Bisimulations for Kripke models of Fuzzy Multimodal Logics

The main objective of the dissertation is to provide a detailed study of several different types of simulations and bisimulations for Kripke models of fuzzy multimodal logics. Two types of simulations (forward and backward) and five types of bisimulations (forward, backward, forward-backward, backward-forward and regular) are presented hereby. For each type of simulation and bisimulation, an algorithm is created to test the existence of the simulation or bisimulation and, if it exists, the algorithm computes the greatest one. The dissertation presents the application of bisimulations in the state reduction of fuzzy Kripke models, while preserving their semantic properties. Next, weak simulations and bisimulations were considered and the Hennessy-Milner property was examined. Finally, an algorithm was created to compute weak simulations and bisimulations for fuzzy Kripke models over locally finite algebras

Poboljšani algoritmi za determinizaciju fazi i težinskih automata

Determinization algorithms are methods that calculate complete deterministic fuzzy (weighted) automaton that is language equivalent to the input fuzzy (weighted) automaton, and they have found application in numerous fields, including lexicographic analysis, analysis of regular expressions, automatic speech recognition, pattern recognition in artificial intelligence, etc. Especially important class of determinization algorithms are canonization algorithms, which produce minimal complete deterministic fuzzy (weighted) automaton equivalent to the input fuzzy (weighted) automaton. The aim of this dissertation is the development of determinization algorithms based on the concept of factorizations, as well as computing and merging of the indistinguishable states of fuzzy (weighted) automaton under construction. At the same time, computing and merging of the indistinguishable states is done by right and left invariant fuzzy relations in the case of fuzzy automata, as well as by right and left invariant Boolean matrices in the case of weighted automata. We apply the partition refinement technique to obtain improved algorithms for computing the greatest right and left invariant Boolean equivalence and quasi – order matrices. In the end, we consider ways to compute the greatest right and left invariant fuzzy equivalences and fuzzy quasi – orders when the algorithms for their computation, based on the partition refinement technique, are unable to stop in a finite number of steps

Mathematics in Software Reliability and Quality Assurance

This monograph concerns the mathematical aspects of software reliability and quality assurance and consists of 11 technical papers in this emerging area. Included are the latest research results related to formal methods and design, automatic software testing, software verification and validation, coalgebra theory, automata theory, hybrid system and software reliability modeling and assessment