Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

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