arXiv subjects

Petr Novotný

Publications and source records attributed to Petr Novotný.

39 records · Page 3Linked to original sources

arXiv2012

Minimizing Expected Termination Time in One-Counter Markov Decision Processes

We consider the problem of computing the value and an optimal strategy for minimizing the expected termination time in one-counter Markov decision processes. Since the value may be irrational and an optimal strategy may be rather complicated, we concentrate on the problems of approximating the value up to a given error epsilon > 0 and computing a finite representation of an epsilon-optimal strategy. We show that these problems are solvable in exponential time for a given configuration, and we also show that they are computationally hard in the sense that a polynomial-time approximation algorithm cannot exist unless P=NP.

cs.FL↗

arXiv2008

On (alpha,beta,gamma)-derivations of Lie algebras and corresponding invariant functions

We consider finite-dimensional complex Lie algebras. We generalize the concept of Lie derivations via certain complex parameters and obtain various Lie and Jordan operator algebras as well as two one-parametric sets of linear operators. Using these parametric sets, we introduce complex functions with fundamental property - invariance under Lie isomorphisms. One of these basis-independent functions represents a complete set of invariant(s) for three-dimensional Lie algebras. We present also its application on physically motivated examples in dimension eight.

math-ph↗

arXiv2007

On Orbits of the Ring $Z_n^m$ under the Action of the Group $SL(m,Z_n)$

We consider the action of the finite matrix group $SL(m,Z_n)$ on the ring $Z_n^m$. We determine orbits of this action for n arbitrary natural number. It is a generalization of the task which was studied by A.A. Kirillov for $m=2$ and $n$ prime number.

math.GR↗