We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings the time complexity is slightly higher (linear instead of logarithmic in the number of states). We...

The seller of a contingent claim H can always find a self-financing investment strategy that (super)hedges the claim H. When the seller wants to endow an initial capital x less than the one required to get perfect (super)hedging, the shortfall risk minimisation problem arises in a natural way. The aim is to find the strategy that minimises E{`([H(ST )−V x,φ T ])} (shortfall risk), where V x,φ t...

This paper investigates the properties of the multiple-reference block motion field. Guided by the results of this investigation, the paper proposes three fast multiple-reference block matching motion estimation algorithms. The proposed algorithms are extensions of the single-reference simplex minimisation search (SMS) algorithm. The algorithms provide different degrees of compromise between pr...

Various kinds of digital commerce depend on digital signatures, which are based on public-key cryptography and one-way hash functions. However, one-way hash functions have properties, which can be exploited to subvert security service. A framework in this paper gives a way to minimise such risks with paying attention to proper structuring (and consequently coding) of electronic documents and th...