dc.contributor.author Egri-Nagy, Attila dc.date.accessioned 2014-08-07T07:51:17Z dc.date.available 2014-08-07T07:51:17Z dc.date.issued 2005 dc.identifier.uri http://hdl.handle.net/2299/14267 dc.description.abstract The theory of algebraic hierarchical decomposition of finite state automata en_US is an important and well developed branch of theoretical computer science (Krohn-Rhodes Theory). Beyond this it gives a general model for some important aspects of our cognitive capabilities and also provides possible means for constructing artificial cognitive systems: a Krohn-Rhodes decomposition may serve as a formal model of understanding since we comprehend the world around us in terms of hierarchical representations. In order to investigate formal models of understanding using this approach, we need efficient tools but despite the significance of the theory there has been no computational implementation until this work. Here the main aim was to open up the vast space of these decompositions by developing a computational toolkit and to make the initial steps of the exploration. Two different decomposition methods were implemented: the VuT and the holonomy decomposition. Since the holonomy method, unlike the VUT method, gives decompositions of reasonable lengths, it was chosen for a more detailed study. In studying the holonomy decomposition our main focus is to develop techniques which enable us to calculate the decompositions efficiently, since eventually we would like to apply the decompositions for real-world problems. As the most crucial part is finding the the group components we present several different ways for solving this problem. Then we investigate actual decompositions generated by the holonomy method: automata with some spatial structure illustrating the core structure of the holonomy decomposition, cases for showing interesting properties of the decomposition (length of the decomposition, number of states of a component), and the decomposition of finite residue class rings of integers modulo n. Finally we analyse the applicability of the holonomy decompositions as formal theories of understanding, and delineate the directions for further research. dc.language.iso en en_US dc.publisher University of Hertfordshire en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.title Algebraic hierarchical decomposition of finite state automata : a computational approach en_US dc.type info:eu-repo/semantics/doctoralThesis en_US dc.type.qualificationlevel Doctoral en_US dc.type.qualificationname PhD en_US herts.preservation.rarelyaccessed true
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