Overview of KLOE results on kaon physics and KLOE–2 perspectives

Kaon physics program of KLOE is being continued at the upgraded KLOE-2 system, therefore an overview of KLOE results in this field is shortly presented together with prospects for KLOE-2

Applications of the Stroboscopic Tomography to Selected 2-Level Decoherence Models

In the paper we discuss possible applications of the so-called stroboscopic tomography (stroboscopic observability) to selected decoherence models of 2-level quantum systems. The main assumption behind our reasoning claims that the time evolution of the analyzed system is given by a master equation of the form $\dot{\rho} = \mathbb{L} \rho$ and the macroscopic information about the system is provided by the mean values $m_i (t_j) = Tr(Q_i \rho(t_j))$ of certain observables $\{Q_i\}_{i=1} ^r$ measured at different time instants $\{t_j\}_{j=1}^p$. The goal of the stroboscopic tomography is to establish the optimal criteria for observability of a quantum system, i.e. minimal value of $r$ and $p$ as well as the properties of the observables $\{Q_i\}_{i=1} ^r$

Random runners are very lonely

Suppose that $k$ runners having different constant speeds run laps on a circular track of unit length. The Lonely Runner Conjecture states that, sooner or later, any given runner will be at distance at least $1/k$ from all the other runners. We prove that, with probability tending to one, a much stronger statement holds for random sets in which the bound $1/k$ is replaced by \thinspace $1/2-\varepsilon$. The proof uses Fourier analytic methods. We also point out some consequences of our result for colouring of random integer distance graphs

Branching Bisimilarity of Normed BPA Processes is in NEXPTIME

Branching bisimilarity on normed BPA processes was recently shown to be decidable by Yuxi Fu (ICALP 2013) but his proof has not provided any upper complexity bound. We present a simpler approach based on relative prime decompositions that leads to a nondeterministic exponential-time algorithm; this is close to the known exponential-time lower bound.Comment: This is the same text as in July 2014, but only with some acknowledgment added due to administrative need

Partially-commutative context-free languages

The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are commutative according to a binary independence relation, very much like in trace theory. The class has been recently proposed as a robust class subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We identify a natural corresponding automaton model: stateless multi-pushdown automata. We show stability of the class under natural operations, including homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to two other relevant classes: CFL extended with shuffle and trace-closures of CFL. Among technical contributions of the paper are pumping lemmas, as an elegant completion of known pumping properties of regular languages, CFL and commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244