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This note advertises the topics that will be covered in the tutorial on finite model theory.

I will present three main themes in current research in semantics: (a) models of programming languages, (b) concurrency and (c) approximation. The first theme covers denotational semantics and operational semantics and the search for tight connections ...

Formal methods is concerned with analyzing systems formally. Here, we focus on three different systems:software systems, dynamical control systems, and biological systems. The analysis questions can be broadly classified into verification and synthesis ...

We study finite automata running over infinite binary trees and we relax the notion of accepting run by allowing a negligible set (in the sense of measure theory) of non-accepting branches. In this qualitative setting, a tree is accepted by the ...

Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order, successor, ...

We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k reward functions, in the expectation objective ...

There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework ...

We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms,...

Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we ...

We present a new fully abstract and effectively presentable denotational model for RefML, a paradigmatic higher-order programming language combining call-by-value evaluation and general references in the style of ML. Our model is built using game ...

We study the probabilistic coherent spaces--a denotational semantics interpreting programs by power series with non negative real coefficients. We prove that this semantics is adequate for a probabilistic extension of the untyped $\lambda$-calculus: the ...

We introduce the domain of continuous random variables (CRV) over a domain, as an alternative to Jones and Plotkin's probabilistic power domain. While no known Cartesian-closed category is stable under the latter, we show that the so-called thin (...

We study the computability of conditional probability, a fundamental notion in probability theory and Bayesian statistics. In the elementary discrete setting, a ratio of probabilities defines conditional probability. In more general settings, ...

We propose a type system for an imperative programming language, which certifies program time bounds. This type system is based on secure flow information analysis. Each program variable has a level and we prevent information from flowing from low level ...

A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely capture the ...

We study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of universes and a first-order theory T built in its conversion relation. The theory T is specified abstractly, by a set of constructors, a set of defined ...

We investigate the problem of type isomorphisms in a programming language with higher-order references. We first recall the game-theoretic model of higher-order references by Abramsky, Honda and McCusker. Solving an open problem by Laurent, we show that ...

There are standard logics DTC, TC, and LFP capturing the complexity classes L, NL, and P on ordered structures, respectively. In [4] we have shown that LFP_{inv}, the ``order-invariant least fixed-point logic LFP,'' captures P (on all finite structures) ...

Quantum logic generalizes, and in dimension one coincides with, Boolean propositional logic. We introduce the weak and strong satisfiability problem for quantum logic formulas, and show both NP-complete in dimension two as well. For higher-dimensional ...

Using Jerábek's framework for probabilistic reasoning, we formalize the correctness of two fundamental RNC^2 algorithms for bipartite perfect matching within the theory VPV for polytime reasoning. The first algorithm is for testing if a bipartite graph ...

This paper is a study of the forcing translation through the proofs as programs correspondence in classical logic, following the methodology introduced by Krivine in [Kri08, Kri10]. For that, we introduce an extension of (classical) higher-order ...

Additive linear logic, the fragment of linear logic concerning linear implication between strictly additive formulae, coincides with sum-product logic, the internal language of categories with free finite products and co products. Deciding equality of ...

The model checking of higher-order recursion schemes (higher-order model checking for short) has been actively studied in the last decade, and has seen significant progress in both theory and practice. From a practical perspective, higher-order model ...

In semantics and in programming practice, algebraic concepts such as monads or, essentially equivalently, (large) Lawvere theories are a well-established tool for modelling generic side-effects. An important issue in this context are combination ...

While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work contributes to the ...