O determinizaci zásobníkových automatů a konverzi regulárních stromových výrazů na determinizovatelné zásobníkové automaty
On Determinisation of Pushdown Automata and Conversion of Regular Tree Expressions to Determinisable Pushdown Automata
Typ dokumentu
disertační prácedoctoral thesis
Autor
Radomír Polách
Vedoucí práce
Janoušek Jan
Oponent práce
Meduna Alexander
Studijní obor
InformatikaStudijní program
InformatikaInstituce přidělující hodnost
katedra teoretické informatikyPráva
A university thesis is a work protected by the Copyright Act. Extracts, copies and transcripts of the thesis are allowed for personal use only and at one?s own expense. The use of thesis should be in compliance with the Copyright Act http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf and the citation ethics http://knihovny.cvut.cz/vychova/vskp.htmlVysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf a citační etikou http://knihovny.cvut.cz/vychova/vskp.html
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Trees are one of the fundamental and well-studied data structures in Computer Science. Arbology uses pushdown automata (PDAs), which read linearised notations of trees, as its suitable model of computation. Regular tree expressions (RTEs) are a formalism for describing regular tree languages (RTLs), whose standard model of computation is usually a finite tree automaton. It has been proven that the class of regular tree languages is a proper subclass of tree languages whose linear notations can be accepted by deterministic (string) PDAs. In this dissertation thesis, two new algorithms for converting RTEs to equivalent real-time height-deterministic PDAs (rHPDAs) that accept the trees in their linear notation are presented. Visibly pushdown automata (VPDAs), introduced by Alur and Madhusudan in 2004 [6], are PDA whose pushdown operations are determined by the input symbol, where the input alphabet is partitioned into three parts for the push, pop, and local pushdown operations. It is well known that nondeterministic VPDAs can be determinised. Height-deterministic pushdown automata (HPDAs), a natural generalisation of VPDAs where for any given input string the stack heights during any (nondeterministic) computation are a priori fixed, were introduced by Dirk Nowotka and Jiˇr´ı Srba in 2007 [36]. This can be seen as a generalisation of the property of VPDAs where the input alphabet is partitioned into three parts for a push, pop and local pushdown operations which implies this condition. The subgroup of rHPDAs was proven to be determinisable. In this dissertation thesis, new algorithms for the determinisation of VPDAs and rHPDAs are presented. The algorithms are based upon theoretical proofs of determinisation and result in reasonably small deterministic PDAs for most practical examples. This is achieved in a way that only necessary and accessible states and pushdown symbols are computed and constructed during the determinisation. Trees are one of the fundamental and well-studied data structures in Computer Science. Arbology uses pushdown automata (PDAs), which read linearised notations of trees, as its suitable model of computation. Regular tree expressions (RTEs) are a formalism for describing regular tree languages (RTLs), whose standard model of computation is usually a finite tree automaton. It has been proven that the class of regular tree languages is a proper subclass of tree languages whose linear notations can be accepted by deterministic (string) PDAs. In this dissertation thesis, two new algorithms for converting RTEs to equivalent real-time height-deterministic PDAs (rHPDAs) that accept the trees in their linear notation are presented. Visibly pushdown automata (VPDAs), introduced by Alur and Madhusudan in 2004 [6], are PDA whose pushdown operations are determined by the input symbol, where the input alphabet is partitioned into three parts for the push, pop, and local pushdown operations. It is well known that nondeterministic VPDAs can be determinised. Height-deterministic pushdown automata (HPDAs), a natural generalisation of VPDAs where for any given input string the stack heights during any (nondeterministic) computation are a priori fixed, were introduced by Dirk Nowotka and Jiˇr´ı Srba in 2007 [36]. This can be seen as a generalisation of the property of VPDAs where the input alphabet is partitioned into three parts for a push, pop and local pushdown operations which implies this condition. The subgroup of rHPDAs was proven to be determinisable. In this dissertation thesis, new algorithms for the determinisation of VPDAs and rHPDAs are presented. The algorithms are based upon theoretical proofs of determinisation and result in reasonably small deterministic PDAs for most practical examples. This is achieved in a way that only necessary and accessible states and pushdown symbols are computed and constructed during the determinisation.
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