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The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…
A system of session types is introduced as induced by a Curry Howard correspondence applied to Bounded Linear Logic, and then extending the thus obtained type system with probabilistic choices and ground types. The obtained system satisfies…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
We investigate the problem of type isomorphisms in the presence of higher-order references. We first introduce a finitary programming language with sum types and higher-order references, for which we build a fully abstract games model…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated,…
This is a survey of {\lambda}-calculi that, through the Curry-Howard isomorphism, correspond to constructive modal logics. We cover the prehistory of the subject and then concentrate on the developments that took place in the 1990s and…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
First, we extend Leifer-Milner RPO theory, by giving general conditions to obtain IPO labelled transition systems (and bisimilarities) with a reduced set of transitions, and possibly finitely branching. Moreover, we study the weak variant…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo. This…