Amina Doumane
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View article: Tree algebras and bisimulation-invariant MSO on finite graphs
Tree algebras and bisimulation-invariant MSO on finite graphs Open
We establish that the bisimulation invariant fragment of MSO over finite transition systems is expressively equivalent over finite transition systems to modal mu-calculus, a question that had remained open for several decades. The proof go…
View article: A Finite Presentation of Graphs of Treewidth at Most Three
A Finite Presentation of Graphs of Treewidth at Most Three Open
We provide a finite equational presentation of graphs of treewidth at most three, solving an instance of an open problem by Courcelle and Engelfriet. We use a syntax generalising series-parallel expressions, denoting graphs with a small in…
View article: On the Fair Termination of Client-Server Sessions
On the Fair Termination of Client-Server Sessions Open
Client-server sessions are based on a variation of the traditional interpretation of linear logic propositions as session types in which non-linear channels (those regulating the interaction between a pool of clients and a single server) a…
View article: Bouncing threads for circular and non-wellfounded proofs -- Towards compositionality with circular proofs (Extended version)
Bouncing threads for circular and non-wellfounded proofs -- Towards compositionality with circular proofs (Extended version) Open
International audience
View article: Regular Expressions for Tree-Width 2 Graphs
Regular Expressions for Tree-Width 2 Graphs Open
We propose a syntax of regular expressions, which describes languages of tree-width 2 graphs. We show that these languages correspond exactly to those languages of tree-width 2 graphs, definable in the counting monadic second-order logic (…
View article: Graph Characterization of the Universal Theory of Relations
Graph Characterization of the Universal Theory of Relations Open
The equational theory of relations can be characterized using graphs and homomorphisms. This result, found independently by Freyd and Scedrov and by Andréka and Bredikhin, shows that the equational theory of relations is decidable. In this…
View article: Non-Axiomatizability of the Equational Theories of Positive Relation Algebras (Invited Talk)
Non-Axiomatizability of the Equational Theories of Positive Relation Algebras (Invited Talk) Open
In the literature, there are two ways to show that the equational theory of relations over a given signature is not finitely axiomatizable. The first-one is based on games and a construction called Rainbow construction. This method is very…
View article: First-order tree-to-tree functions
First-order tree-to-tree functions Open
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as tree-…
View article: Bouncing threads for infinitary and circular proofs
Bouncing threads for infinitary and circular proofs Open
We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…
View article: First-order tree-to-tree functions
First-order tree-to-tree functions Open
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as tree-…
View article: Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms
Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms Open
We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation). Without these constants, the equational theory coincides with that of sem…
View article: Kleene Algebra with Hypotheses
Kleene Algebra with Hypotheses Open
We study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexity point of view. While their equational theories coincide and are PSpace -complete, their Horn theories differ and are undecidable. We cha…
View article: Left-Handed Completeness for Kleene algebra, via Cyclic Proofs
Left-Handed Completeness for Kleene algebra, via Cyclic Proofs Open
We give a new proof that the axioms of left-handed Kleene algebra are complete with respect to language containments. This proof is significantly simpler than both the proof of Boffa (which relies on Krob’s completeness result), and the mo…
View article: On the infinitary proof theory of logics with fixed points
On the infinitary proof theory of logics with fixed points Open
The subject of this thesis is the proof theory of logics with fixed points, such as the μ-calculus,linear-logic with fixed points, etc. These logics are usually equipped with finitary deductive systemsthat rely on Park’s rules for inductio…
View article: Constructive completeness for the linear-time µ-calculus
Constructive completeness for the linear-time µ-calculus Open
International audience
View article: Towards Completeness via Proof Search in the Linear Time mu-Calculus: The case of Büchi inclusions
Towards Completeness via Proof Search in the Linear Time mu-Calculus: The case of Büchi inclusions Open
Modal µ-calculus is one of the central languages of logic and verification , whose study involves notoriously complex objects: au-tomata over infinite structures on the model-theoretical side; infinite proofs and proofs by (co)induction on…
View article: Infinitary Proof Theory: the Multiplicative Additive Case
Infinitary Proof Theory: the Multiplicative Additive Case Open
Infinitary and regular proofs are commonly used in fixed point logics. Being natural intermediate devices between semantics and traditional finitary proof systems, they are commonly found in completeness arguments, automated deduction, ver…