Rational dilation of tetrablock contractions revisited

The Semantics of Rational Contractions

This paper is concerned with the revision of beliefs in the face of new and possibly contradicting information. In the Logic of Theory Change developed by Alchourron, Gärdenfors and Makinson this nonmonotonic process consists of a contraction and an expansion of a set of formulas. To achieve minimal change they formulated widely accepted postulates that rational contractions have to fulfill. Co...

Rational Secret Sharing, Revisited

We consider the problem of secret sharing among n rational players. This problem was introduced by Halpern and Teague (STOC 2004), who claim that a solution is impossible for n = 2 but show a solution for the case n ≥ 3. Contrary to their claim, we show a protocol for rational secret sharing among n = 2 players; our protocol extends to the case n ≥ 3, where it is simpler than the Halpern-Teague...

Edit Distance with Duplications and Contractions Revisited

In this paper, we propose three algorithms for the problem of string edit distance with duplication and contraction operations, which improve the time complexity of previous algorithms for this problem. These include a faster algorithm for the general case of the problem, and two improvements which apply under certain assumptions on the cost function. The general algorithm is based on fast min-...

Rational Pricing of Internet Companies Revisited

The Failure of Rational Dilation on a Triply Connected Domain

Let R denote a domain in C with boundary B. Let X denote the closure of R. An operator T on a complex Hilbert space H has X as a spectral set if σ(T ) ⊂ X and ‖f(T )‖ ≤ ‖f‖R = sup{|f(z)| : z ∈ R} for every rational function f with poles off X. The expression f(T ) may be interpreted either in terms of the Riesz functional calculus, or simply by writing the rational function f as pq−1 for polyno...