Quotient Complexity of Regular Languages

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it "quotient complexity". The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations

Conflict resolution

U radu se na sustavan i jezgrovit način objašnjavaju temeljne značajke sukoba, vrste sukoba te način podučavanja djece konstruktivnom, nenasilnom rješavanju istih. Istraživanje započinje definiranjem osnovnih značajki komunikacije i naglašavanjem važnosti same sposobnosti komuniciranja. Čovjek je od najranije dobi u svakodnevnoj komunikaciji s ljudima oko sebe. Ona je temelj za razvoj svih daljnjih socijalnih vještina. Socijalna kompetencija razvija se tijekom odrastanja prvo u roditeljskom domu, a zatim i kroz socijalnu interakciju s drugim ljudima. Sposobnost socijalne interakcije nužno je razvijati te je bitno kod djece poticati razvoj socijalnih vještina, jer nam one omogućavaju da u komunikaciji s okolinom ostvarimo sve svoje želje i potrebe. Socijalne vještine koje kod djece treba posebno poticati su vještine slušanja, suradnje i empatije te ujedno i samopoštovanje. Djeca moraju naučiti na koji način reagirati na sukob i to će uvelike utjecati na kvalitetu njihova života izvan i unutar zajednice. Teorijske spoznaje o komunikaciji, stjecanju socijalnih vještina, te učenju konstruktivnog rješavanja sukoba upotpunjene su praktičnim saznanjima te provođenjem radionica konstruktivnog rješavanja sukoba s djecom predškolske dobi.This thesis systematically and concisely explains fundamental principles of conflict, types of conflict and ways of teaching children about constructive, nonviolent resolution of such. Research begins by defining basic principles of communication and emphasizing importance of the sole ability to communicate. From the earliest age people are daily involved in communication with others. This is the foundation for development of any other social skill. Social competence is being developed during growing up, it begins in the family home and it continues through social interaction with other people. It is essential to develop social interaction skills and it is also important to encourage development of these skills in children, because social skills enable us to achieve all our desires and needs through communication. Social skills that should be specially encouraged in children are skills of listening, cooperation, empathy towards others and self respect. . Children must learn how to react to conflict and this will greatly influence the quality of their personal life as well as their life within the community. Theoretical knowledge on communication, on growing social skills and on learning how to constructively resolve conflicts is accompanied with practical findings and through workshops on constructive conflict resolution among children of preschool age