An algebraic characterization of some principal regulated rational cones

AbstractThe aim of this paper is to deal with formal power series over a commutative semiring A. Generalizing Wechler's pushdown automata and pushdown transition matrices yields a characterization of the A-semi-algebraic power series in terms of acceptance by pushdown automata. Principal regulated rational cones generated by cone generators of a certain form are characterized by algebraic systems given in certain matrix form. This yields a characterization of some principal full semi-AFL's in terms of context-free grammars. As an application of the theory, the principal regulated rational cone of one-counter “languages” is considered

Algebraic Systems and Pushdown Automata

The theory of algebraic power series in noncommuting variables, as we un-derstand it today, was initiated in [2] and developed in its early stages by the French school. The main motivation was the interconnection with context-free grammars: the defining equations were made to correspond to context-fre

The Equational Theory of Fixed Points with Applications to Generalized Language Theory

We review the rudiments of the equational logic of (least) fixed points and provide some of its applications for axiomatization problems with respect to regular languages, tree languages, and synchronization trees

A common algebraic description for probabilistic and quantum computations

AbstractThrough the study of gate arrays we develop a unified framework to deal with probabilistic and quantum computations, where the former is shown to be a natural special case of the latter. On this basis we show how to encode a probabilistic or quantum gate array into a sum-free tensor formula which satisfies the conditions of the partial trace problem, and vice-versa; that is, given a tensor formula F of order n×1 over a semiring S plus a positive integer k, deciding whether the kth partial trace of the matrix valSn,n(F·FT) fulfills a certain property. We use this to show that a certain promise version of the sum-free partial trace problem is complete for the class pr- BPP (promise BPP) for formulas over the semiring (Q+,+,·) of the positive rational numbers, for pr-BQP (promise BQP) in the case of formulas defined over the field (Q+,+,·), and if the promise is given up, then completeness for PP is shown, regardless whether tensor formulas over positive rationals or rationals in general are used. This suggests that the difference between probabilistic and quantum polytime computers may ultimately lie in the possibility, in the latter case, of having destructive interference between computations occurring in parallel. Moreover, by considering variants of this problem, classes like ⊕P, NP, C=P, its complement co-C=P, the promise version of Valiant's class UP, its generalization promise SPP, and unique polytime US can be characterized by carrying the problem properties and the underlying semiring

\b{eta}-delayed three-proton decay of 31Ar

The beta decay of 31Ar, produced by fragmentation of a 36Ar beam at 880 MeV/nucleon, was investigated. Identified ions of 31Ar were stopped in a gaseous time projection chamber with optical readout allowing to record decay events with emission of protons. In addition to \b{eta}-delayed emission of one and two protons we have clearly observed the beta-delayed three-proton branch. The branching ratio for this channel in 31Ar is found to be 0.07(2)%.Comment: 5 pages, 3 figures, submitted to Physical Rev.

Active target TPC for study of photonuclear reactions at astrophysical energies

A setup designed to study photonuclear reactions at astrophysical energies - an active target Time Projection Chamber was developed and constructed at the Faculty of Physics, University of Warsaw. The device was successfully employed in two experiments at the Institute of Nuclear Physics Polish Academy of Sciences in Cracow, in which {\gamma}- and neutron-induced reactions with CO2 gas target were measured. The reaction products were detected and their momenta reconstructed. Preliminary results are shown.Comment: Presented at Zakopane Conference on Nuclear Physics 202