We propose two novel numerical schemes for the approximate implementation of dynamic programming (DP) operation concerned with finite-horizon optimal control discrete-time systems input-affine dynamics. The proposed algorithms involve discretization state and input spaces are based on an alternative path that solves dual problem corresponding to DP operation. provide error bounds algorithms, al...

Most commercial anti-virus software uses signature based techniques to detect whether a file is infected by a virus or not. However, signature based detection systems are unable to detect metamorphic viruses, since such viruses change their internal structure from generation to generation. Previous work has shown that hidden Markov models (HMMs) can be used to detect metamorphic viruses. In thi...

The k differences approximate string matching problem specifies a text string of length n, a pattern string of length m, the number k of differences (insertions, deletions, substitutions) allowed in a match, and asks for every location in the text where a match occurs. Previous algorithms require at least O(nk) time. When k is as large as a fraction of m, no substantial progress has been made o...

This proposal describes a project that is going to investigate algorithms for counting knapsack solutions and related sets, with a focus on algorithms that utilise dynamic programming. Both the feasibility of the implementation and the performance characteristics of the algorithms are going to be examined; additional goals pertain to actual algorithmic improvements, with derandomisation being t...

We provide a characterization of aggregation in the neoclassical growth model with aggregate shocks and uninsurable employment risk. The extent to which an economy aggregates can be determined by examining the (lack of) linearity with respect to wealth in the household’s savings function. We take advantage of this fact and separate the consumption-savings problem of the individual household fro...

• Option Pricing. An American option allows us to buy or sell an asset at any time up to a specified time, where we make money when the price goes under or over (respectively) a set strike price. Valuing the option requires finding an optimal policy for determining when to exercise the option. • Playing Games. Computer algorithms have been designed to play backgammon, bridge, chess, and recentl...