The value of model checking counterexamples for debugging programs (and specifications) is widely recognized. Unfortunately, bounded model checkers often produce counterexamples that are difficult to understand due to the values chosen by a SAT solver. This paper presents two approaches to making better use of BMC counterexamples. The first contribution is a new notion of counterexample minimiz...

Let k be a global field, with Galois group Gk and Weil group Wk relative to a choice of separable closure ks/k. Let Γ be either Gk or Wk, and H a linear algebraic group over F = C or Qp with p 6= char(k). Let ρ : Γ→ H(F ) be a (continuous) representation, always understood to be ramified at only finitely many places (as is automatic for commutative H, but not for H = GL2 with k = Q and F = Qp, ...

Witnesses and counterexamples produced by model checkers provide a very useful source of diagnostic information. They are usually returned in the form of a single computation path along the model of the system. However, a single computation path is not enough to explain all reasons of a validity or a failure. Our work in this area is motivated by the application of action-based model checking a...

In these lectures we discuss examples that are relevant to two questions in the theory of singular integrals. The first question is the L boundedness of the maximal operator formed by dilates of Mikhlin-Hörmander multipliers, while the second concerns the L boundedness of a well-known object, the classical L-bounded Calderón-Zygmund homogeneous singular integral associated with an integrable fu...

There exist (C0) semigroups Tx(i), T2(t) on Hubert space with the following properties: 7f has a bounded generator and is uniformly bounded, but is not similar to a contraction semigroup. T2 is uniformly bounded, and there exists no scalar a such that e~"'T2(t) is similar to a contraction semigroup.

We disprove Holtz and Ron’s conjecture that the power ideal CA,−2 of a hyperplane arrangement A (also called the internal zonotopal space) is generated by A-monomials. We also show that, in contrast with the case k ≥ −2, the Hilbert series of CA,k is not determined by the matroid of A for k ≤ −6. Remark. This note is a corrigendum to our article [1], and we follow the notation of that paper.

We construct a complete lattice Z such that the binary supremum function sup : Z × Z → Z is discontinuous with respect to the product topology on Z × Z of the Scott topologies on each copy of Z. In addition, we show that bounded completeness of a complete lattice Z is in general not inherited by the dcpo C(X,Z) of continuous functions from X to Z where X may be any topological space and where o...

Counterexample minimization is a hot research topic, which tries to remove irrelevant variables from counterexamples, such that they are easier to be understood. Existing approaches can only deal with path-like counterexamples of invariant AG f . For the first time, this paper proposes a novel approach to minimize loop-like and path-like counterexamples of ACTL properties. For a counterexample ...