Abstract Pebble transducers are nested two-way which can drop marks (named “pebbles”) on their input word. Such machines compute functions whose output size is polynomial in the of input. They be seen as simple recursive programs recursion height bounded. A natural problem is, given a pebble transducer, to an equivalent transducer with minimal height. This has been open since introduction model...

This paper investigates error-entropy-minimization in adaptive systems training. We prove the equivalence between minimization of error’s Renyi entropy of order and minimization of a Csiszar distance measure between the densities of desired and system outputs. A nonparametric estimator for Renyi’s entropy is presented, and it is shown that the global minimum of this estimator is the same as the...

One measure of riskiness of an investment is “drawdown”, defined, most often in the asset management space, as the decline in net asset value from a historic high point. Mathematically, if the net asset value is denoted by Vt , t ≥ 0, then the current “peak-to-trough” drawdown is given by Dt = Vt − max0≤u≤t Vu. The maximum drawdown, max0≤u≤t Du, is a statistic that the CFTC forces managed futur...

The problem of minimizing the number of misclassiied points by a plane, attempting to separate two point sets with intersecting convex hulls in n-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed f...

We compare deterministic finite automata (DFAs) and biautomata under the following two aspects: structural similarities between minimal and hyper-minimal automata, and computational complexity of the minimization and hyper-minimization problem. Concerning classical minimality, the known results such as isomorphism between minimal DFAs, and NL-completeness of the DFA minimization problem carry o...