Dynamic programs, or fixpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (“verification”), computing shortest paths on weighted graphs (“optimization”), computing the value of games played on game graphs (“control”). For Kripke structures, a rich fixpoint theory is available in the form of the μ-calculus. Yet few connec...

In this paper, we explain how the connection between higherorder 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 Carayol and Serre using collapsible pushdown automata. The main idea is to start from an infinitary and colored relational semantics of the λY -calculus already for...

We consider the problem of construction of optimal experimental designs (approximate theory) on a compact subset X of R with nonempty interior, for a concave and Lipschitz differentiable design criterion φ(·) based on the information matrix. The proposed algorithm combines (a) convex optimization for the determination of optimal weights on a support set, (b) sequential updating of this support ...

We present a method for verifying the correctness of an imperative program with respect to a specification defined in terms of a set of possibly recursive Horn clauses. Given a program prog, we consider a partial correctness specification of the form {φ} prog {ψ}, where the assertions φ and ψ are predicates defined by a set Spec of Horn clauses. The verification method consists in: (i) encoding...

ion-Refinement 1. Generate an initial abstraction function h. 2. Build abstract machine M̂ based on h. Model check M̂ . If M̂ |= φ, then M |= φ. Return TRUE. 3. If M̂ 6|= φ, check the counterexample on the concrete model. If the counterexample is real, M 6|= φ. Return FALSE. 4. Refine h, and go to step 2. SAT based Abstraction-Refinement using ILP and Machine Learning Techniques 13 Abstraction Func...