed consensus and leader election are two communication problems that quantum computers can solve in a deterministic way, while classical computers can only solve them probabilistically. These two quantum protocols can in fact be put in one-to-one correspondance with the GHZ and W states, the only two ways to entangle three qubits (up to LOCC, local operations and classical communication). In this talk, we will give an abstract formulation of quantum consensus and leader election in terms of spiders, also known as Frobenius algebras. In both cases, a single equation allows to create global entanglement from local interactions: spider fusion. We will conclude with some applications to quantum natural language processing (QNLP) where spiders allow to formalise the notion of anaphora and co-reference: we can compute a global meaning for text as the entanglement of local meanings for sentences.

## An Abstraction of the Unit Interval with Denominators

Speaker: Marco Abbadini

Wednesday, 4 January 2023, 14:00, visio link: https://zoom.us/j/97278780690?pwd=cGU5Yi9UVTk0aXhndWtuanY4dHp0QT09

**Abstract:** Compact Hausdorff spaces are the topological abstraction of the unit
interval [0,1] (in a sense that can be made precise). Let us now equip the
unit interval with the "denominator map" den: [0,1] -> N that maps a
rational number to its denominator and an irrational number to 0. We
characterize the abstraction of [0,1] that takes into account both the
topology and the denominator map.

(We use this result to provide a representation theorem for a class of lattice-ordered groups, generalizing a result of M.H. Stone (1941).)

## Keynote: The Skolem Landscape

Speaker: Joël Ouaknine, Max Planck Institute for Software Systems, Saarbrücken, Germany

Tuesday, 13 December 2022, 14:00, Room 1Z56

**Abstract:** The Skolem Problem asks how to determine algorithmically whether a given linear recurrence sequence (such as the Fibonacci numbers) has a zero. It is a central question in dynamical systems and number theory, and has many connections to other branches of mathematics and computer science. Unfortunately, the decidability of the Skolem Problem has been open for nearly a century! In this talk, I will present a survey of what is known on this problem and related questions, including recent and ongoing developments.

## Consistent Circuits for Indefinite Causal Order

Speaker: Augustin Vanrietvelde, LMF

Tuesday, 6 December 2022, 14:00, Room 1Z53

**Abstract**
Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there exists no general formal method to construct a process with an exotic causal structure in a way that ensures, and makes clear why, it is consistent. Here we provide such a method, given by an extended circuit formalism. This only requires directed graphs endowed with boolean matrices, which encode basic constraints on operations. Our framework (a) defines a set of elementary rules for checking the validity of any such graph, (b) provides a way of constructing consistent processes as a circuit from valid graphs, and (c) yields an intuitive interpretation of the causal relations within a process and an explanation of why they do not lead to inconsistencies. We display how several standard examples of exotic processes, including ones that violate causal inequalities, are among the class of processes that can be generated in this way; we conjecture that this class in fact includes all unitarily extendible processes.