Jan Masopust

This study deals with the synthesis of selected attributes of public transport accessibility. The aim is to present a new method of multi-criteria analysis. As the research area, the city of Cracow has been chosen. The GTFS (General Transit Feed Specification) system has been used to obtain traffic data for buses and trams within the city‘s transport company (MPK Krakow). The analysis itself consists of 4 main accessibility indicators (walking time to each stop, number of lines, directions, and connections from each stop). The problem of exceeding the stops accessibility beyond the administrative border of Cracow has been solved by using a 500 m wide buffer zone around the city. To connect the individual layers of indicators into a multicriteria analysis, the Voronoi diagram function has been applied. The results of the method are presented in the form of synthetic maps of transport accessibility for each bus and tram stop in Cracow. Together with the synthetic accessibility maps, an index of a stop importance has been created as well, which consists of the sum of the mean percentages from 3 indicators (number of lines, directions, connections). The synthetic method used and acquired detailed values not only for the city of Cracow as a whole, but also its individual parts make it possible to provide a comprehensive picture of accessibility by public transport. This multicriteria analysis can also be extended for a comparative study of selected cities.

In this paper, we place some left restrictions on derivations in CD grammar systems with phrase- structure grammars, controlled by the regular languages. The rst restriction requires that every production is always applied within the rst k nonterminals in every sentential form, for some k  1. The second restriction says how many blocks of non-terminals can be in each sentential form. The third restriction extends the second restriction and says how many blocks of non-terminals with limited length can be in each sentential form. We demonstrate that under these restrictions, the grammar systems generate dierent families of languages. Indeed, under the rst restriction, these systems generate only context-free languages. Under the second restriction, even one-component systems characterize the entire family of recursively enumerable languages. In the end, the family of languages generated by grammar systems under the third restriction is equal to the family of languages generated by programmed grammars with context-free rules without -rules of nite index.