For a number of years, temporal and modal logics have been applied outside pure logic in areas such as formal methods, theoretical computer science and artiicial intelligence. In our research we are particularly interested in the use of modal logics in the characterisation of complex components within software systems as intelligent or rational agents. This approach allows the system designer t...

Boolean satisfiability (SAT) solvers have improved enormously in performance over the last 10–15 years and are today an indispensable tool for solving a wide range of computational problems. However, our understanding of what makes SAT instances hard or easy in practice is still quite limited. A recent line of research in proof complexity has studied theoretical complexity measures such as leng...

This paper is a tutorial on using the Coq proof-assistant for reasoning on software correctness. It illustrates features of Coq like inductive definitions and proof automation on a few examples including arithmetic, algorithms on functional and imperative lists and cryptographic protocols. Coq is not a tool dedicated to software verification but a general purpose environment for developing math...

Partial functions are frequently used when specifying and reasoning about computer programs. Using partial functions entails reasoning about potentially ill-defined expressions. In this paper we show how to formally reason about partial functions without abandoning the well understood domain of classical two-valued predicate calculus. In order to achieve this, we extend standard predicate calcu...

Type theories need to enforce some restrictions on recursive definitions in order to remain sound. Depending on the implementation, these restrictions may prevent the user from defining recursive functions as conveniently as in a functional programming language. This paper describes a fixed point combinator that can be applied to any functional. A fixed point equation can be derived for the rec...

We address the problem of authenticating pattern matching queries over textual data that is outsourced to an untrusted cloud server. By employing cryptographic accumulators in a novel optimal integritychecking tool built directly over a suffix tree, we design the first authenticated data structure for verifiable answers to pattern matching queries featuring fast generation of constant-size proo...

The ability to consistently handle faults in a distributed environment requires, among a small set of basic routines, an agreement algorithm allowing surviving entities to reach a consensual decision between a bounded set of volatile resources. This paper presents an algorithm that implements an Early Returning Agreement (ERA) in pseudo-synchronous systems, which optimistically allows a process...

The purpose of this paper is to clarify the short-term and long-term objectives of screening for various cancers, and to indicate the kinds of data that are needed to determine whether or not the objectives are met. Cancers at various sites differ with respect to their innate suitability for screening. Criteria that enhance screening suitability include the potential for serious complications a...

This paper presents on-going researches on theoretical and practical issues of combining rewriting based automated theorem proving and user-guided proof development, with the strong constraint of safe cooperation of both. In practice, we instantiate the theoretical study on the Coq proof assistant and the ELAN rewriting based system, focusing first on equational and then on inductive proofs. Di...

I develop some of the theory of self-referential systems. I present the necessary semantic ideas, and combine this with work in proof theory, on the necessary properties of a proof predicate, to develop practical theories for reasoning about such systems. I propose to use this to exploit the idea of a reflection principle as a systematic way to extend such self-referential theories safely. I al...