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Abstraction in Automata Algorithms
Kocourek, Tomáš ; Lengál, Ondřej (oponent) ; Holík, Lukáš (vedoucí práce)
The goal of this thesis is to implement and experimentally compare antichain-based algorithms with and without abstraction, which decide the emptiness of alternating finite automata. The author also proposes his own algorithms using abstraction and comes up with a few optimizations of existing abstract algorithms. The thesis introduces the theoretical background of studied algorithms and describes efficient ways to implement data structures which are used by these algorithms. The experimental evaluation over random automata shows that the algorithms without abstraction give us better results in general because they do not perform costly evaluation of closed set intersection and complementation. However, in case of automata with high transition density, the algorithms without abstraction tend to decelerate, while the abstract ones accelerate.
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Simulace a protiřetězce pro efektivní práci s konečnými automaty
Holík, Lukáš ; Černá, Ivana (oponent) ; Jančar, Petr (oponent) ; Vojnar, Tomáš (vedoucí práce)
This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two problems that are crucial for many applications of tree automata. For size reduction of tree automata, we adapt the simulation quotient technique that is well established for finite word automata. We give efficient algorithms for computing tree automata simulations and we also introduce a new type of relation that arises from a combination of tree automata downward and upward simulation and that is very well suited for quotienting. The combination principle is relevant also for word automata. We then generalise the so called antichain universality and language inclusion checking technique developed originally for finite word automata for tree automata. Subsequently, we improve the antichain technique for both word and tree automata by combining it with the simulation-based inclusion checking techniques, significantly improving efficiency of the antichain method. We then show how the developed reduction and inclusion checking methods improve the method of abstract regular tree model checking, the method that was the original motivation for starting the work on tree automata. Both the reduction and the language inclusion methods are based on relatively simple and general principles that can be further extended for other types of automata and related formalisms. An example is our adaptation of the reduction methods for alternating Büchi automata, which results in an efficient alternating automata size reduction technique.
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Abstraction in Automata Algorithms
Kocourek, Tomáš ; Lengál, Ondřej (oponent) ; Holík, Lukáš (vedoucí práce)
The goal of this thesis is to implement and experimentally compare antichain-based algorithms with and without abstraction, which decide the emptiness of alternating finite automata. The author also proposes his own algorithms using abstraction and comes up with a few optimizations of existing abstract algorithms. The thesis introduces the theoretical background of studied algorithms and describes efficient ways to implement data structures which are used by these algorithms. The experimental evaluation over random automata shows that the algorithms without abstraction give us better results in general because they do not perform costly evaluation of closed set intersection and complementation. However, in case of automata with high transition density, the algorithms without abstraction tend to decelerate, while the abstract ones accelerate.
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Simulace a protiřetězce pro efektivní práci s konečnými automaty
Holík, Lukáš ; Černá, Ivana (oponent) ; Jančar, Petr (oponent) ; Vojnar, Tomáš (vedoucí práce)
This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two problems that are crucial for many applications of tree automata. For size reduction of tree automata, we adapt the simulation quotient technique that is well established for finite word automata. We give efficient algorithms for computing tree automata simulations and we also introduce a new type of relation that arises from a combination of tree automata downward and upward simulation and that is very well suited for quotienting. The combination principle is relevant also for word automata. We then generalise the so called antichain universality and language inclusion checking technique developed originally for finite word automata for tree automata. Subsequently, we improve the antichain technique for both word and tree automata by combining it with the simulation-based inclusion checking techniques, significantly improving efficiency of the antichain method. We then show how the developed reduction and inclusion checking methods improve the method of abstract regular tree model checking, the method that was the original motivation for starting the work on tree automata. Both the reduction and the language inclusion methods are based on relatively simple and general principles that can be further extended for other types of automata and related formalisms. An example is our adaptation of the reduction methods for alternating Büchi automata, which results in an efficient alternating automata size reduction technique.
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