The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints

It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized language with a cutpoint and then by using the fact that there are uncountably many cutpoints. In this note, we prove the same results for fixed cutpoints: each recognized language is associated with an automaton (i.e., algorithm), and the proofs use the fact that there are uncountably many automata. For each case, we present a new construction.Comment: 12 pages, minor revisions, changing the format to "dmtcs-episciences" styl

The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints

It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized language with a cutpoint and then by using the fact that there are uncountably many cutpoints. In this note, we prove the same results for fixed cutpoints: each recognized language is associated with an automaton (i.e., algorithm), and the proofs use the fact that there are uncountably many automata. For each case, we present a new construction.Comment: 12 pages, minor revisions, changing the format to "dmtcs-episciences" styl

Escaping special local maxima in solving the vehicle routing problem by the local search

Transportlīdzekļu maršrutizēšanas problēma (VRP) ir viena no izplatītākām problēmām transportēšanas un loģistikas nozarē. Daudzos uzņēmumos maršrutu plānošana joprojām ir atstāta vadītāju atbildībā, kas noved pie papildus izmaksām un CO2 emisijām. Problēmas, ar kuriem sastopas industrijā, bieži pieprasa smalko detaļu analīzi un iedziļināšanas biznesa realitātēs. Darbā tiek aplūkotas dažas no reālas dzīves problēmām, ar kuriem autors sastapās, strādājot maršrutu optimizācijas nozarē. Ir piedāvāti un implementēti divi risinājumi šo problēmu novēršanai.Vehicle routing problem (VRP) is one of the most popoular problems in the field of logistics. In a large number of companies route planning is still driver's responisibility which leads to increased costs and additional CO2 emissions. Industrial size problems require in-depth analysis of various factors which are often uniqe for every specific business. In this thesis a few real-world problems from routing optimization sphere are reviewed and two solutions are suggested and implemented

The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints

It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized language with a cutpoint and then by using the fact that there are uncountably many cutpoints. In this note, we prove the same results for fixed cutpoints: each recognized language is associated with an automaton (i.e., algorithm), and the proofs use the fact that there are uncountably many automata. For each case, we present a new construction