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Braibant T.,CNRS Informatics Laboratory of Grenoble
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently typed) data-type that models the architecture of circuits, and a meaning function. We propose tactics that ease the reasoning about the behavior of the circuits, and we demonstrate that our approach is practicable by proving the correctness of various circuits: a text-book divide and conquer adder of parametric size, some higher-order combinators of circuits, and some sequential circuits: a buffer, and a register. © 2011 Springer-Verlag. Source


Peltier N.,CNRS Informatics Laboratory of Grenoble
Journal of Logic and Computation | Year: 2014

We study the complexity of the satisfiability problem for a class of logical formulae called iterated propositional schemata, modelling infinite sequences of structurally similar propositional formulae (such as the sequence (Equation), where n ∈ ℕ). We prove that the problem is EXPSPACE-complete in general and PSPACE-complete if the numbers occurring in the formula are polynomially bounded by the size of the schema. We then consider more restricted classes: we prove that the problem is still PSPACE-complete for the Horn class, but only NP-complete for the Krom class (sets of clauses of length 2). Finally, we devise a simple criterion ensuring that the satisfiability problem is in P. © The Author, 2012. Source


Pous D.,CNRS Informatics Laboratory of Grenoble
Logical Methods in Computer Science | Year: 2012

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the corresponding untyped decision procedures can be extended for free to the typed settings. Some of these theorems are obtained via a detour through fragments of cyclic linear logic, and give rise to a substantial optimisation of standard proof search algorithms. © D. Pous. Source


Pous D.,CNRS Informatics Laboratory of Grenoble
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the corresponding untyped decision procedures can be extended for free to the typed settings. Some of these theorems are obtained via a detour through fragments of cyclic linear logic, and give rise to a substantial optimisation of standard proof search algorithms. © 2010 Springer-Verlag Berlin Heidelberg. Source


Braibant T.,CNRS Informatics Laboratory of Grenoble | Pous D.,CNRS Informatics Laboratory of Grenoble
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element. © 2011 Springer-Verlag. Source

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